mathematics essay 2022

The Best Writing on Mathematics 12

Mircea pitici,  series editor.

This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics makes mathematical writing available to a wide audience.

The year’s finest mathematical writing from around the world

The year's finest mathematical writing from around the world

The year's finest mathematics writing from around the world

The year's finest writing on mathematics from around the world

The year's finest writing on mathematics from around the world, with a foreword by Nobel Prize – winning physicist Roger Penrose

The year’s most memorable writing on mathematics

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What Students Are Saying About the Value of Math

We asked teenagers: Do you see the point in learning math? The answer from many was “yes.”

By The Learning Network

“Mathematics, I now see, is important because it expands the world,” Alec Wilkinson writes in a recent guest essay . “It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention.”

In our writing prompt “ Do You See the Point in Learning Math? ” we wanted to know if students agreed. Basic arithmetic, sure, but is there value in learning higher-level math, such as algebra, geometry and calculus? Do we appreciate math enough?

The answer from many students — those who love and those who “detest” the subject alike — was yes. Of course math helps us balance checkbooks and work up budgets, they said, but it also helps us learn how to follow a formula, appreciate music, draw, shoot three-pointers and even skateboard. It gives us different perspectives, helps us organize our chaotic thoughts, makes us more creative, and shows us how to think rationally.

Not all were convinced that young people should have to take higher-level math classes all through high school, but, as one student said, “I can see myself understanding even more how important it is and appreciating it more as I get older.”

Thank you to all the teenagers who joined the conversation on our writing prompts this week, including students from Bentonville West High School in Centerton, Ark, ; Harvard-Westlake School in Los Angeles ; and North High School in North St. Paul, Minn.

Please note: Student comments have been lightly edited for length, but otherwise appear as they were originally submitted.

“Math is a valuable tool and function of the world.”

As a musician, math is intrinsically related to my passion. As a sailor, math is intertwined with the workings of my boat. As a human, math is the building block for all that functions. When I was a child, I could very much relate to wanting a reason behind math. I soon learned that math IS the reason behind all of the world’s workings. Besides the benefits that math provides to one’s intellect, it becomes obvious later in life that math is a valuable tool and function of the world. In music for example, “adolescent mathematics” are used to portray functions of audio engineering. For example, phase shifting a sine wave to better project sound or understanding waves emitted by electricity and how they affect audio signals. To better understand music, math is a recurring pattern of intervals between generating pitches that are all mathematically related. The frets on a guitar are measured precisely to provide intervals based on a tuning system surrounding 440Hz, which is the mathematically calculated middle of the pitches humans can perceive and a string can effectively generate. The difference between intervals in making a chord are not all uniform, so guitar frets are placed in a way where all chords can sound equally consonant and not favor any chord. The power of mathematics! I am fascinated by the way that math creeps its way into all that I do, despite my plentiful efforts to keep it at a safe distance …

— Renan, Miami Country Day School

“Math isn’t about taking derivatives or solving for x, it’s about having the skills to do so and putting them to use elsewhere in life.”

I believe learning mathematics is both crucial to the learning and development of 21st century students and yet also not to be imposed upon learners too heavily. Aside from the rise in career opportunity in fields centered around mathematics, the skills gained while learning math are able to be translated to many facets of life after a student’s education. Learning mathematics develops problem solving skills which combine logic and reasoning in students as they grow. The average calculus student may complain of learning how to take derivatives, arguing that they will never have to use this after high school, and in that, they may be right. Many students in these math classes will become writers, musicians, or historians and may never take a derivative in their life after high school, and thus deem the skill to do so useless. However, learning mathematics isn’t about taking derivatives or solving for x, it’s about having the skills to do so and putting them to use elsewhere in life. A student who excels at calculus may never use it again, but with the skills of creativity and rational thinking presented by this course, learning mathematics will have had a profound effect on their life.

— Cam, Glenbard West

“Just stop and consider your hobbies and pastimes … all of it needs math.”

