how to write an introduction for a scientific research paper pdf

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How to Write a Research Paper Introduction (with Examples)

The research paper introduction section, along with the Title and Abstract, can be considered the face of any research paper. The following article is intended to guide you in organizing and writing the research paper introduction for a quality academic article or dissertation.

The research paper introduction aims to present the topic to the reader. A study will only be accepted for publishing if you can ascertain that the available literature cannot answer your research question. So it is important to ensure that you have read important studies on that particular topic, especially those within the last five to ten years, and that they are properly referenced in this section. 1 What should be included in the research paper introduction is decided by what you want to tell readers about the reason behind the research and how you plan to fill the knowledge gap. The best research paper introduction provides a systemic review of existing work and demonstrates additional work that needs to be done. It needs to be brief, captivating, and well-referenced; a well-drafted research paper introduction will help the researcher win half the battle.

The introduction for a research paper is where you set up your topic and approach for the reader. It has several key goals:

• Present your research topic
• Capture reader interest
• Summarize existing research
• Position your own approach
• Define your specific research problem and problem statement
• Highlight the novelty and contributions of the study
• Give an overview of the paper’s structure

The research paper introduction can vary in size and structure depending on whether your paper presents the results of original empirical research or is a review paper. Some research paper introduction examples are only half a page while others are a few pages long. In many cases, the introduction will be shorter than all of the other sections of your paper; its length depends on the size of your paper as a whole.

• Break through writer’s block. Write your research paper introduction with Paperpal Copilot

Table of Contents

What is the introduction for a research paper, why is the introduction important in a research paper, craft a compelling introduction section with paperpal. try now, 1. introduce the research topic:, 2. determine a research niche:, 3. place your research within the research niche:, craft accurate research paper introductions with paperpal. start writing now, frequently asked questions on research paper introduction, key points to remember.

The introduction in a research paper is placed at the beginning to guide the reader from a broad subject area to the specific topic that your research addresses. They present the following information to the reader

• Scope: The topic covered in the research paper
• Context: Background of your topic
• Importance: Why your research matters in that particular area of research and the industry problem that can be targeted

The research paper introduction conveys a lot of information and can be considered an essential roadmap for the rest of your paper. A good introduction for a research paper is important for the following reasons:

• It stimulates your reader’s interest: A good introduction section can make your readers want to read your paper by capturing their interest. It informs the reader what they are going to learn and helps determine if the topic is of interest to them.
• It helps the reader understand the research background: Without a clear introduction, your readers may feel confused and even struggle when reading your paper. A good research paper introduction will prepare them for the in-depth research to come. It provides you the opportunity to engage with the readers and demonstrate your knowledge and authority on the specific topic.
• It explains why your research paper is worth reading: Your introduction can convey a lot of information to your readers. It introduces the topic, why the topic is important, and how you plan to proceed with your research.
• It helps guide the reader through the rest of the paper: The research paper introduction gives the reader a sense of the nature of the information that will support your arguments and the general organization of the paragraphs that will follow. It offers an overview of what to expect when reading the main body of your paper.

What are the parts of introduction in the research?

A good research paper introduction section should comprise three main elements: 2

• What is known: This sets the stage for your research. It informs the readers of what is known on the subject.
• What is lacking: This is aimed at justifying the reason for carrying out your research. This could involve investigating a new concept or method or building upon previous research.
• What you aim to do: This part briefly states the objectives of your research and its major contributions. Your detailed hypothesis will also form a part of this section.

How to write a research paper introduction?

The first step in writing the research paper introduction is to inform the reader what your topic is and why it’s interesting or important. This is generally accomplished with a strong opening statement. The second step involves establishing the kinds of research that have been done and ending with limitations or gaps in the research that you intend to address. Finally, the research paper introduction clarifies how your own research fits in and what problem it addresses. If your research involved testing hypotheses, these should be stated along with your research question. The hypothesis should be presented in the past tense since it will have been tested by the time you are writing the research paper introduction.

