george dantzig homework

The Legend of the 'Unsolvable Math Problem'

A student mistook examples of unsolved math problems for a homework assignment and solved them., david mikkelson, published dec. 3, 1996.

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A legend about the "unsolvable math problem" combines one of the ultimate academic wish-fulfillment fantasies — a student not only proves himself the smartest one in his class, but also bests his professor and every other scholar in his field of study — with a "positive thinking" motif that turns up in other urban legends: when people are free to pursue goals unfettered by presumed limitations on what they can accomplish, they just may manage some extraordinary feats through the combined application of native talent and hard work:

A young college student was working hard in an upper-level math course, for fear that he would be unable to pass. On the night before the final, he studied so long that he overslept the morning of the test. When he ran into the classroom several minutes late, he found three equations written on the blackboard. The first two went rather easily, but the third one seemed impossible. He worked frantically on it until — just ten minutes short of the deadline — he found a method that worked, and he finished the problems just as time was called. The student turned in his test paper and left. That evening he received a phone call from his professor. "Do you realize what you did on the test today?" he shouted at the student. "Oh, no," thought the student. I must not have gotten the problems right after all. "You were only supposed to do the first two problems," the professor explained. "That last one was an example of an equation that mathematicians since Einstein have been trying to solve without success. I discussed it with the class before starting the test. And you just solved it!"

And this particular version is all the more interesting for being based on a real-life incident!

One day in 1939, George Bernard Dantzig, a doctoral candidate at the University of California, Berkeley, arrived late for a graduate-level statistics class and found two problems written on the board. Not knowing they were examples of "unsolved" statistics problems, he mistook them for part of a homework assignment, jotted them down, and solved them. (The equations Dantzig tackled are more accurately described not as unsolvable problems, but rather as unproven statistical theorems for which he worked out proofs.)

Six weeks later, Dantzig's statistics professor notified him that he had prepared one of his two "homework" proofs for publication, and Dantzig was given co-author credit on a second paper several years later when another mathematician independently worked out the same solution to the second problem.

George Dantzig recounted his feat in a 1986 interview for the College Mathematics Journal :

It happened because during my first year at Berkeley I arrived late one day at one of [Jerzy] Neyman's classes. On the blackboard there were two problems that I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework — the problems seemed to be a little harder than usual. I asked him if he still wanted it. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever. About six weeks later, one Sunday morning about eight o'clock, [my wife] Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard that I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them. A year later, when I began to worry about a thesis topic, Neyman just shrugged and told me to wrap the two problems in a binder and he would accept them as my thesis. The second of the two problems, however, was not published until after World War II. It happened this way. Around 1950 I received a letter from Abraham Wald enclosing the final galley proofs of a paper of his about to go to press in the Annals of Mathematical Statistics. Someone had just pointed out to him that the main result in his paper was the same as the second "homework" problem solved in my thesis. I wrote back suggesting we publish jointly. He simply inserted my name as coauthor into the galley proof.

Dr. Dantzig also explained how his story passed into the realm of urban legendry:

The other day, as I was taking an early morning walk, I was hailed by Don Knuth as he rode by on his bicycle. He is a colleague at Stanford. He stopped and said, "Hey, George — I was visiting in Indiana recently and heard a sermon about you in church. Do you know that you are an influence on Christians of middle America?" I looked at him, amazed. "After the sermon," he went on, "the minister came over and asked me if I knew a George Dantzig at Stanford, because that was the name of the person his sermon was about." The origin of that minister's sermon can be traced to another Lutheran minister, the Reverend Schuler [sic] of the Crystal Cathedral in Los Angeles. He told me his ideas about thinking positively, and I told him my story about the homework problems and my thesis. A few months later I received a letter from him asking permission to include my story in a book he was writing on the power of positive thinking. Schuler's published version was a bit garbled and exaggerated but essentially correct. The moral of his sermon was this: If I had known that the problem were not homework but were in fact two famous unsolved problems in statistics, I probably would not have thought positively, would have become discouraged, and would never have solved them.

The version of Dantzig's story published by Christian televangelist Robert Schuller contained a good deal of embellishment and misinformation which has since been propagated in urban legend-like forms of the tale such as the one quoted at the head of this page: Schuller converted the mistaken homework assignment into a "final exam" with ten problems (eight of which were real and two of which were "unsolvable"), claimed that "even Einstein was unable to unlock the secrets" of the two extra problems, and erroneously stated that Dantzig's professor was so impressed that he "gave Dantzig a job as his assistant, and Dantzig has been at Stanford ever since."

George Dantzig (himself the son of a mathematician) received a Bachelor's degree from University of Maryland in 1936 and a Master's from the University of Michigan in 1937 before completing his Doctorate (interrupted by World War II) at UC Berkeley in 1946. He later worked for the Air Force, took a position with the RAND Corporation as a research mathematician in 1952, became professor of operations research at Berkeley in 1960, and joined the faculty of Stanford University in 1966, where he taught and published as a professor of operations research until the 1990s. In 1975, Dr. Dantzig was awarded the National Medal of Science by President Gerald Ford.

George Dantzig passed away at his Stanford home at age 90 on 13 May 2005.

Sightings: This legend is used as the setup of the plot in the 1997 movie Good Will Hunting . As well, one of the early scenes in the 1999 film Rushmore shows the main character daydreaming about solving the impossible question and winning approbation from all.

Albers, Donald J. and Constance Reid. "An Interview of George B. Dantzig: The Father of Linear Programming." College Mathematics Journal. Volume 17, Number 4; 1986 (pp. 293-314).

Brunvand, Jan Harold. Curses! Broiled Again! New York: W. W. Norton, 1989. ISBN 0-393-30711-5 (pp. 278-283).

Dantzig, George B. "On the Non-Existence of Tests of 'Student's' Hypothesis Having Power Functions Independent of Sigma." Annals of Mathematical Statistics . No. 11; 1940 (pp. 186-192).

Dantzig, George B. and Abraham Wald. "On the Fundamental Lemma of Neyman and Pearson." Annals of Mathematical Statistics . No. 22; 1951 (pp. 87-93).

Pearce, Jeremy. "George B. Dantzig Dies at 90." The New York Times . 23 May 2005.

By David Mikkelson

David Mikkelson founded the site now known as snopes.com back in 1994.

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Winter 2021 Issue
Winter 2021 Articles

George Bernard Dantzig: The Pioneer of Linear Optimization

John R. Birge University of Chicago Booth School of Business

George Dantzig introduced the world to the power of optimization, creating trillions of dollars of value and saving countless years of life across the globe. In this laudation, John Birge describes the fascinating life and incredible accomplishments of a scholar whose footprints led the way to almost everything the global economy produces.

George Bernard Dantzig (1914-2005) introduced the world to linear programming and, more generally, to the power of optimization. His work created trillions of dollars of value and preserved countless years of life across the globe. By creating the simplex method for solving linear programs he made vastly complex decisions amenable to computation. By demonstrating the duality between activities and prices he paved the way for new analyses resulting in greater market efficiency. His work has supported growing economies and improved healthcare, saving many from hunger and extending lives around the world. Dantzig’s optimism and determination inspired many to increase their own achievements.

Dantzig became interested in mathematics as a child, although his parents, Tobias and Anja, had named him after George Bernard Shaw in the hope that he would become a writer. His father, a mathematics professor at the University of Maryland, gave George “thousands of geometry problems” that fascinated him and honed his powers of analysis. After earning an undergraduate degree in mathematics and physics at Maryland, Dantzig went on to pursue graduate studies in mathematics at the University of Michigan. Finding the program’s focus on abstract mathematics uninspiring, he left Ann Arbor and returned to Washington to work at the Bureau of Labor Statistics (BLS). His new profession prompted him to begin working on practical applications of mathematics. As he often remarked later in life, his many mathematical discoveries, while sometimes stated abstractly, were all inspired by practical problems facing firms, organizations, or governments. 1

After a few years at BLS, Dantzig found new inspiration for research in the work of Jerzy Neyman at the University of California, Berkeley. The real tale of Dantzig’s world-changing career and professional fame began with the now-legendary moment when he arrived late to Neyman’s class. In previous weeks, Neyman had customarily written the week’s homework problems on the board at the beginning of the period. So when Dantzig saw two problems on the board, he wrote them down to work on and hand in before the next class session. He found the problems a bit more difficult than usual and was a few days late in completing them. He took his solutions to Neyman’s office to ask the professor if he still wanted to review the homework. Neyman told him to leave them on his desk, which was so covered with papers that Dantzig feared his hard work would be lost forever.

Dantzig heard nothing from Neyman for several weeks, but then he was awakened early on a Sunday morning by the sound of vigorous knocking on his downstairs door. When he answered, Neyman abruptly informed him that his dissertation was done. The two problems Dantzig had solved for homework were actually two famous unsolved (and until then, unsolvable) problems in statistics. Dantzig’s unshakeable belief that he could solve the problems has become a symbol of the power of positive thinking. His story continues to inspire others to undertake difficult tasks.

As well as offering a stunning example of individual achievement, Dantzig’s solutions of the ‘homework’ problems laid the groundwork for the beginning of linear programming and countless subsequent applications. While working for the U.S. Air Force during and after World War II, Dantzig began to see ways to improve its efficiency. He sought to automate the planning or programming process of delineating detailed requirements for producing, assembling, training, and locating all of the military’s personnel and equipment. He developed a model for finding the best combination and levels of activities and uses of resources which became known as linear programming. Its solutions were provided by the pioneering algorithm inspired by his dissertation: the simplex method. Fortuitously, his development of this numerical procedure coincided with the advent of computers and contributed to their development as well. 2

Linear programs and Dantzig’s many other contributions to optimization have driven enormous increases in productivity throughout the global economy.