Math is timing, it’s logic, it’s precision, it’s structure, and it’s the way most of the physical world works. I love math — especially algebra and geometry — as it all follows a formula, and if you set it up just right, you can create almost anything you want in at least two different ways. Just stop and consider your hobbies and pastimes. You could be into skateboarding, basketball, or skiing. You could be like me, and sit at home for hours on end grinding out solves on a Rubik’s cube. Or you could be into sketching. Did you know that a proper drawing of the human face places the eyes exactly halfway down from the top of the head? All of it needs math. Author Alec Wilkinson, when sharing his high school doubting view on mathematics, laments “If I had understood how deeply mathematics is embedded in the world …” You can’t draw a face without proportions. You can’t stop with your skis at just any angle. You can’t get three points without shooting at least 22 feet away from the basket, and get this: you can’t even ride a skateboard if you can’t create four congruent wheels to put on it.

— Marshall, Union High School, Vancouver, WA

“Math gives us a different perspective on everyday activities.”

Even though the question “why do we even do math?” is asked all the time, there is a deeper meaning to the values it shares. Math gives us a different perspective on everyday activities, even if those activities in our routine have absolutely nothing to do with mathematical concepts itself. Geometry, for instance, allows us to think on a different level than simply achieving accuracy maintains. It trains our mind to look at something from various viewpoints as well as teaching us to think before acting and organizing chaotic thoughts. The build up of learning math can allow someone to mature beyond the point where if they didn’t learn math and thought through everything. It paves a way where we develop certain characteristics and traits that are favorable when assisting someone with difficult tasks in the future.

— Linden, Harvard-Westlake High School, CA

“Math teaches us how to think.”

As explained in the article, math is all around us. Shapes, numbers, statistics, you can find math in almost anything and everything. But is it important for all students to learn? I would say so. Math in elementary school years is very important because it teaches how to do simple calculations that can be used in your everyday life; however middle and high school math isn’t used as directly. Math teaches us how to think. It’s far different from any other subject in school, and truly understanding it can be very rewarding. There are also many career paths that are based around math, such as engineering, statistics, or computer programming, for example. These careers are all crucial for society to function, and many pay well. Without a solid background in math, these careers wouldn’t be possible. While math is a very important subject, I also feel it should become optional at some point, perhaps part way through high school. Upper level math classes often lose their educational value if the student isn’t genuinely interested in learning it. I would encourage all students to learn math, but not require it.

— Grey, Cary High School

“Math is a valuable tool for everyone to learn, but students need better influences to show them why it’s useful.”

Although I loved math as a kid, as I got older it felt more like a chore; all the kids would say “when am I ever going to use this in real life?” and even I, who had loved math, couldn’t figure out how it benefits me either. This was until I started asking my dad for help with my homework. He would go on and on about how he used the math I was learning everyday at work and even started giving me examples of when and where I could use it, which changed my perspective completely. Ultimately, I believe that math is a valuable tool for everyone to learn, but students need better influences to show them why it’s useful and where they can use it outside of class.

— Lilly, Union High School

“At the roots of math, it teaches people how to follow a process.”

I do believe that the math outside of arithmetic, percentages, and fractions are the only math skills truly needed for everyone, with all other concepts being only used for certain careers. However, at the same time, I can’t help but want to still learn it. I believe that at the roots of math, it teaches people how to follow a process. All mathematics is about following a formula and then getting the result of it as accurately as possible. It teaches us that in order to get the results needed, all the work must be put and no shortcuts or guesses can be made. Every equation, number, and symbol in math all interconnect with each other, to create formulas that if followed correctly gives us the answer needed. Everything is essential to getting the results needed, and skipping a step will lead to a wrong answer. Although I do understand why many would see no reason to learn math outside of arithmetic, I also see lessons of work ethics and understanding the process that can be applied to many real world scenarios.

— Takuma, Irvine High School

“I see now that math not only works through logic but also creativity.”