The following key points, with examples, can guide you when writing the research paper introduction section:

• Highlight the importance of the research field or topic
• Describe the background of the topic
• Present an overview of current research on the topic

Example: The inclusion of experiential and competency-based learning has benefitted electronics engineering education. Industry partnerships provide an excellent alternative for students wanting to engage in solving real-world challenges. Industry-academia participation has grown in recent years due to the need for skilled engineers with practical training and specialized expertise. However, from the educational perspective, many activities are needed to incorporate sustainable development goals into the university curricula and consolidate learning innovation in universities.

• Reveal a gap in existing research or oppose an existing assumption
• Formulate the research question

Example: There have been plausible efforts to integrate educational activities in higher education electronics engineering programs. However, very few studies have considered using educational research methods for performance evaluation of competency-based higher engineering education, with a focus on technical and or transversal skills. To remedy the current need for evaluating competencies in STEM fields and providing sustainable development goals in engineering education, in this study, a comparison was drawn between study groups without and with industry partners.

• State the purpose of your study
• Highlight the key characteristics of your study
• Describe important results
• Highlight the novelty of the study.
• Offer a brief overview of the structure of the paper.

Example: The study evaluates the main competency needed in the applied electronics course, which is a fundamental core subject for many electronics engineering undergraduate programs. We compared two groups, without and with an industrial partner, that offered real-world projects to solve during the semester. This comparison can help determine significant differences in both groups in terms of developing subject competency and achieving sustainable development goals.

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With Paperpal Copilot, create a research paper introduction effortlessly. In this step-by-step guide, we’ll walk you through how Paperpal transforms your initial ideas into a polished and publication-ready introduction.

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You can use the same process to develop each section of your article, and finally your research paper in half the time and without any of the stress.

The purpose of the research paper introduction is to introduce the reader to the problem definition, justify the need for the study, and describe the main theme of the study. The aim is to gain the reader’s attention by providing them with necessary background information and establishing the main purpose and direction of the research.

The length of the research paper introduction can vary across journals and disciplines. While there are no strict word limits for writing the research paper introduction, an ideal length would be one page, with a maximum of 400 words over 1-4 paragraphs. Generally, it is one of the shorter sections of the paper as the reader is assumed to have at least a reasonable knowledge about the topic. 2 For example, for a study evaluating the role of building design in ensuring fire safety, there is no need to discuss definitions and nature of fire in the introduction; you could start by commenting upon the existing practices for fire safety and how your study will add to the existing knowledge and practice.

When deciding what to include in the research paper introduction, the rest of the paper should also be considered. The aim is to introduce the reader smoothly to the topic and facilitate an easy read without much dependency on external sources. 3 Below is a list of elements you can include to prepare a research paper introduction outline and follow it when you are writing the research paper introduction. Topic introduction: This can include key definitions and a brief history of the topic. Research context and background: Offer the readers some general information and then narrow it down to specific aspects. Details of the research you conducted: A brief literature review can be included to support your arguments or line of thought. Rationale for the study: This establishes the relevance of your study and establishes its importance. Importance of your research: The main contributions are highlighted to help establish the novelty of your study Research hypothesis: Introduce your research question and propose an expected outcome. Organization of the paper: Include a short paragraph of 3-4 sentences that highlights your plan for the entire paper

Cite only works that are most relevant to your topic; as a general rule, you can include one to three. Note that readers want to see evidence of original thinking. So it is better to avoid using too many references as it does not leave much room for your personal standpoint to shine through. Citations in your research paper introduction support the key points, and the number of citations depend on the subject matter and the point discussed. If the research paper introduction is too long or overflowing with citations, it is better to cite a few review articles rather than the individual articles summarized in the review. A good point to remember when citing research papers in the introduction section is to include at least one-third of the references in the introduction.

The literature review plays a significant role in the research paper introduction section. A good literature review accomplishes the following: Introduces the topic – Establishes the study’s significance – Provides an overview of the relevant literature – Provides context for the study using literature – Identifies knowledge gaps However, remember to avoid making the following mistakes when writing a research paper introduction: Do not use studies from the literature review to aggressively support your research Avoid direct quoting Do not allow literature review to be the focus of this section. Instead, the literature review should only aid in setting a foundation for the manuscript.