Linear programs and Dantzig’s many other contributions to optimization have driven enormous increases in productivity throughout the global economy. Industries with expensive capacity or limited production flexibility, like airlines, hotels, rental cars, and many retailers, have used revenue management models, often built on linear programming, to achieve revenue increases of 5 percent or more. The electric power industry also uses advanced optimization methods to reap cost savings that exceed 5 percent of their overall energy. The logistics field has also benefited enormously from optimization, reducing shipping costs by up to 50 percent in many industries including retail, chemical, tech, and consumer goods. In addition, much of modern finance and asset management is built on Markowitz’s efficient portfolio model, which was rooted in Dantzig’s work. 3 Combining these accomplishments with uses in telecommunications, manufacturing, and more, and particularly in complex process industries like chemical manufacturing, linear optimization probably contributes over 5 percent to the overall output, or about $1 trillion each year, in the US alone.

Linear programming has become a vital tool in advancing artificial intelligence and machine learning, and it is used in electrical stimulation therapy, chemotherapy plans, drug discovery, radiation therapy designs, and finding optimal diets.

Beyond traditional industrial uses, linear programming has become a vital tool in advancing artificial intelligence and machine learning. Such optimization procedures have not just reduced costs and increased outputs across the globe, they have also saved countless lives. Linear programming is used in the phylogenetic analysis that determines the origins of organisms (including viruses, such as SARS-CoV-2, better known as the novel coronavirus). It is also used in electrical stimulation therapy, chemotherapy plans, drug discovery, radiation therapy designs, and finding optimal diets, an application which has drawn interest for more than seventy-five years. 4

Linear programming and its various extensions continue to play an influential role in the economy and in all our lives.

Linear programming and its various extensions continue to play an influential role in the economy and in all our lives. The simplex method is also a remarkable tool, named one of the top ten algorithms of the twentieth century and an indispensable part of optimization to this day. Dantzig’s other contributions constitute the foundation upon which the development of many other decision-making tools over the past seventy years was built. Nonetheless, as Dantzig himself was known to point out, his most fundamental contribution may have been the very concept of an objective function. 5 As he wrote, earlier planners and managers may have shied away from the notion of optimizing an objective because they thought it inconceivable to find an optimal solution among possibilities more numerous than the atoms in the universe. Dantzig dared to conceive of surmounting that imposing obstacle and succeeded, to the substantial benefit of us all.

Booth's John Birge, September 6, 2016. (Photo by Jean Lachat)

John Birge is the Hobart W. Williams Distinguished Service Professor of Operations Management at the University of Chicago Booth School of Business. His work follows that of his doctoral advisor, George Dantzig, in exploring ways to make better decisions.

Much of this history appears in Dantzig’s interview in D.J. Albers and C. Reid, “An Interview with George B. Dantzig: The Father of Linear Programming,” The College Mathematics Journal , 17 (4) (Sep., 1986), pp. 293-314.
Dantzig’s account of the simplex method’s role in the development of digital computers appears in G.B. Dantzig, “Impact of linear programming on computer development,” Technical Report SOL 85-07, Stanford University, 1985, https://apps.dtic.mil/dtic/tr/fulltext/u2/a157659.pdf .
Markowitz’s discussion of Dantzig’s influence on his work appears at: http://hmarkowitz.com/about-harry-markowitz/.
Dantzig’s discussion of the early history of this problem is in: G.B. Dantzig, “The diet problem,” Interfaces 20 (4) (1990), pp. 43-47.
Dantzig’s description is in: G.B. Dantzig, “Linear programming,” Operations Research 50 (1) (2002), pp. 42—47.

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George bernard dantzig.

... gave me thousands of geometry problems while I was still in high school. ... the mental exercise required to solve them was the great gift from my father. The solving of thousands of problems during my high school days - at the time when my brain was growing - did more than anything else to develop my analytic power.

As a teenager, I prepared some of the figures that appeared in the book.

Since its first appearance nearly half a century ago the book has gone through a number of printings and has deservedly maintained its popularity.

During my first year at Berkeley I arrived late one day to one of Neyman 's classes. On the blackboard were two problems which I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework - the problems seemed to be a little harder to do than usual. I asked him if he still wanted the work. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever. About six weeks later, one Sunday morning about eight o'clock, Anne and I were awakened by someone banging on our front door. It was Neyman . He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard which I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them.

My office collected data about sorties flown, bombs dropped, aircraft lost... I also helped other divisions of the Air Staff prepare plans called "programs". ... everything was planned in greatest detail: all the nuts and bolts, the procurement of airplanes, the detailed manufacture of everything. There were hundreds of thousands of different kinds of material goods and perhaps fifty thousand specialties of people. My office collected data about the air combat such as the number of sorties flown, the tons of bombs dropped, attrition rates. I also became a skilled expert on doing planning by hand techniques.

Berkeley made me an offer, but I didn't like it because it was too small. Or, to be more exact, my wife did not like it. It was a grand salary of fourteen hundred dollars a year. She did not see how we could live on that with our child David.

One of the first applications of the simplex algorithm was to the determination of an adequate diet that was of least cost. In the fall of 1947 , Jack Laderman of the Mathematical Tables Project of the National Bureau of Standards undertook, as a test of the newly proposed simplex method, the first large-scale computation in this field. It was a system with nine equations in seventy-seven unknowns. Using hand-operated desk calculators, approximately 120 man-days were required to obtain a solution. ... The particular problem solved was one which had been studied earlier by George Stigler ( who later became a Nobel Laureate ) who proposed a solution based on the substitution of certain foods by others which gave more nutrition per dollar. He then examined a "handful" of the possible 510 ways to combine the selected foods. He did not claim the solution to be the cheapest but gave his reasons for believing that the cost per annum could not be reduced by more than a few dollars. Indeed, it turned out that Stigler's solution ( expressed in 1945 dollars ) was only 24 cents higher than the true minimum per year $ 39 . 69 .

Linear programming is viewed as a revolutionary development giving man the ability to state general objectives and to find, by means of the simplex method, optimal policy decisions for a broad class of practical decision problems of great complexity. In the real world, planning tends to be ad hoc because of the many special-interest groups with their multiple objectives.

The tremendous power of the simplex method is a constant surprise to me.

If one would take statistics about which mathematical problem is using up most of the computer time in the world, then ... the answer would probably be linear programming.

[ Linear programming ] is used to allocate resources, plan production, schedule workers, plan investment portfolios and formulate marketing ( and military ) strategies. The versatility and economic impact of linear programming in today's industrial world is truly awesome.

Mathematical programming has been blessed by the involvement of at least two exceptionally creative geniuses: George Dantzig and Leonid Kantorovich .

The systematic development of practical computing methods for linear programming began in 1952 at the Rand Corporation in Santa Monica, under the direction of George B Dantzig. The author worked intensively on this project there until late 1956 , by which time great progress had been made on first-generation computers.

An impressive book, the work is very complete, its scientific level high, and its reading pleasant.

... it is interesting to note that the original problem that started my research is still outstanding - namely the problem of planning or scheduling dynamically over time, particularly planning dynamically under uncertainty. If such a problem could be successfully solved it could eventually through better planning contribute to the well-being and stability of the world.

For inventing linear programming and discovering methods that led to wide-scale scientific and technical applications to important problems in logistics, scheduling, and network optimization, and to the use of computers in making efficient use of the mathematical theory.

In recognition of his outstanding contribution to engineering and the sciences through his pioneering work in mathematical programming and his development of the simplex method. His work permits the solution of many previously intractable problems and has made linear programming into one of the most frequently used techniques of modern applied mathematics.

A member of the National Academy of Engineering, the National Academy of Science , the American Academy of Arts and Sciences and recipient of the National Medal of Science, plus eight honorary degrees, Professor Dantzig's seminal work has laid the foundation for much of the field of systems engineering and is widely used in network design and component design in computer, mechanical, and electrical engineering.