A story that will never finish resembling the universe constantly expanding, this is what math is. I detest math, but I love a never-ending tale of mystery and suspense. If we were to see math as an adventure it would make it more enjoyable. I have often had a closed mindset on math, however, viewing it from this perspective, I find it much more appealing. Teachers urge students to try on math and though it seems daunting and useless, once you get to higher math it is still important. I see now that math not only works through logic but also creativity and as the author emphasizes, it is “a fundamental part of the world’s design.” This view on math will help students succeed and have a more open mindset toward math. How is this never-ending story of suspense going to affect YOU?

— Audrey, Vancouver, WA union high school

“In some word problems, I encounter problems that thoroughly interest me.”

I believe math is a crucial thing to learn as you grow up. Math is easily my favorite subject and I wish more people would share my enthusiasm. As Alec Wilkinson writes, “Mathematics, I now see, is important because it expands the world.” I have always enjoyed math, but until the past year, I have not seen a point in higher-level math. In some of the word problems I deal with in these classes, I encounter problems that thoroughly interest me. The problems that I am working on in math involve the speed of a plane being affected by wind. I know this is not riveting to everyone, but I thoroughly wonder about things like this on a daily basis. The type of math used in the plane problems is similar to what Alec is learning — trigonometry. It may not serve the most use to me now, but I believe a thorough understanding of the world is a big part of living a meaningful life.

— Rehan, Cary High School

“Without high school classes, fewer people get that spark of wonder about math.”

I think that math should be required through high school because math is a use-it-or-lose-it subject. If we stop teaching math in high school and just teach it up to middle school, not only will many people lose their ability to do basic math, but we will have fewer and fewer people get that spark of wonder about math that the author had when taking math for a second time; after having that spark myself, I realized that people start getting the spark once they are in harder math classes. At first, I thought that if math stopped being required in high school, and was offered as an elective, then only people with the spark would continue with it, and everything would be okay. After thinking about the consequences of the idea, I realized that technology requires knowing the seemingly unneeded math. There is already a shortage of IT professionals, and stopping math earlier will only worsen that shortage. Math is tricky. If you try your best to understand it, it isn’t too hard. However, the problem is people had bad math teachers when they were younger, which made them hate math. I have learned that the key to learning math is to have an open mind.

— Andrew, Cary High School

“I think math is a waste of my time because I don’t think I will ever get it.”

In the article Mr. Wilkinson writes, “When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life.” His experience as a boy resonates with my experience now. I feel like math is extremely difficult at some points and it is not my strongest subject. Whenever I am having a hard time with something I get a little upset with myself because I feel like I need to get everything perfect. So therefore, I think it is a waste of my time because I don’t think I will ever get it. At the age of 65 Mr. Wilkinson decided to see if he could learn more/relearn algebra, geometry and calculus and I can’t imagine myself doing this but I can see myself understanding even more how important it is and appreciating it more as I get older. When my dad was young he hated history but, as he got older he learned to appreciate it and see how we can learn from our past mistakes and he now loves learning new things about history.

— Kate, Cary High School

“Not all children need to learn higher level math.”

The higher levels of math like calculus, algebra, and geometry have shaped the world we live in today. Just designing a house relates to math. To be in many professions you have to know algebra, geometry, and calculus such as being an economist, engineer, and architect. Although higher-level math isn’t useful to some people. If you want to do something that pertains to math, you should be able to do so and learn those high levels of math. Many things children learn in math they will never use again, so learning those skills isn’t very helpful … Children went through so much stress and anxiety to learn these skills that they will never see again in their lives. In school, children are using their time learning calculus when they could be learning something more meaningful that can prepare them for life.

— Julyssa, Hanover Horton High School

“Once you understand the basics, more math classes should be a choice.”

I believe that once you get to the point where you have a great understanding of the basics of math, you should be able to take more useful classes that will prepare you for the future better, rather than memorizing equations after equations about weird shapes that will be irrelevant to anything in my future. Yes, all math levels can be useful to others’ futures depending on what career path they choose, but for the ones like me who know they are not planning on encountering extremely high level math equations on the daily, we should not have to take math after a certain point.

— Tessa, Glenbard West High School

“Math could shape the world if it were taught differently.”