Remember the following key points for writing a good research paper introduction: 4

• Avoid stuffing too much general information: Avoid including what an average reader would know and include only that information related to the problem being addressed in the research paper introduction. For example, when describing a comparative study of non-traditional methods for mechanical design optimization, information related to the traditional methods and differences between traditional and non-traditional methods would not be relevant. In this case, the introduction for the research paper should begin with the state-of-the-art non-traditional methods and methods to evaluate the efficiency of newly developed algorithms.
• Avoid packing too many references: Cite only the required works in your research paper introduction. The other works can be included in the discussion section to strengthen your findings.
• Avoid extensive criticism of previous studies: Avoid being overly critical of earlier studies while setting the rationale for your study. A better place for this would be the Discussion section, where you can highlight the advantages of your method.
• Avoid describing conclusions of the study: When writing a research paper introduction remember not to include the findings of your study. The aim is to let the readers know what question is being answered. The actual answer should only be given in the Results and Discussion section.

To summarize, the research paper introduction section should be brief yet informative. It should convince the reader the need to conduct the study and motivate him to read further. If you’re feeling stuck or unsure, choose trusted AI academic writing assistants like Paperpal to effortlessly craft your research paper introduction and other sections of your research article.

1. Jawaid, S. A., & Jawaid, M. (2019). How to write introduction and discussion. Saudi Journal of Anaesthesia, 13(Suppl 1), S18.

2. Dewan, P., & Gupta, P. (2016). Writing the title, abstract and introduction: Looks matter!. Indian pediatrics, 53, 235-241.

3. Cetin, S., & Hackam, D. J. (2005). An approach to the writing of a scientific Manuscript1. Journal of Surgical Research, 128(2), 165-167.

4. Bavdekar, S. B. (2015). Writing introduction: Laying the foundations of a research paper. Journal of the Association of Physicians of India, 63(7), 44-6.

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• 08 May 2019

Toolkit: How to write a great paper

A clear format will ensure that your research paper is understood by your readers. Follow:

1. Context — your introduction

2. Content — your results

3. Conclusion — your discussion

Plan your paper carefully and decide where each point will sit within the framework before you begin writing.

Collection: Careers toolkit

Straightforward writing

Scientific writing should always aim to be A, B and C: Accurate, Brief, and Clear. Never choose a long word when a short one will do. Use simple language to communicate your results. Always aim to distill your message down into the simplest sentence possible.

Choose a title

A carefully conceived title will communicate the single core message of your research paper. It should be D, E, F: Declarative, Engaging and Focused.

Conclusions

Add a sentence or two at the end of your concluding statement that sets out your plans for further research. What is next for you or others working in your field?

Find out more

See additional information .

doi: https://doi.org/10.1038/d41586-019-01362-9

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Writing an Introduction for a Scientific Paper

Dr. michelle harris, dr. janet batzli, biocore.

This section provides guidelines on how to construct a solid introduction to a scientific paper including background information, study question , biological rationale, hypothesis , and general approach . If the Introduction is done well, there should be no question in the reader’s mind why and on what basis you have posed a specific hypothesis.

Broad Question : based on an initial observation (e.g., “I see a lot of guppies close to the shore. Do guppies like living in shallow water?”). This observation of the natural world may inspire you to investigate background literature or your observation could be based on previous research by others or your own pilot study. Broad questions are not always included in your written text, but are essential for establishing the direction of your research.

Background Information : key issues, concepts, terminology, and definitions needed to understand the biological rationale for the experiment. It often includes a summary of findings from previous, relevant studies. Remember to cite references, be concise, and only include relevant information given your audience and your experimental design. Concisely summarized background information leads to the identification of specific scientific knowledge gaps that still exist. (e.g., “No studies to date have examined whether guppies do indeed spend more time in shallow water.”)

Testable Question : these questions are much more focused than the initial broad question, are specific to the knowledge gap identified, and can be addressed with data. (e.g., “Do guppies spend different amounts of time in water <1 meter deep as compared to their time in water that is >1 meter deep?”)

Biological Rationale : describes the purpose of your experiment distilling what is known and what is not known that defines the knowledge gap that you are addressing. The “BR” provides the logic for your hypothesis and experimental approach, describing the biological mechanism and assumptions that explain why your hypothesis should be true.

The biological rationale is based on your interpretation of the scientific literature, your personal observations, and the underlying assumptions you are making about how you think the system works. If you have written your biological rationale, your reader should see your hypothesis in your introduction section and say to themselves, “Of course, this hypothesis seems very logical based on the rationale presented.”