References ( show )

M Aigner, Diskrete Mathematik, in Ein Jahrhundert Mathematik 1890 - 1990 ( Braunschweig, 1990) , 83 - 112 .
D J Albers and C Reid, An interview with George B. Dantzig : the father of linear programming, College Math. J. 17 (4) (1986) , 293 - 314 .
D J Albers, G L Alexanderson and C Reid, More mathematical people. Contemporary conversations ( Boston, MA, 1990) .
M L Balinski, Mathematical programming : journal, society, recollections, in J K Lenstra, A H G Rinnooy, K Schrijver and A Schrijver ( eds. ) , History of mathematical programming ( Amsterdam, 1991) , 5 - 18 .
G B Dantzig, A look back at the origins of linear programming ( Chinese ) , Chinese J. Oper. Res. 3 (1) (1984) , 71 - 78 .
G B Dantzig, Impact of linear programming on computer development, in Computers in mathematics, Stanford, CA, 1986 ( New York, 1990) , 233 - 240 .
G B Dantzig, Linear programming. The story about how it began: some legends, a little about its historical significance, and comments about where its many mathematical programming extensions may be headed, in J K Lenstra, A H G Rinnooy, K Schrijver and A Schrijver ( eds. ) , History of mathematical programming ( Amsterdam, 1991) , 19 - 31 .
G B Dantzig, Origins of the simplex method, in S G Nash ( ed. ) , A history of scientific computing ( Reading, MA, 1990) , 141 - 151 .
G B Dantzig, Reminiscences about the origins of linear programming, in Mathematical programming, Rio de Janeiro, 1981 ( Amsterdam, 1984) , 105 - 112 .
G B Dantzig, Reminiscences about the origins of linear programming, in A Schlissel ( ed. ) , Essays in the history of mathematics, American Mathematical Society, San Francisco, Calif., January 1981 ( Providence, R.I., 1984) , 1 - 11 .
G B Dantzig, Reminiscences about the origins of linear programming, in Mathematical programming : the state of the art, Bonn, 1982 ( New York, 1983) , 78 - 86 .
G B Dantzig, Reminiscences about the origins of linear programming, Oper. Res. Lett. 1 (2) (1981 / 82) , 43 - 48 .
G B Dantzig, Time-staged methods in linear programming : comments, early history, future prospects, in Large scale systems, Cleveland, Ohio, 1980 ( Amsterdam-New York, 1982) , 19 - 30 .
G B Dorfman, R The discovery of linear programming, Ann. Hist. Comput. 6 (3) (1984) , 283 - 295 .
T H Kjeldsen, The emergence of nonlinear programming : interactions between practical mathematics and mathematics proper, Math. Intelligencer 22 (3) (2000) , 50 - 54 .
W Orchard-Hays, History of mathematical programming systems, Ann. Hist. Comput. 6 (3) (1984) , 296 - 312 .
Professor George Dantzig : Linear Programming Founder Turns 80 , SIAM News ( November 1994) .
Selected publications of George B Dantzig, in Mathematical programming I, Math. Programming Stud. No. 24 (1985) , xi.

Additional Resources ( show )

Other pages about George Dantzig:

New York Times obituary
Washington Post obituary
Heinz Klaus Strick biography

Other websites about George Dantzig:

Mathematical Genealogy Project
MathSciNet Author profile
zbMATH entry
ERAM Jahrbuch entry

Honours ( show )

Honours awarded to George Dantzig

NAS Award in Applied Mathematics 1977
AMS Gibbs Lecturer 1990
Popular biographies list Number 133

Cross-references ( show )

History Topics: Statistics index
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Courtesy Paul Dantzig

In his first year as a UC-Berkeley doctoral student, George Bernard Dantzig arrived late to his class with famed statistician Jerzy Neyman. Dantzig scribbled down two problems written on the blackboard that he assumed to be assignments. “A few days later, I apologized to Neyman for taking so long to do the homework—the problems seemed a little harder to do than usual,” Dantzig recalled years later. The apology was unnecessary—Dantzig had solved two famous unsolved problems in statistics. (The story, soon legendary in the math world, inspired a similar scene in the film Good Will Hunting .)

In a mathematics career that spanned seven decades, Dantzig created the field of linear programming from his “simplex method,” an algorithm for solving complex problems that revolutionized scientific computation. Professor emeritus of operations research and of computer science, Dantzig died May 13 of complications from diabetes and cardiovascular disease at his Stanford home. He was 90.

Combined with the calculating power of today’s computers, Dantzig’s algorithm is a tool that allows businesses and governments to identify optimal solutions to problems involving many variables. Linear programming applies to thousands of diverse applications—from pricing products, scheduling shipments and workers, and managing supply chains to evaluating policy alternatives, assigning personnel, rotating crops and targeting weapons. Professor of management science and engineering Arthur F. Veinott Jr. calls Dantzig’s simplex method “the single most widely used algorithm originated in the last six decades.”

Dantzig was born in Portland, Ore., to Tobias Dantzig, a Russian mathematician, and Anja Ourisson, a linguist. When George was in high school, Tobias challenged his son’s analytic ability with thousands of complex geometry problems.

In 1936, George Dantzig married Anne Shmuner and earned his bachelor’s degree in mathematics and physics from the University of Maryland. He received his master’s in mathematics from the University of Michigan. An analyst for the Army Air Forces during World War II, Dantzig earned his doctorate in 1946 and discovered the simplex method in 1947. He was a researcher for the Rand Corporation from 1952 to 1960, then chair and professor at Berkeley’s Operations Research Center until he joined Stanford’s faculty in 1966.

Dantzig’s 1963 book, Linear Programming and Extensions , explains his methods. He also co-wrote Compact City: A Plan for a Livable Urban Environment and, after retiring in 1997, completed two volumes on linear programming and wrote a science fiction novel. In 1975, President Gerald Ford awarded him the National Medal of Science.

He enjoyed painting, woodworking and movies. Professor emeritus of management science and engineering Richard Cottle says Dantzig was “a great colleague” who was “always providing opportunities for people.”

Dantzig is survived by his wife of 68 years, Anne; sons David, MS ’72, and Paul, ’75, MS ’75; daughter Jessica Klass; three grandchildren; and two great-grandchildren.

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Memorial Tributes
Memorial Tributes: National Academy of Engineering, Volume 12
GEORGE B. DANTZIG 1914–2005

This is the twelfth volume in the series of Memorial Tributes compiled by the National Academy of Engineering as a personal remembrance of the lives and outstanding achievements of its members and international members. These volumes are intended to stand as an enduring record of the many contributions of engineers and engineering to the benefit of humankind. In most cases, the authors of the tributes are contemporaries or colleagues who had personal knowledge of the interests and the engineering accomplishments of the deceased..

Gass, Saul I.

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Table of Contents
WILLIS ALFRED ADCOCK 1922–2003
ROBERT ADLER 1913–2007
RUTHERFORD ARIS 1929–2005
STANLEY BACKER 1920–2003
WILLIAM OLIVER BAKER 1915–2005
HOWARD C. BARNES 1912–2003
ROBERT R. BERG 1924–2006
FREDERICK STUCKY BILLIG 1933–2006
RICHARD HENRY BOLT 1911–2002
LEON E. BORGMAN 1928–2007
SOL BURSTEIN 1922–2002
MELVIN W. CARTER 1926–2007
HAROLD CHESTNUT 1917–2001
EDGAR F. CODD 1923–2003
MORRIS COHEN 1911–2005
RALPH CROSS 1910–2003
JOHN LARRY DUDA 1936–2006
MAXIME A. FAGET 1921–2004
RICHARD H. GALLAGHER 1927–1997
IVAN A. GETTING 1912–2003
KENNETH W. HAMMING 1918–2005
HEINZ HEINEMANN 1913–2005
STANLEY HILLER, JR. 1924–2006
WILLIAM HERBERT HUGGINS 1919–2001
CHALMER GATLIN KIRKBRIDE 1906–1998
HENDRICK KRAMERS 1917–2006
THOMAS DUANE LARSON 1928–2006
ERASTUS H. LEE 1916–2006
JOSEPH T. LING 1919–2006
RALPH A. LOGAN 1926–2006
ROBERT W. MANN 1924–2006
JOHN L. MCLUCAS 1920–2002
RUBEN F. METTLER 1924–2006
ALAN S. MICHAELS 1922–2000
A. RICHARD NEWTON 1951–2007
CHARLES NOBLE 1916–2003
FREDERIC C.E. ODER 1919–2006
RONALD SAMUEL RIVLIN 1915–2005
GEORGE A. SAMARA 1936–2006
REUBEN SAMUELS 1926–2004
DUDLEY A. SAVILLE 1933–2006
MILTON CLAYTON SHAW 1915–2006
SHAN-FU SHEN 1921–2006
ALAN F. SHUGART 1930–2006
JOHN WISTAR SIMPSON 1914–2007
ROBERT M. SNEIDER 1929–2005
VIVIAN T. STANNETT 1917–2002
DAVID TABOR 1913–2005
CHEN-TO TAI 1915–2004
GORDON K. TEAL 1907–2003
ALEXANDER R. TROIANO 1908–2002
ALAN MANNERS VOORHEES 1922–2005
PAUL WEIDLINGER 1914–1999
ALVIN M. WEINBERG 1915–2006
JAMES WILLIAM WESTWATER 1919–2006
J. EDWARD WHITE 1918–2003
DEAN E. WOOLDRIDGE 1913–2006
LEO YOUNG 1926–2006
Table of Contents
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BY SAUL I. GASS SUBMITTED BY THE NAE HOME SECRETARY

GEORGE B. DANTZIG, pioneer in operations research and management science, mathematician, professor, educator, consultant, author, and “father” of linear programming, died on May 13, 2005, at the age of 90, in Stanford, California. George’s formal education was in mathematics, which reflected his early interest in the subject and the influence of his father, Tobias Dantzig, a mathematics professor.

George’s seminal work can be summed up as the recognition and definition of the broad class of practical problems that can be studied as linear programs and the development of the simplex algorithm for solving them. These developments were essential to the emerging field of operations research, which was developed by British scientists during World War II. Linear programming was barely mentioned in early books and reports on operations research, but, before long, it became a mainstay of research methods and applications in the field. An amazing story! George was elected to the National Academy of Engineering in 1985.