If we learned how to balance checkbooks and learn about actual life situations, math could be more helpful. Instead of learning about rare situations that probably won’t come up in our lives, we should be learning how to live on a budget and succeed money-wise. Since it is a required class, learning this would save more people from going into debt and overspending. In schools today, we have to take a specific class that doesn’t sound appealing to the average teenager to learn how to save and spend money responsibly. If it was required in math to learn about that instead of how far Sally has to walk then we would be a more successful nation as a whole. Math could shape the world differently but the way it is taught in schools does not have much impact on everyday life.

— Becca, Bentonville West High School

“To be honest, I don’t see the point in learning all of the complicated math.”

In a realistic point of view, I need to know how to cut a cake or a piece of pie or know how to divide 25,000 dollars into 10 paychecks. On the other hand, I don’t need to know the arc and angle. I need to throw a piece of paper into a trash can. I say this because, in all reality and I know a lot of people say this but it’s true, when are we actually going to need this in our real world lives? Learning complicated math is a waste of precious learning time unless you desire to have a career that requires these studies like becoming an engineer, or a math professor. I think that the fact that schools are still requiring us to learn these types of mathematics is just ignorance from the past generations. I believe that if we have the technology to complete these problems in a few seconds then we should use this technology, but the past generations are salty because they didn’t have these resources so they want to do the same thing they did when they were learning math. So to be honest, I don’t see the point in learning all of the complicated math but I do think it’s necessary to know the basic math.

— Shai, Julia R Masterman, Philadelphia, PA

Learn more about Current Events Conversation here and find all of our posts in this column .

Tom Rocks Maths: Essay Competition 2024

This exciting competition asks students of all ages and abilities to explain their favourite mathematical topic in an essay aimed at a non-specialist audience. Originally launched in 2020 as a partnership between Tom Rocks Maths and St Edmund Hall, the competition aims to provide the participants with the opportunity to communicate complex ideas in an understandable manner, and to encourage them to engage with maths beyond any curriculum. 

Competition details

There are no eligibility requirements, all you need is a passion for maths and a flair for writing to participate! The closing date is  Monday 1st April 2024  and the showcase of entries (including the announcement of the winners) will take place throughout summer 2024. 

There are two strands of entry:

• 16-18's (student); and
• Over 18's (adult)

Please note: A ‘student' is defined as anyone who is still studying full-time at school or college, university students fall into the ‘adult’' category.

There is no word limit for the essays, but as a guideline 1000-2000 words is sufficient. All entries must be submitted using the online form as PDF or Microsoft Word documents.

• The submission form can be accessed here >

The winners will be selected by Dr Tom Crawford, Public Engagement Lead and Departmental Lecturer, and the creator of the award-winning ’Tom Rocks Maths’. All entries will be published on the  Tom Rocks Maths website  as part of the essay showcase. 

The student prizewinner will receive a cash prize of £100 alongside the publication of their winning essay on the University website. 

The adult prizewinner will receive free registration to an  online live-time weekly class (WOW)  of their choosing and the publication of their winning essay on the University website. The full list of courses available can be found here .

Choosing your essay topic

The mathematical topic of your essay can be anything you choose, but if you’re struggling to come up with ideas, here are a few examples to get you started:

• How to build a giant dome - Numberphile
• Which is the Fastest Dinosaur? The Maths of Dinosaurs
• Making Mathematical Art with L-Systems

Previous years' entries:

Previous editions of the competition have received extremely high numbers of excellent submissions, all of which can be found at the links below:

• 2023 entries
• 2022 entries
• 2021 entries
• 2020 entries

If you have any questions about the competition or would like some more information, please contact Tom at  [email protected] .

• Submit your entry here >

Data policy

Personal data.

Personal data is information that relates to you. In the course of completing this Tom Rocks Maths: Essay Competition submission form, you have provided the Department with information about yourself, which is known as personal data.

What will the Department do with your data?