• A thorough rationale defines your assumptions about the system that have not been revealed in scientific literature or from previous systematic observation. These assumptions drive the direction of your specific hypothesis or general predictions.
• Defining the rationale is probably the most critical task for a writer, as it tells your reader why your research is biologically meaningful. It may help to think about the rationale as an answer to the questions— how is this investigation related to what we know, what assumptions am I making about what we don’t yet know, AND how will this experiment add to our knowledge? *There may or may not be broader implications for your study; be careful not to overstate these (see note on social justifications below).
• Expect to spend time and mental effort on this. You may have to do considerable digging into the scientific literature to define how your experiment fits into what is already known and why it is relevant to pursue.
• Be open to the possibility that as you work with and think about your data, you may develop a deeper, more accurate understanding of the experimental system. You may find the original rationale needs to be revised to reflect your new, more sophisticated understanding.
• As you progress through Biocore and upper level biology courses, your rationale should become more focused and matched with the level of study e ., cellular, biochemical, or physiological mechanisms that underlie the rationale. Achieving this type of understanding takes effort, but it will lead to better communication of your science.

***Special note on avoiding social justifications: You should not overemphasize the relevance of your experiment and the possible connections to large-scale processes. Be realistic and logical —do not overgeneralize or state grand implications that are not sensible given the structure of your experimental system. Not all science is easily applied to improving the human condition. Performing an investigation just for the sake of adding to our scientific knowledge (“pure or basic science”) is just as important as applied science. In fact, basic science often provides the foundation for applied studies.

Hypothesis / Predictions : specific prediction(s) that you will test during your experiment. For manipulative experiments, the hypothesis should include the independent variable (what you manipulate), the dependent variable(s) (what you measure), the organism or system , the direction of your results, and comparison to be made.

If you are doing a systematic observation , your hypothesis presents a variable or set of variables that you predict are important for helping you characterize the system as a whole, or predict differences between components/areas of the system that help you explain how the system functions or changes over time.

Experimental Approach : Briefly gives the reader a general sense of the experiment, the type of data it will yield, and the kind of conclusions you expect to obtain from the data. Do not confuse the experimental approach with the experimental protocol . The experimental protocol consists of the detailed step-by-step procedures and techniques used during the experiment that are to be reported in the Methods and Materials section.

Some Final Tips on Writing an Introduction

• As you progress through the Biocore sequence, for instance, from organismal level of Biocore 301/302 to the cellular level in Biocore 303/304, we expect the contents of your “Introduction” paragraphs to reflect the level of your coursework and previous writing experience. For example, in Biocore 304 (Cell Biology Lab) biological rationale should draw upon assumptions we are making about cellular and biochemical processes.
• Be Concise yet Specific: Remember to be concise and only include relevant information given your audience and your experimental design. As you write, keep asking, “Is this necessary information or is this irrelevant detail?” For example, if you are writing a paper claiming that a certain compound is a competitive inhibitor to the enzyme alkaline phosphatase and acts by binding to the active site, you need to explain (briefly) Michaelis-Menton kinetics and the meaning and significance of Km and Vmax. This explanation is not necessary if you are reporting the dependence of enzyme activity on pH because you do not need to measure Km and Vmax to get an estimate of enzyme activity.
• Another example: if you are writing a paper reporting an increase in Daphnia magna heart rate upon exposure to caffeine you need not describe the reproductive cycle of magna unless it is germane to your results and discussion. Be specific and concrete, especially when making introductory or summary statements.

Where Do You Discuss Pilot Studies? Many times it is important to do pilot studies to help you get familiar with your experimental system or to improve your experimental design. If your pilot study influences your biological rationale or hypothesis, you need to describe it in your Introduction. If your pilot study simply informs the logistics or techniques, but does not influence your rationale, then the description of your pilot study belongs in the Materials and Methods section.  

How will introductions be evaluated? The following is part of the rubric we will be using to evaluate your papers.

How to Write the Introduction to a Scientific Paper?

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• How to Write a Literature Review | Guide, Examples, & Templates

How to Write a Literature Review | Guide, Examples, & Templates

Published on January 2, 2023 by Shona McCombes . Revised on September 11, 2023.