He was a fellow of the Econometric Society, Institute of Mathematical Statistics, Association for the Advancement of Science, and Institute of Operations Research and the Management Sciences. He was president of the Institute for Management Sciences and a founder of the Mathematical Programming Society. He was the first recipient of the Operations Research Society of America’s von Neumann Theory Prize and the first inductee into the International Federation of Operational Research Societies’ Operational Research Hall of Fame.

He was awarded the Silver Medal of the British Operational Research Society and the Harvey Prize in Science and Technology from Technion University. In 1975, President Ford presented him with the National Medal of Science. George was born on November 8, 1914, in Portland, Oregon, the first of two sons of Tobias and Anja (Ourisson) Dantzig.

Tobias, who was Russian, and Anja, who was Polish, met at the Sorbonne where they both studied mathematics; they moved to Oregon in 1910, where Tobias held a variety of jobs— lumberjack, road builder, housepainter—before he obtained a teaching position at Indiana University. He received his Ph.D. in mathematics there in 1916. He then taught at Johns Hopkins University and the University of Maryland, where he was chair of the Mathematics Department.

He attended the University of Maryland, College Park, where he received his A.B. in mathematics and physics in 1936. That summer he married Anne Shmuner and moved to Ann Arbor, where George received his M.A. in mathematics in 1938 from the University of Michigan. Although he had taken only one graduate course in statistics, he qualified for the Civil Service as a junior statistician, and in 1937, he accepted a job at the U.S. Bureau of Labor Statistics in Washington, D.C. At first, he thought statistics was “just a bag of tricks,” but, after learning many practical applications on the job and becoming familiar with the work of Jerzy Neyman, he changed his mind.

George wrote to Neyman, who had just moved to the University of California, Berkeley, about taking a Ph.D. under his direction. Neyman managed to get him a teaching assistantship, and George and Anne moved west in 1939. In those years, statistics was included in the Mathematics Department, and, although George had taken only two coursesin statistics, both from Neyman, his dissertation was in statistics.

That was when the George Dantzig “urban legend” originated. If you search the Web for “urban legend George Dantzig,” you will probably be directed to the URL for “Snopes.com, The Unsolvable Math Problem.” That site recounts how George, coming in late for class, mistakenly thought two problems Neyman had written on the board were homework problems. After a few days of struggling, he turned in his answers.

About six weeks later, at 8:00 a.m. on a Sunday morning, he and Anne were awakened by someone banging on their front door. It was Neyman, who said: “I have just written an introduction to one of your papers. Read it so I can send it out right away for publication.” George’s answers to the homework problems were proofs of two unproven theorems in statistics.

The Snopes website tells in detail how George’s experiences ended up as a sermon for a Lutheran minister and the basis for the film Good Will Hunting. The solution to the second homework problem became part of a joint paper with Abraham Wald, who found the solution independently in 1950, unaware that George had already solved it until a journal referee called it to his attention.

Neyman had George submit his answers to the “homework” problems as his Ph.D. dissertation. In June 1941, prior to defending his dissertation, George accepted a job in Washington with the Army Air Force Combat Analysis Branch of Statistical Control. Thus he did not receive his Ph.D. in mathematics from Berkeley until 1946, at which time he was offered a teaching position there.

He decided to stay at the Pentagon, however, and become the mathematical advisor to the comptroller of the newly established Department of the Air Force. The deciding factor in his decision was that the salary he was offered at Berkeley was “too little.”

Although he considered the Pentagon a holding place until he found a decent-paying academic position, that job choice started him down a life-changing research path that led to the development of linear programming. Thus, his decision had momentous results: It set operations research on a new course of research and applications, and, more important, it made enterprises and governments everywhere more effective and efficient.

Thus he was able to state mathematically, for the first time, a wide class of practical and important problems that fell into the newly defined structure of linear programming. This was in July 1947. By the end of that summer, he had developed the simplex method of solving such problems. In June 1947, the Air Force had established a major task force to work on high-speed computation of its planning process, later named Project SCOOP (scientific computation of optimal programs), with George as chief mathematician.

He remained with Project SCOOP until June 1952 when he joined the RAND Corporation as a research mathematician. George’s accomplishments in his research for the Air Force included the first statement of the linear-programming problem and the recognition of its applicability to a wide range of decision problems; the invention of the simplex method (IEEE named the simplex algorithm one of the top 10 algorithms of the twentieth century); the testing and proof of the linearprogramming model and the simplex method; the statement and proof of linear-programming primal-dual problems and their relationship via the simplex algorithm; the development of the simplex transportation algorithm; and the establishment of the equivalence between linear-programming and zero-sum, two-person games.

In 1960, George began an illustrious academic career as professor of engineering science and chairman of the Operations Research Center, University of California, Berkeley. He moved to Stanford University in 1966 as professor of operations research and computer science and was appointed to the C.A. Criley Endowed Chair in Transportation in 1973. He retired in 1985 as professor emeritus, but he continued to teach and maintain an active research agenda until the fall of 1997.

During his academic career, he authored or coauthored seven books and more than 150 papers. George’s legacy goes far beyond his research and teaching, however. It includes his friendship, mentoring, and unselfishness with time and ideas. He guided more than 50 Ph.D. students through Berkeley and Stanford. George was a frequent visitor to the International Institute of Applied Systems Analysis (IIASA), “a non-governmental research organization, headquartered in Laxenburg, Austria, that conducts interdisciplinary scientific studies on environmental, economic, technological, and social issues in the context of human dimensions of global change.”

In 1973–1974, he spent a sabbatical year at IIASA as head of the Methodology Group. For more than 50 years, George’s continuing innovations were of the highest order, and the scientific and economic impacts that have resulted from his work are immeasurable.

How does one measure the fact that all major (and most minor) industries directly or indirectly use linear programming to aid them in the allocation of their resources and decision making; that all computer systems (mainframes and PCs) “learn” how to solve linear-programming problems as soon as they are “born”; that the simplex method is imbedded into all PC spreadsheet systems; that national economic planning for the third world and developing countries is being guided by linearprogramming techniques; that strategic and tactical military planning, management of military personnel, and a wide variety of logistical (peacetime and combat) problems are solved using linear programming; that mathematical and computer science research such as combinatorics, numerical analysis, and the solution of large-scale problems have been aided by linear programming; and that such diverse applications as cancer screening, airlines scheduling, agricultural development, transportation and delivery systems, scheduling of personnel, and petroleum refinery operations have been influenced by the work of George Dantzig?

The professional and academic fields of operations research, management science, industrial engineering, as well as the mathematical and computer sciences, rest heavily upon his lifetime of work. George was survived by his wife Anne (née Shmuner), who died August 10, 2006. They are survived by son David Dantzig (wife: Nancy) of Cleveland, Ohio; daughter Jessica Klass (husband: Michael) of El Cerrito, California; son Paul Dantzig (wife: Susan Abrams) of Scarsdale, New York; three grandchildren: Audra Zelvy (husband: Michael), Aron Dantzig, and Jeremy Dantzig; two great-grandchildren, Ivy and Brian Zelvy; and Anne’s brother Daniel Shaw of Baltimore, Maryland.

Memorial Tributes: Volume 12 (2008)

Chapter: george b. dantzig.

GEORGE B. DANTZIG 1914–2005

Elected in 1985

“For outstanding pioneering contributions to the science and practice of operations research.”

BY SAUL I. GASS

SUBMITTED BY THE NAE HOME SECRETARY

George’s formal education was in mathematics, which reflected his early interest in the subject and the influence of his father, Tobias Dantzig, a mathematics professor. George’s seminal work can be summed up as the recognition and definition of the broad class of practical problems that can be studied as linear programs and the development of the simplex algorithm for solving them. These developments were essential to the emerging field of operations research, which was developed by British scientists during World War II. Linear programming was barely mentioned in early books and reports on operations research, but, before long, it became a mainstay of research methods and applications in the field. An amazing story!

George was elected to the National Academy of Engineering in 1985. He was a fellow of the Econometric Society, Institute of Mathematical Statistics, Association for the Advancement of Science, and Institute of Operations Research and the Management Sciences. He was president of the Institute for

Management Sciences and a founder of the Mathematical Programming Society. He was the first recipient of the Operations Research Society of America’s von Neumann Theory Prize and the first inductee into the International Federation of Operational Research Societies’ Operational Research Hall of Fame. He was awarded the Silver Medal of the British Operational Research Society and the Harvey Prize in Science and Technology from Technion University. In 1975, President Ford presented him with the National Medal of Science.

George was born on November 8, 1914, in Portland, Oregon, the first of two sons of Tobias and Anja (Ourisson) Dantzig. Tobias, who was Russian, and Anja, who was Polish, met at the Sorbonne where they both studied mathematics; they moved to Oregon in 1910, where Tobias held a variety of jobs—lumberjack, road builder, housepainter—before he obtained a teaching position at Indiana University. He received his Ph.D. in mathematics there in 1916. He then taught at Johns Hopkins University and the University of Maryland, where he was chair of the Mathematics Department.

In the book More Mathematical People (Simon & Schuster, 1990), George recounts his struggles with ninth-grade algebra and how he became a top student in mathematics and science when he was introduced to geometry, which “really turned [him] on.” The thousands of geometry problems Tobias fed George—to keep him from getting underfoot—helped George develop his analytical power. He attended the University of Maryland, College Park, where he received his A.B. in mathematics and physics in 1936. That summer he married Anne Shmuner and moved to Ann Arbor, where George received his M.A. in mathematics in 1938 from the University of Michigan.