The Department will collect, process, share, and use personal data for the purposes of notifying you if you are successful in the competition. You will only be notified shortly after the competition closes on Monday 1 April 2024. The Department will normally only discuss your personal information with you, unless you have nominated a third party.

This information will be retained until the winner of the competition has been announced, after which it will be securely deleted.

Legal Basis of Processing

The legal basis for processing your information is that this processing is necessary to notify you if you have been successful in the competition.

Read our full Privacy Policy terms .

Get in touch

If you have any questions, please contact Tom at  [email protected] .

Dr Tom Crawford

Data science, computing and maths, weekly oxford worldwide, open-access short courses.

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2022 Student Essay Contest: Grades 6-8 First Place

The world of mathematics has changed, by: haley song (frances c. richmond middle school), interviewee: carolyn gordon (dartmouth college).

How have times changed from the twentieth century to now? Well, for one, math was once considered boys’ territory, and academics were rarely taught by women. In the 1960s, Dr. Carolyn Gordon was just a teenager in middle school and was seen as an anomaly. After years of being looked down on, she proved her worth, not just by majoring in math at Purdue University, but also continuing onto graduate school. And now, in 2022, Dr. Gordon is an accomplished, prodigious, emerita in isospectral geometry at Dartmouth. 

Growing up in Charleston, West Virginia, middle and high school was harsh to Dr. Carolyn Gordon, with boys constantly teasing her, the stress of puberty, and middle school in general. Gordon was seen as different because she wasn’t like other girls her age. Nowadays, being unique is greatly admired. But, when kids were mean, and school was tough, she looked to her sister. Her sister was seven years older, and she had also respected math. When the puzzle of life got taken apart, Dr. Gordon and her sister would try to put the pieces back together. “That [having a sister] really was helpful to me especially if I felt like an oddity, having a sister who also liked it [math] made it much more okay.” Dr. Gordon told me with a tiny laugh, and a big, warm smile. 

At Purdue University Dr. Gordon majored in math. She told me that she always saw herself ending up doing math in college, and when that vision came true, she couldn’t have been happier. Although at times she still felt like she was out of place, she knew that she had to keep going. “The way I see it, if you want the rainbow, you gotta put up with the rain.” -Dolly Parton 

Although Dr. Gordon is a retired geometry professor, she told me she hasn’t always liked it. In fact, (my eyes grew wide at this, and my jaw might’ve dropped to the ground) she used to hate it. Remember, she was a professor at Dartmouth, so she knows how strong the word hate is. It wasn’t until graduate school that her love for shapes even started to develop. She had been forced to take the class, and albeit she was not happy at first, but by the end of the semester she was in love with the subject. 

One year all the national math societies had their annual meetings in St. Louis, where, almost like fate, was where Dr. Gordon was going to graduate school. She decided that she was going to go to some meetings, and one day, she stumbled upon one of the meetings for the new Association for Women in Mathematics. “I walked into a room full of women mathematicians, and it was really like an electric shock! I hadn’t been aware that I had missed seeing women mathematicians, but when I saw a whole room full of them, I just felt so joyous.” Dr. Gordon exclaimed with a grin the size of Texas stuck on her face. As she said this her eyes lit up like how a kid’s face would when you gave them a lollipop, balloon, and a whole week at Disney World, which made my smile stretch from ear to ear. 

At the end of the interview, I asked her if she had any advice, or anything else to add, and what she said broke my heart. “I know for me, I’ve always struggled with feeling like an imposter, you know. ‘If they really realize how little I know, they’re going to find me out. I’m not really good enough.’” Dr. Gordon whispered in a small, insecure voice. Then she added that people tend to judge themselves too much, and that is what’s holding us back from thriving in the things we love. She then gave me phenomenal advice that I will never forget, “If you like the math, don’t judge yourself…just do it.” 

Times can change. Times have changed. Women have a voice in mathematics, just like men do. Last year, the Association for Women in Mathematics celebrated its 50th anniversary. After sixty years, Dr. Gordon can tell you how much this world has grown, and how it will continue to grow. And, always remember, when you have a dream, just do it.