What is a literature review? A literature review is a survey of scholarly sources on a specific topic. It provides an overview of current knowledge, allowing you to identify relevant theories, methods, and gaps in the existing research that you can later apply to your paper, thesis, or dissertation topic .

There are five key steps to writing a literature review:

• Search for relevant literature
• Evaluate sources
• Identify themes, debates, and gaps
• Outline the structure
• Write your literature review

A good literature review doesn’t just summarize sources—it analyzes, synthesizes , and critically evaluates to give a clear picture of the state of knowledge on the subject.

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Table of contents

What is the purpose of a literature review, examples of literature reviews, step 1 – search for relevant literature, step 2 – evaluate and select sources, step 3 – identify themes, debates, and gaps, step 4 – outline your literature review’s structure, step 5 – write your literature review, free lecture slides, other interesting articles, frequently asked questions, introduction.

• Quick Run-through
• Step 1 & 2

When you write a thesis , dissertation , or research paper , you will likely have to conduct a literature review to situate your research within existing knowledge. The literature review gives you a chance to:

• Demonstrate your familiarity with the topic and its scholarly context
• Develop a theoretical framework and methodology for your research
• Position your work in relation to other researchers and theorists
• Show how your research addresses a gap or contributes to a debate
• Evaluate the current state of research and demonstrate your knowledge of the scholarly debates around your topic.

Writing literature reviews is a particularly important skill if you want to apply for graduate school or pursue a career in research. We’ve written a step-by-step guide that you can follow below.

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

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See an example

Writing literature reviews can be quite challenging! A good starting point could be to look at some examples, depending on what kind of literature review you’d like to write.

• Example literature review #1: “Why Do People Migrate? A Review of the Theoretical Literature” ( Theoretical literature review about the development of economic migration theory from the 1950s to today.)
• Example literature review #2: “Literature review as a research methodology: An overview and guidelines” ( Methodological literature review about interdisciplinary knowledge acquisition and production.)
• Example literature review #3: “The Use of Technology in English Language Learning: A Literature Review” ( Thematic literature review about the effects of technology on language acquisition.)
• Example literature review #4: “Learners’ Listening Comprehension Difficulties in English Language Learning: A Literature Review” ( Chronological literature review about how the concept of listening skills has changed over time.)

You can also check out our templates with literature review examples and sample outlines at the links below.

Download Word doc Download Google doc

Before you begin searching for literature, you need a clearly defined topic .

If you are writing the literature review section of a dissertation or research paper, you will search for literature related to your research problem and questions .

Make a list of keywords

Start by creating a list of keywords related to your research question. Include each of the key concepts or variables you’re interested in, and list any synonyms and related terms. You can add to this list as you discover new keywords in the process of your literature search.

• Social media, Facebook, Instagram, Twitter, Snapchat, TikTok
• Body image, self-perception, self-esteem, mental health
• Generation Z, teenagers, adolescents, youth

Search for relevant sources

Use your keywords to begin searching for sources. Some useful databases to search for journals and articles include:

• Your university’s library catalogue
• Google Scholar
• Project Muse (humanities and social sciences)
• Medline (life sciences and biomedicine)
• EconLit (economics)
• Inspec (physics, engineering and computer science)

You can also use boolean operators to help narrow down your search.

Make sure to read the abstract to find out whether an article is relevant to your question. When you find a useful book or article, you can check the bibliography to find other relevant sources.

You likely won’t be able to read absolutely everything that has been written on your topic, so it will be necessary to evaluate which sources are most relevant to your research question.

For each publication, ask yourself:

• What question or problem is the author addressing?
• What are the key concepts and how are they defined?
• What are the key theories, models, and methods?
• Does the research use established frameworks or take an innovative approach?
• What are the results and conclusions of the study?
• How does the publication relate to other literature in the field? Does it confirm, add to, or challenge established knowledge?
• What are the strengths and weaknesses of the research?

Make sure the sources you use are credible , and make sure you read any landmark studies and major theories in your field of research.

You can use our template to summarize and evaluate sources you’re thinking about using. Click on either button below to download.

Take notes and cite your sources

As you read, you should also begin the writing process. Take notes that you can later incorporate into the text of your literature review.