Although he had taken only one graduate course in statistics, he qualified for the Civil Service as a junior statistician, and in 1937, he accepted a job at the U.S. Bureau of Labor Statistics in Washington, D.C. At first, he thought statistics was “just a bag of tricks,” but, after learning many practical applications on the job and becoming familiar with the work of Jerzy Neyman, he changed his mind.

George wrote to Neyman, who had just moved to the University of California, Berkeley, about taking a Ph.D. under his direction. Neyman managed to get him a teaching assistantship, and George and Anne moved west in 1939. In those years, statistics was included in the Mathematics Department, and, although George had taken only two courses in statistics, both from Neyman, his dissertation was in statistics. That was when the George Dantzig “urban legend” originated.

If you search the Web for “urban legend George Dantzig,” you will probably be directed to the URL for “ Snopes.com , The Unsolvable Math Problem.” That site recounts how George, coming in late for class, mistakenly thought two problems Neyman had written on the board were homework problems. After a few days of struggling, he turned in his answers. About six weeks later, at 8:00 a.m. on a Sunday morning, he and Anne were awakened by someone banging on their front door. It was Neyman, who said: “I have just written an introduction to one of your papers. Read it so I can send it out right away for publication.” George’s answers to the homework problems were proofs of two unproven theorems in statistics.

In June 1941, prior to defending his dissertation, George accepted a job in Washington with the Army Air Force Combat Analysis Branch of Statistical Control. Thus he did not receive his Ph.D. in mathematics from Berkeley until 1946, at which time he was offered a teaching position there. He decided to stay at the Pentagon, however, and become the mathematical advisor to the comptroller of the newly established Department of the Air Force. The deciding factor in his decision was that the salary he was offered at Berkeley was “too little.”

George’s Pentagon colleagues challenged him to figure out how the Air Force could mechanize its planning process to speed up computation of the deployment of forces and equipment, training, and logistical support. Keep in mind that all he had then were desk calculators and IBM accounting equipment. Based on his study of Air Force requirements, he adapted and generalized the structure behind Wassily Leontief’s interindustry model. Thus he was able to state mathematically, for the first time, a wide class of practical and important problems that fell into the newly defined structure of linear programming. This was in July 1947. By the end of that summer, he had developed the simplex method of solving such problems.

In June 1947, the Air Force had established a major task force to work on high-speed computation of its planning process, later named Project SCOOP (scientific computation of optimal programs), with George as chief mathematician. He remained with Project SCOOP until June 1952 when he joined the RAND Corporation as a research mathematician. George’s accomplishments in his research for the Air Force included the first statement of the linear-programming problem and the recognition of its applicability to a wide range of decision problems; the invention of the simplex method (IEEE named the simplex algorithm one of the top 10 algorithms of the twentieth century); the testing and proof of the linear-programming model and the simplex method; the statement and proof of linear-programming primal-dual problems and their relationship via the simplex algorithm; the development of the simplex transportation algorithm; and the establishment of the equivalence between linear-programming and zero-sum, two-person games.

George’s legacy goes far beyond his research and teaching, however. It includes his friendship, mentoring, and unselfishness with time and ideas. He guided more than 50 Ph.D. students through Berkeley and Stanford.

George was a frequent visitor to the International Institute of Applied Systems Analysis (IIASA), “a non-governmental research organization, headquartered in Laxenburg, Austria, that conducts interdisciplinary scientific studies on environmental, economic, technological, and social issues in the context of human dimensions of global change.” In 1973–1974, he spent a sabbatical year at IIASA as head of the Methodology Group.

For more than 50 years, George’s continuing innovations were of the highest order, and the scientific and economic impacts that have resulted from his work are immeasurable. How does one measure the fact that all major (and most minor) industries directly or indirectly use linear programming to aid them in the allocation of their resources and decision making; that all computer systems (mainframes and PCs) “learn” how to solve linear-programming problems as soon as they are “born”; that the simplex method is imbedded into all PC spreadsheet systems; that national economic planning for the third world and developing countries is being guided by linear-programming techniques; that strategic and tactical military planning, management of military personnel, and a wide variety of logistical (peacetime and combat) problems are solved using linear programming; that mathematical and computer science research such as combinatorics, numerical analysis, and

the solution of large-scale problems have been aided by linear programming; and that such diverse applications as cancer screening, airlines scheduling, agricultural development, transportation and delivery systems, scheduling of personnel, and petroleum refinery operations have been influenced by the work of George Dantzig?

The professional and academic fields of operations research, management science, industrial engineering, as well as the mathematical and computer sciences, rest heavily upon his lifetime of work.

George was survived by his wife Anne (née Shmuner), who died August 10, 2006. They are survived by son David Dantzig (wife: Nancy) of Cleveland, Ohio; daughter Jessica Klass (husband: Michael) of El Cerrito, California; son Paul Dantzig (wife: Susan Abrams) of Scarsdale, New York; three grandchildren: Audra Zelvy (husband: Michael), Aron Dantzig, and Jeremy Dantzig; two great-grandchildren, Ivy and Brian Zelvy; and Anne’s brother Daniel Shaw of Baltimore, Maryland.

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Austria will be ice-free in around 40 years, why nausea makes us lose our appetite, the fronde: from the parliamentary revolt to the revolt of the princes, was beethoven’s musicality in his genes, do monkeys also get cranky with age , george dantzig: the story of the overlooked genius.

The unappreciated talent. George Dantzig “accidentally” solved two unresolved statistics questions. But he was passed up for the Nobel Prize.

In 1939, George Bernard Dantzig, a doctorate candidate at the University of California, Berkeley, arrived a few minutes late to Jerzy Neyman’s statistics lecture while there were two homework problems posted on the board. He wrote them down and spent many days figuring out the answers. He was unaware that these were really two well-known statistics theorems that had never been proved before, not just regular exercise problems.

Dantzig subsequently said in an interview that:

A few days later I apologized to Neyman for taking so long to do the homework—the problems seemed to be a little harder than usual. I asked him if he still wanted it. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever. About six weeks later, one Sunday morning about eight o’clock, we were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: “I’ve just written an introduction to one of your papers. Read it so I can send it out right away for publication.” For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard that I had solved thinking they were homework were in fact two famous unsolved problems in statistics.

The most renowned statistician in the world at the time, Neyman, was then asked by Dantzig the next year what subject he should choose for his doctoral thesis. Neyman shrugged and said, “Just put your treatments of the two issues in a folder.” He would accept it as a doctoral thesis.

Dantzig’s Early Life

The eldest child of Tobias Dantzig and Anja Ourisson, George Bernard Dantzig was born in Portland, Oregon. The parents had met while attending Henri Poincaré lectures at the Sorbonne in Paris, where they were both students.

They moved to the United States after getting married, where Tobias Dantzig, a native of Lithuania, had to start out by working odd jobs like a road builder and a lumberjack due to language barriers before obtaining a Ph.D. in mathematics from Indiana University; his wife took the master’s degree in French.

The parents thought that their children would have better chances in life if they were given the first names of famous people. Thus, the younger boy was given the first name Henri (after Henri Poincaré) in the hopes that he would one day become a mathematician, while the elder son was given the name George Bernard in the hopes that he would one day become a writer (like George Bernard Shaw).

The father taught mathematics at different institutions, including Johns Hopkins (Baltimore, Maryland), Columbia University (New York), and the University of Maryland, while the mother worked at the Library of Congress in Washington, DC. A book he released in 1930 on the history of the evolution of mathematics, Number – The Language of Science , has been reissued several times (most recently in 2005).

Dantzig continued to struggle with arithmetic in the early grades, but owing to his father’s daily assignment training regimen, particularly in geometry, Dantzig finally received top marks.

George Dantzig started his mathematical studies at the University of Maryland because, despite the fact that both of his parents were employed, the family did not have enough money to finance his studies in physics and mathematics at a prestigious university.

George Dantzig moved to the University of Michigan after receiving a bachelor’s degree, where he went on to complete his graduate studies in 1937. He subsequently accepted a position at the U.S. Bureau of Labor Statistics and participated in research on urban consumers’ purchasing habits after becoming weary of abstract mathematics.

Dantzig Was a Heartfelt Statistician

Dantzig first became interested in statistical concerns and techniques while working in this position. He requested Jerzy Neyman’s permission in 1939 to attend his PhD studies at the University of California, Berkeley (with a “teaching assistantship”). And thus, one day, the event that was described above occurred.

The PhD program was still in progress when the United States joined World War II . Dantzig relocated to Washington, D.C., and accepted a post as the director of the Statistical Control Division at the headquarters of the U.S. Air Force. He discovered that the military’s knowledge of the real inventory of aircraft and equipment was insufficient.

He devised a method to collect the necessary data in detail, particularly to make a thorough contract award, including the need for nuts and bolts.

Dantzig briefly returned to Berkeley after the war, where he eventually received his degree. Not simply for financial reasons but also because he preferred the chances and challenges of working for the Air Force, he declined an offer from the university to continue working there.

Dantzig saw the need to dynamize this rather static model and was motivated by the input-output analysis approach of the Russian-American mathematician Wassily Leontief, who had a position at Harvard University in Cambridge starting in 1931. Additionally, he aimed to improve it to the point where hundreds or even thousands of actions and locations could be recorded and optimized; at the time, this was a fascinating computing hurdle.

Dantzig’s Advancements in Military Planning

George Dantzig, Anne Dantzig, and President Gerald Ford (National Medal of Honor ceremony, 1971).

While employed by the Pentagon, Dantzig came to the conclusion that many planning choices were based solely on experience rather than objective criteria, yielding less than ideal outcomes. Linear inequalities are often used to characterize the requirements (restrictions), and specifying an objective function establishes the purpose of optimization, such as maximizing profit or decreasing resource consumption.

In English, the planning technique created by Dantzig is known as “linear programming,” where “ programming ” refers not to programming in the modern meaning of the word but rather to the phrase used in the military for the planning of procedures. The selected linear function modeling is referred to as being “linear.”

A half-plane in two dimensions and a half-space in three dimensions are both defined by a linear inequality. Convex polygons or convex polyhedrons are produced when many inequalities are taken into account; in the n-dimensional case, the corresponding convex structure is known as a “simplex”.

The so-called Simplex Algorithm , which Dantzig created in 1947, is a systematic approach for computing the best answer. Dantzig himself said of it: “The tremendous power of the simplex method is a constant surprise to me.”

The creation of the simplex algorithm, a technique for resolving linear programming problems, is widely regarded as one of Dantzig’s most important accomplishments. The goal of linear programming is to maximize a linear objective function within a set of linear constraints using a mathematical approach. The simplex algorithm has had a significant influence on many fields, including business, economics, and engineering, as a tool for tackling problems in linear programming.

His work on duality in linear programming is a cornerstone of modern optimization theory. To describe the association between a dependent variable and one or more independent variables, he also made significant contributions to the statistical procedure known as linear regression. George Dantzig is called “the father of linear programming” for that.

He Wasn’t Seen Worthy of the Nobel Prize

George Dantzig close-up colored portrait photograph

When Dantzig visited Princeton University to speak with John von Neumann towards the end of the year, the algorithm saw its first refinement. This bright mathematician and computer scientist quickly saw similarities between the methods he and Oskar Morgenstern outlined in their newly released book, “The Theory of Games,” (1944) and the linear optimization approach.

The search techniques have significantly improved over time, notably with the advent of computer use. Although other strategies, such as nonlinear modeling, were also studied, Dantzig’s “linear programming” technique was finally proven to be adequate.

Tjalling C. Koopmans, professor of research in economics at the University of Chicago, realized the value of linear planning from an economic perspective after speaking with Dantzig. His famous theory on the optimal use of exhaustible resources was born out of this. To the surprise of everyone in the field, Dantzig was left unaccomplished when Koopmans received the Nobel Prize in Economics in 1975, together with the Russian mathematician Leonid Vitaliyevich Kantorovich, who had earlier proposed comparable methods in 1939. But it took the West two decades to learn about them. Dantzig, who was always kind to his fellow men, handled this with remarkable perseverance, demonstrating his high degree of expertise.

Dantzig went to the RAND Corporation in Santa Monica in 1952 to continue developing computerized execution of processes after his work with the Air Force. He established the Operations Research Center after accepting a post at Berkeley’s Department of Industrial Engineering in 1960.

When it was first published in 1963 by Princeton University Press, his book Linear Programming and Extensions established the field of linear optimization. Dantzig began working at Stanford in 1966, when he also established the Systems Optimization Lab (SOL). He oversaw a total of 41 PhD students over the course of more than 30 years; all of them had bright futures in academia and the workplace after receiving their degrees from Dantzig.

Dantzig has received multiple honorary degrees and memberships in academies in recognition of his significant scientific accomplishments, including the National Medal of Science and the John von Neumann Theory Prize. The George B. Dantzig Prize is given every three years by the Mathematical Optimization Society (MOS) and the Society for Industrial and Applied Mathematics (SIAM) in recognition of the scientist and his achievements.

His health quickly deteriorated shortly after a celebration of his 90th birthday in 2004; a diabetes condition mixed with cardiovascular issues ultimately caused his death.

The Two Unsolved Homework Problems That George Dantzig Solved

The doctoral student George Bernard Dantzig came late to Jerzy Neyman’s statistics lecture in 1939, when two homework assignments were already written on the board. He put them in writing and spent many days trying to solve them. To him, these seemed like ordinary math exercises, but upon further investigation, he discovered that they were, in fact, proofs of two well-known theorems in statistics that had never been proven previously.

1. “On the Non-Existence of Tests of “Student’s” Hypothesis Having Power Functions Independent of σ”, 1940

In the paper, Dantzig investigates whether or not the power function (i.e., the likelihood of rejecting the null hypothesis) of the statistical test for the “Student’s” hypothesis (commonly known as the t-test) can be designed to be independent of the standard deviation of the population (σ).

The “Student’s” hypothesis is a statistical hypothesis test used to evaluate whether the means of two populations are substantially different from each other; it was named after the statistician William Sealy Gosset, who wrote under the pseudonym “Student.” A common statistical procedure for comparing the means of two samples, the t-test is based on the “Student’s” hypothesis and has extensive use.

Dantzig demonstrated that a power function independent of σ cannot be designed for a statistical test of the “Student’s” hypothesis. He then explained his results and gave evidence for them. The study has received several citations because of its significance for the development of statistical theory.

2. “On the Fundamental Lemma of Neyman and Pearson”, 1951

In 1951, George Dantzig published an article in the Annals of Mathematical Statistics titled “On the Fundamental Lemma of Neyman and Pearson.” As a result of statistical theory, Neyman and Pearson’s fundamental lemma has to do with the power of statistical tests, which Dantzig proves in his article.

Neyman and Pearson’s “fundamental lemma” is a universal conclusion that establishes a connection between the null and alternative hypotheses in a statistical test. If the null hypothesis holds, then the likelihood of detecting a test statistic that is more extreme than a specified value (the critical value) is proportional to the sample size of the test. If the null hypothesis is correct, then the test’s power (the probability of rejecting the null) will be proportional to the test size.

Dantzig provides a demonstration of Neyman and Pearson’s fundamental lemma and examines how this finding has practical consequences for statistical testing in his work. The study has again received a lot of attention for its groundbreaking addition to statistical theory.

George Dantzig, the Real Good Will Hunting

A scene from the Good Will Hunting movie with a character inspired from George Dantzig,

The American drama film “Good Will Hunting,” starring Matt Damon and Robin Williams, was directed by Gus Van Sant and released in 1997. Will Hunting, a young guy from South Boston who is a math prodigy yet works as a janitor at MIT, is the protagonist of this film. An MIT professor sees potential in Will, encourages him to pursue mathematics, and ultimately helps him conquer his own personal issues.

A memorable scene from Good Will Hunting has Matt Damon’s character, a janitor at a university, tackling an almost impossible graph problem on a chalkboard. Certain details were changed for dramatic effect, but the basic tale is based on real events related to George Dantzig. One day, future renowned mathematician George Dantzig was running late to his statistics class when he saw two statistical questions written on the whiteboard and assumed they were homework assignments. Dantzig later casually solved the long-unsolved problems of statistics.

George Dantzig’s Discoveries and Contributions

George Dantzig made important contributions to operations research and mathematical modeling. These are the important discoveries and contributions he made that bear mentioning:

The simplex algorithm : In particular, Dantzig is lauded for creating the simplex algorithm, a standard technique for resolving linear programming issues. If you have a linear objective function and linear constraints, the simplex method may help you find the best solution.
The theory of duality in linear programming : Dantzig established a cornerstone notion in optimization theory known as the principle of duality in linear programming. The best solution to a linear programming problem can be found with the help of duality theory, which establishes a link between the original problem and its dual problem.
Contributions to linear regression : Dantzig’s contributions to the field of linear regression are substantial. Linear regression is a statistical technique for modeling the association between a dependent variable and one or more independent variables, and Dantzig made significant contributions to this area.
Work on the transportation problem : Dantzig also did important work in the area of transportation problems, a kind of linear programming issue that includes determining the best possible route for resources to take between different points on a map.

When taken as a whole, Dantzig’s contributions to the fields of mathematics and computer science were influential and shaped the manner in which modern corporations and organizations use mathematical modeling to address difficult issues.

Joe Holley (2005). “Obituaries of George Dantzig” .
Donald J. Albers. (1990). “ More Mathematical People: Contemporary Conversations “
On the Fundamental Lemma of Neyman and Pearson – Projecteuclid.org
On the Non-Existence of Tests of “Student’s” Hypothesis Having Power Functions Independent of σ – Projecteuclid.org
Dantzig, George (1940). “ On the non-existence of tests of “Student’s” hypothesis having power functions independent of σ “

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In 1939, George Dantzig enrolled as a graduate student studying statistics under Polish-born professor Jerzy Neyman. At the beginning of one class session, Dr. Neyman chalked two examples of famous unsolvable problems on the blackboard. George happened to arrive late to class that day, and mistakenly thought the unsolvable problems were their homework assignment, so he transcribed them in his notebook and went to work. Eventually George solved both problems. Six weeks later, an ecstatic Dr. Neyrnan knocked on George's door to share the news. A bewildered George actually apologized, thinking the assignment was overdue. That's when Dr. Neyman informed George that he had solved two of statistics' unsolvable problems."The problems seemed to be a little harder than usual," George would later recall.