It is important to keep track of your sources with citations to avoid plagiarism . It can be helpful to make an annotated bibliography , where you compile full citation information and write a paragraph of summary and analysis for each source. This helps you remember what you read and saves time later in the process.

Prevent plagiarism. Run a free check.

To begin organizing your literature review’s argument and structure, be sure you understand the connections and relationships between the sources you’ve read. Based on your reading and notes, you can look for:

• Trends and patterns (in theory, method or results): do certain approaches become more or less popular over time?
• Themes: what questions or concepts recur across the literature?
• Debates, conflicts and contradictions: where do sources disagree?
• Pivotal publications: are there any influential theories or studies that changed the direction of the field?
• Gaps: what is missing from the literature? Are there weaknesses that need to be addressed?

This step will help you work out the structure of your literature review and (if applicable) show how your own research will contribute to existing knowledge.

• Most research has focused on young women.
• There is an increasing interest in the visual aspects of social media.
• But there is still a lack of robust research on highly visual platforms like Instagram and Snapchat—this is a gap that you could address in your own research.

There are various approaches to organizing the body of a literature review. Depending on the length of your literature review, you can combine several of these strategies (for example, your overall structure might be thematic, but each theme is discussed chronologically).

Chronological

The simplest approach is to trace the development of the topic over time. However, if you choose this strategy, be careful to avoid simply listing and summarizing sources in order.

Try to analyze patterns, turning points and key debates that have shaped the direction of the field. Give your interpretation of how and why certain developments occurred.

If you have found some recurring central themes, you can organize your literature review into subsections that address different aspects of the topic.

For example, if you are reviewing literature about inequalities in migrant health outcomes, key themes might include healthcare policy, language barriers, cultural attitudes, legal status, and economic access.

Methodological

If you draw your sources from different disciplines or fields that use a variety of research methods , you might want to compare the results and conclusions that emerge from different approaches. For example:

• Look at what results have emerged in qualitative versus quantitative research
• Discuss how the topic has been approached by empirical versus theoretical scholarship
• Divide the literature into sociological, historical, and cultural sources

Theoretical

A literature review is often the foundation for a theoretical framework . You can use it to discuss various theories, models, and definitions of key concepts.

You might argue for the relevance of a specific theoretical approach, or combine various theoretical concepts to create a framework for your research.

Like any other academic text , your literature review should have an introduction , a main body, and a conclusion . What you include in each depends on the objective of your literature review.

The introduction should clearly establish the focus and purpose of the literature review.

Depending on the length of your literature review, you might want to divide the body into subsections. You can use a subheading for each theme, time period, or methodological approach.

As you write, you can follow these tips:

• Summarize and synthesize: give an overview of the main points of each source and combine them into a coherent whole
• Analyze and interpret: don’t just paraphrase other researchers — add your own interpretations where possible, discussing the significance of findings in relation to the literature as a whole
• Critically evaluate: mention the strengths and weaknesses of your sources
• Write in well-structured paragraphs: use transition words and topic sentences to draw connections, comparisons and contrasts

In the conclusion, you should summarize the key findings you have taken from the literature and emphasize their significance.

When you’ve finished writing and revising your literature review, don’t forget to proofread thoroughly before submitting. Not a language expert? Check out Scribbr’s professional proofreading services !

This article has been adapted into lecture slides that you can use to teach your students about writing a literature review.

Scribbr slides are free to use, customize, and distribute for educational purposes.

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If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

A literature review is a survey of scholarly sources (such as books, journal articles, and theses) related to a specific topic or research question .

It is often written as part of a thesis, dissertation , or research paper , in order to situate your work in relation to existing knowledge.

There are several reasons to conduct a literature review at the beginning of a research project:

• To familiarize yourself with the current state of knowledge on your topic
• To ensure that you’re not just repeating what others have already done
• To identify gaps in knowledge and unresolved problems that your research can address
• To develop your theoretical framework and methodology
• To provide an overview of the key findings and debates on the topic

Writing the literature review shows your reader how your work relates to existing research and what new insights it will contribute.

The literature review usually comes near the beginning of your thesis or dissertation . After the introduction , it grounds your research in a scholarly field and leads directly to your theoretical framework or methodology .