Over the ensuing years George Dantzig served the United States Air Force as civilian head of the combat analysis branch, earned a doctorate, worked as a mathematical adviser to the Defense Department, and joined the faculty of Stanford University as professor of operations research and computer science. Dr. George Dantzig received numerous awards during his distinguished career, including the National Medal of Science in 1975. The tools Dantzig developed have shaped the way airlines schedule their fleets, shipping companies deploy their trucks, oil companies run their refineries, and businesses manage their revenue projections. But the genesis of his genius can be traced back to those two problems scribbled on the chalkboard while he was a statistics student. In his own words, "If someone had told me they were two famous unsolved problems, I probably wouldn't have even tried to solve them."

Possible Preaching Angles: George Dantzig solved those unsolvable problems because he didn't know it couldn't be done. Do we limit God's power because we've already decided what God cannot do?

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George Dantzig, 90; Created Linear Programming

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George B. Dantzig, the mathematician who invented the field of linear programming, which revolutionized the way government and private enterprise planned, scheduled and generally conducted their business, has died. He was 90.

A professor emeritus at Stanford, Dantzig died May 13 at his home in Palo Alto. He had been in failing health, with diabetes and cardiovascular disease.

The scholar developed linear programming -- in essence, a decision-support tool that is ideal for resource allocation -- while working for the Defense Department after World War II.

As BusinessWeek reported some years ago, “Dantzig’s idea was to develop a mathematical model that includes all of the variables of any given manufacturing, scheduling or distribution scenario. With all the pertinent data in place, a linear program computes the most efficient, lowest-cost way to achieve the desired objective.”

About the same time, he invented the “simplex method,” an algorithm for solving linear programming problems.

“The virtually simultaneous development of linear programming and computers led to an explosion of applications, especially in the industrial sector,” Arthur F. Veinott Jr., a Stanford professor, said in a statement.

By the early 1950s, private enterprise -- initially petroleum companies -- had started using Dantzig’s methods.

“They started out with the simple problem of how to blend the gasoline for the right flash point, the right viscosity and the right octane and try to do it in the cheapest way possible,” Dantzig told Computerworld magazine some years ago.

In addition to blending gasoline, oil companies used linear programming in computers to schedule tanker fleets, design port facilities and create financial models. Shipping companies employed the concept to determine truck and plane scheduling.

Eventually linear programming came to be used in everything from manufacturing to diet planning.

George Bernard Dantzig was born in Portland, Ore., on Nov. 8, 1914. His father was Tobias Dantzig, a prominent Latvian mathematician who studied at the Sorbonne in Paris and married before immigrating with his wife to the United States in 1909.

George Dantzig showed an early interest in mathematics, especially geometry, and studied at the University of Maryland, where his father was a professor.

Dantzig earned his master’s degree at the University of Michigan and, after two years of work at the U.S. Bureau of Labor Statistics in Washington, enrolled in a PhD program at UC Berkeley.

At the outset of World War II, he left to become chief of the combat analysis branch of the Army Air Forces. He later said his mission was to help create order in aircraft-supply flow lines.

“Everything was planned in the greatest detail: all the nuts and bolts, the procurement of airplanes, the detailed manufacture of everything,” Dantzig said. “There were hundreds of thousands of different kinds of material goods and perhaps 50,000 specialties of people.”

In 1944, he received the War Department’s Exceptional Civilian Service Medal for his efforts.

After the war, he returned to Berkeley and finished his PhD work, continuing his studies with mathematician Jerzy Neyman. Their relationship became legend in the math world.

“During my first year at Berkeley, I arrived late one day to one of Neyman’s classes,” Dantzig recalled years later. “On the blackboard were two problems, which I assumed had been assigned for homework. I copied them down.

“A few days later,” he said, “I apologized to Neyman for taking so long to do the homework -- the problems seemed to be a little harder to do than the usual. He told me to throw [the homework] on his desk.”

Early one morning about six weeks later, Dantzig found Neyman banging excitedly on the front door of his apartment. What Dantzig had copied off the blackboard was not homework but examples of two famous unsolved problems in statistics.

Dantzig had solved one, and Neyman wanted to send out one of his papers for immediate publication.

After earning his doctorate, Dantzig returned to Washington to work for what had by then become the Air Force. His job was mechanizing the planning process. It was during this period that he discovered that linear programs could be used to solve a wide array of planning issues.

His creation of the simplex method and the development of the modern use of computer research made complicated equations much easier and faster to solve. For instance, they allowed industry to quickly compare the several factors involved in interdependent courses of action.

In the early 1950s, Dantzig started working for Rand Corp., where he played a major role in developing the new discipline of operations research using linear programming.

He returned to academia in 1960, as chairman of the Operations Research Center at UC Berkeley. Six years later he moved on to Stanford as professor of operations research and computer science. He retired in 1997.

Over the years, he wrote or co-wrote several influential books, including “Linear Programming and Extensions” (1963) and “Compact City” (1973).

He was awarded the National Science Medal in 1975.

Dantzig is survived by his wife, Anne; three children; three grandchildren; and three great-grandchildren.

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The New Palgrave Dictionary of Economics pp 2576–2589 Cite as

Dantzig, George B. (1914–2005)

Richard W. Cottle 1 ,
B. Curtis Eaves 1 &
Mukund N. Thapa 1
Reference work entry
First Online: 01 January 2018

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George Dantzig is known as ‘father of linear programming’ and ‘inventor of the simplex method’. This biographical sketch traces the high points of George Dantzig’s professional life and scholarly achievements. The discussion covers his graduate student years, his wartime service at the US Air Force’s Statistical Control Division, his post-war creativity while serving as a mathematical advisor at the US Air Force Comptroller’s Office and as a research mathematician at the RAND Corporation, his distinguished career in academia – at UC Berkeley and later at Stanford University – and finally as an emeritus professor of operations research.

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Acknowledgments

Acknowledgments The authors are grateful to David Dantzig, Jessica Dantzig Klass, and many of Dantzig’s friends and colleagues who have contributed to this bio- graphical article. These include A.J. Hoffman, G. Infanger, E. Klotz, J.C. Stone, M.J. Todd, J.A. Tomlin and M.H. Wright. This article has also benefited from other writings on G.B. Dantzig’s life, namely: Albers and Reid ( 1986 ), Albers, Alexanderson and Reid (1990), Cottle ( 2003 , 2005 , 2006 ), Cottle and Wright ( 2006 ), Dantzig (1982, 1991), Dorfman ( 1984 ), Gill et al. ( 2007 ), Kersey ( 1989 ), Lustig ( 2001 ), Gass ( 1989 , 2002 , 2005 ).

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Cottle, R.W., Eaves, B.C., Thapa, M.N. (2018). Dantzig, George B. (1914–2005). In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2839

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14 mind-blowing facts about george dantzig.

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14-mind-blowing-facts-about-george-dantzig

George Dantzig, the renowned mathematician, is a man whose life and work continue to fascinate people around the world. Born on November 8, 1914, in Portland, Oregon, Dantzig’s contributions to the field of mathematics are nothing short of extraordinary. He is best known for his revolutionary work in linear programming and his development of the simplex algorithm, which has revolutionized optimization and decision-making processes.

In this article, we will delve into the intriguing life and mind of George Dantzig and uncover 14 mind-blowing facts that shed light on his exceptional talent and achievements. From his groundbreaking contributions to the development of operations research to his incredible ability to solve complex mathematical problems, Dantzig’s story is one that will awe and inspire you.

Key Takeaways:

George Dantzig, the “Father of Linear Programming,” solved unsolvable problems and revolutionized optimization, impacting industries and inspiring future mathematicians.
Dantzig’s mathematical breakthroughs during World War II and beyond continue to shape business decisions and inspire problem solvers worldwide.

“The Father of Linear Programming”

George Dantzig, an American mathematician, is widely regarded as the pioneer and “Father of Linear Programming.” His groundbreaking work revolutionized the field of optimization and laid the foundation for various applications in business, engineering, and economics.

The Unsolvable Homework Problem

In 1939, Dantzig arrived late for a statistics class at the University of California, Berkeley. He quickly scribbled the two unsolved problems written on the blackboard, thinking they were assigned homework. Little did he know that these problems were not homework but unsolved statistical theorems.

The Challenge That Led to Success

George Dantzig managed to solve those two “homework problems” in a matter of days, not realizing their significance. His solution to what later became known as “Dantzig’s Simplex Algorithm” was a seminal moment in the world of optimization.

Mathematical Breakthrough

Dantzig’s Simplex Algorithm laid the foundation for the field of linear programming, allowing scientists and researchers to efficiently solve complex optimization problems, from resource allocation to production planning.

Influence on World War II

During World War II, George Dantzig’s mathematical skills were put to use in the war effort. He worked on solving logistics and supply chain problems for the United States’ military, optimizing the allocation of resources and improving efficiency.

Presidential Recognition

In 1975, George Dantzig was awarded the National Medal of Science by President Gerald Ford for his significant contributions to mathematics and operations research.

Dantzig’s Long Academic Career

George Dantzig spent more than four decades teaching and conducting research at Stanford University. He mentored numerous students who went on to become influential mathematicians and researchers themselves.

Recognition from Professional Societies

Dantzig was a Fellow of the American Academy of Arts and Sciences, the National Academy of Engineering, and the Institute for Operations Research and the Management Sciences (INFORMS), among other prestigious organizations.

Contributions Beyond Linear Programming

While best known for his work in linear programming, Dantzig made significant contributions to other areas of mathematics, including integer programming, nonlinear programming, and mathematical economics.

A Mind for Optimization

George Dantzig had an exceptional ability to see the world through the lens of optimization. He applied his mathematical expertise to diverse fields such as transportation planning, resource management, and even political decision-making processes.

Legacy in Operations Research

Dantzig’s pioneering work in optimization and operations research paved the way for advancements in decision science, supply chain management, and data analytics, shaping the modern landscape of business and industry.

Impact on Business World

George Dantzig’s mathematical models and algorithms continue to be implemented by businesses worldwide, enabling them to make informed decisions, streamline operations, and maximize efficiency.

Recognition Amongst Peers

George Dantzig received numerous accolades for his contributions to the field of mathematics, including the John von Neumann Theory Prize and the National Medal of Science.

Enduring Inspiration

The life and work of George Dantzig, the “Father of Linear Programming,” continues to inspire future generations of mathematicians, researchers, and problem solvers, who strive to push the boundaries of optimization and create innovative solutions to complex challenges.

In conclusion, George Dantzig was an extraordinary mathematician who made significant contributions to the field of operations research and linear programming. His remarkable life and achievements continue to inspire and influence future generations of mathematicians and researchers.

From his humble beginnings as a college student solving a math problem he thought was homework, to his groundbreaking work in optimizing logistical operations during World War II, Dantzig’s story is a testament to the power of perseverance and the brilliance of the human mind.

Through his innovative methods and mathematical models, Dantzig revolutionized decision-making processes and paved the way for countless practical applications in various industries. His work not only improved efficiency and productivity, but also had far-reaching implications in transportation, manufacturing, and resource allocation.

Moreover, Dantzig’s legacy extends beyond his academic and professional achievements. He was known for his humility, kindness, and willingness to help others. He mentored numerous students and colleagues, leaving an indelible impact on their lives and careers.

All in all, George Dantzig’s life and work serve as an inspiration to us all, reminding us of the boundless potential of the human intellect and the profound impact one individual can make on the world.

1. Who was George Dantzig?

George Dantzig was a renowned mathematician who is best known for his contributions to linear programming and operations research. He was born in 1914 in Portland, Oregon, and went on to receive his PhD in mathematics from the University of California, Berkeley.

2. What was George Dantzig’s biggest achievement?

George Dantzig’s biggest achievement was the development of the simplex algorithm, which revolutionized the field of linear programming. This algorithm provided a method for efficiently solving optimization problems with linear constraints.

3. How did George Dantzig discover the simplex algorithm?

Legend has it that George Dantzig accidentally stumbled upon the idea for the simplex algorithm when he mistakenly thought two linear programming problems were homework assignments. He managed to solve these problems and later realized the significance of his method.

4. What is linear programming?

Linear programming is a mathematical technique used to optimize the allocation of resources. It involves maximizing or minimizing a linear objective function, subject to a set of linear constraints.

5. How did George Dantzig impact the field of operations research?

George Dantzig’s work in linear programming and operations research had a profound impact on various industries. His methods and models provided valuable tools for optimizing logistical operations, improving efficiency, and making more informed decisions.

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COMMENTS

Dantzig's unsolved homework problems
Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a ...
The Legend of the 'Unsolvable Math Problem'
A student mistook examples of unsolved math problems for a homework assignment and solved them. Become a Member. Search. My Profile. Logout. ... One day in 1939, George Bernard Dantzig, a doctoral ...
George Dantzig
George Bernard Dantzig (/ ˈ d æ n t s ɪ ɡ /; November 8, 1914 - May 13, 2005) was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics.. Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, and for his other work with linear ...
Remembering George Dantzig: The real Will Hunting
George Dantzig, who would later become a famous mathematician, was late to his graduate statistics class one day when he saw two statistical problems on a blackboard that he mistook for homework.
PDF The Pioneer of Linear Optimization
homework problems on the board at the beginning of the period. So when Dantzig saw two problems on the board, he wrote them down to work ... George Dantzig introduced the world to the power of optimization, creating trillions of dollars of value and saving countless years of life across the globe. In this laudation, John Birge describes
George Bernard Dantzig: The Pioneer of Linear Optimization
George Dantzig introduced the world to the power of optimization, creating trillions of dollars of value and saving countless years of life across the globe. ... The two problems Dantzig had solved for homework were actually two famous unsolved (and until then, unsolvable) problems in statistics. Dantzig's unshakeable belief that he could ...
George B. Dantzig: Operations Research Icon
board that doctoral student George Dantzig thought was homework when, in fact, it was two unsolved problems in mathematical statistics. His determination in solving these difficult problems has been fashioned into a moral, if not an actual homily. 2. Early Professional Years World events, primarily the Depression and World War II,
George Dantzig
George Dantzig was an American mathematical scientist who worked in operations research, computer science, economics and statistics. He is best known for inventing the simplex algorithm for linear programming. ... A few days later I apologized to Neyman for taking so long to do the homework - the problems seemed to be a little harder to do than ...
Dantzig, George B. (1914-2005)
George Bernard Dantzig was born to Tobias Dantzig and his wife, Anja Ourisson, in Portland Oregon, on 8 November 1914. Tobias, a housepainter and pedlar in his early years in the United States, later held professional positions at John Hopkins University (1919-1920) and the University of Maryland (1927-1946) where he chaired the mathematics ...
Math Whiz Transformed Resource Management
Dantzig scribbled down two problems written on the blackboard that he assumed to be assignments. "A few days later, I apologized to Neyman for taking so long to do the homework—the problems seemed a little harder to do than usual," Dantzig recalled years later. ... George Dantzig married Anne Shmuner and earned his bachelor's degree in ...
NAE Website
GEORGE B. DANTZIG 1914-2005. GEORGE B. DANTZIG, pioneer in operations research and management science, mathematician, professor, educator, consultant, author, and "father" of linear programming, died on May 13, 2005, at the age of 90, in Stanford, California. George's formal education was in mathematics, which reflected his early ...
George B. Dantzig
If you search the Web for "urban legend George Dantzig," you will probably be directed to the URL for "Snopes.com, The Unsolvable Math Problem." That site recounts how George, coming in late for class, mistakenly thought two problems Neyman had written on the board were homework problems.
George Dantzig: The Story of The Overlooked Genius
The Two Unsolved Homework Problems That George Dantzig Solved. The doctoral student George Bernard Dantzig came late to Jerzy Neyman's statistics lecture in 1939, when two homework assignments were already written on the board. He put them in writing and spent many days trying to solve them. To him, these seemed like ordinary math exercises ...
In Memoriam
homework. Dantzig would later recall: "A few days later I apologized to Neyman for taking so long to do the homework—the problems seemed harder to do than usual". It turned out the conundrums, which Dantzig solved, were two famous unsolved problems in statistics. When the United States entered World War II in 1941, Dantzig put his graduate
PDF George B. Dantzig (1914-2005), Volume 54, Number 3
George B. Dantzig he had a remarkable ex-perience that was to be-come a famous legend. Arriving late to one of Neyman'sclasses,Dantzig saw two problems writ-ten on the blackboard and mistook them for a homework assignment. Hefound themmorechal-lenging than usual, but managed to solve them and submitted them di-rectly to Neyman. As it turned ...
Who Was George B. Dantzig?
Tobias Dantzig eventually took a PhD at the University of Indiana, and his wife, after taking a degree in French, became a linguist at the Library of Congress in Washington DC. George Dantzig received degrees from Maryland (1936) and the University of Michigan before earning his doctorate from the University of California, Berkeley, in 1946.
Student Arrives Late For Class And Solves Famous Unsolved Math ...
George Dantzig recounted his feat in a 1986 interview for the College Mathematics Journal: ... A few days later I apologized to Neyman for taking so long to do the homework — the problems seemed ...
College Student Solves Two 'Impossible' Math Problems
George happened to arrive late to class that day, and mistakenly thought the unsolvable problems were their homework assignment, so he transcribed them in his notebook and went to work. Eventually George solved both problems. ... Over the ensuing years George Dantzig served the United States Air Force as civilian head of the combat analysis ...
history
We all know the (apparently verified 1) anecdote recounting George Dantzig arriving late to a lecture (by Jerzy Neyman), and later solving two open problems written on the board, mistaking them for homework. My question is: Q.Are there other examples of a similar misunderstanding that led to the solution of an unsolved problem?
George Dantzig, 90; Created Linear Programming
May 22, 2005 12 AM PT. From Times Staff and Wire Reports. George B. Dantzig, the mathematician who invented the field of linear programming, which revolutionized the way government and private ...
Dantzig, George B. (1914-2005)
George Bernard Dantzig was born to Tobias Dantzig and his wife, Anja Ourisson, in Portland Oregon, on 8 November 1914. Tobias, a housepainter and pedlar in his early years in the United States, later held professional positions at John Hopkins University (1919-1920) and the University of Maryland (1927-1946) where he chaired the mathematics department from 1930 to 1941.
14 Mind-blowing Facts About George Dantzig
George Dantzig managed to solve those two "homework problems" in a matter of days, not realizing their significance. His solution to what later became known as "Dantzig's Simplex Algorithm" was a seminal moment in the world of optimization.
PDF George B. Dantzig: Operations Research Icon
board that doctoral student George Dantzig thought was homework when, in fact, it was two unsolved problems in mathematical statistics. His determination in solving these difﬁcult problems has been fashioned into a moral, if not an actual homily. 2. Early Professional Years World events, primarily the Depression and World War II,