A literature review is a survey of credible sources on a topic, often used in dissertations , theses, and research papers . Literature reviews give an overview of knowledge on a subject, helping you identify relevant theories and methods, as well as gaps in existing research. Literature reviews are set up similarly to other  academic texts , with an introduction , a main body, and a conclusion .

An  annotated bibliography is a list of  source references that has a short description (called an annotation ) for each of the sources. It is often assigned as part of the research process for a  paper .  

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The Principles of Biomedical Scientific Writing: Introduction

Zahra bahadoran.

1 Nutrition and Endocrine Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Sajad Jeddi

2 Endocrine Physiology Research Center, Research Institute for Endocrine Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran

Parvin Mirmiran

Asghar ghasemi.

A well-written introduction of a scientific paper provides relevant background knowledge to convince the readers about the rationale, importance, and novelty of the research. The introduction should inform the readers about the “problem”, “existing solutions”, and “main limitations or gaps of knowledge”. The authors’ hypothesis and methodological approach used to examine the research hypothesis should also be stated. After reading a good introduction, readers should be guided through “a general context” to “a specific area” and “a research question”. Incomplete, inaccurate, or outdated reviews of the literature are the more common pitfalls of an introduction that may lead to rejection. This review focuses on the principles of writing the introduction of an article and provides a quick look at the essential points that should be considered for writing an optimal introduction.

1. Introduction

Writing scientific papers is currently the most accepted outlet of research dissemination and scientific contribution. A scientific paper is structured by four main sections according to IMRAD (Introduction, Methods, Results, and Discussion) style ( 1 ).

To quote Plato, the Greek philosopher, “the beginning is half of the whole”, and the introduction is probably one of the most difficult sections in writing a paper ( 2 ). For writing introduction of a scientific paper, a “deductive approach” is generally used; deduction is the reasoning used to apply general theories and principles to reach specific consequences or hypotheses ( 3 ).

The initial impression of readers about writing style, the overall quality of research, validity of its findings, and the conclusion is strongly influenced by the introduction ( 4 ). A poor introduction misleads the readers about the content of the paper, possibly discouraging them from reading the subsequent sections; a well-written introduction, however, convinces the reader about the research logic ( 4 , 5 ). A good introduction is hence the main challenge faced by authors when drafting a research manuscript ( 2 ).

Historically, writing an introduction as an independent section of a research paper was underscored in the 1980s ( 6 ). Studies available on scientific writing provide evidence emphasizing the complexity of the compositional process of writing an introduction; these studies concluded that “introduction is not just wrestling with words to fit the facts, but it is also strongly modulated by perceptions of the anticipated reactions of peer-colleagues” ( 6 ).

Although there is no single correct way to organize different components of a research paper ( 7 ), scientific writing is an experimental science ( 7 ), and several guides have been developed to improve the quality of research disseminations ( 8 - 11 ). Typically, an introduction contains a summary of relevant literature and background knowledge, highlights the gap of knowledge, states the research question or hypothesis, and describes the methodological approach used to fill in the gap and respond to the question ( 12 - 14 ). Some believe that introduction can be a major context for debate about research methodology ( 6 ).

This review focuses on the principles of writing the introduction section and provides a quick look at the main points that must be considered for writing a good introduction.

2. Functions of the Introduction

The introduction of a scientific paper may be described as the gate to a city ( 5 ). It may also resemble a mental road map that should elucidate “the known”, “the unknown”, and “the new knowledge added by findings of the current study” ( 4 ); it presents the background knowledge to convince the readers of the importance of data added to that available in the field ( 15 ); in addition, the introduction sets the scene for readers ( 16 ) and paves the way for what is to follow ( 17 ). The introduction should be tailored to the journal to which the manuscript is being submitted ( 18 ). It has two functions, to be informative enough for understanding the paper and to evoke the reader’s interest ( 19 , 20 ). An introduction should serve as a hook, informing the readers of the question they should expect the paper to address ( 7 ). “A good introduction will sell the study to editors, reviewers, and readers” ( 18 , 21 ).

3. Common Models of Writing an Introduction

A historical overview of scientific writing shows that several models have been proposed overtime on how to organize the introduction of a research paper. One of the most common approaches is the “problem-solving model” developed in 1979; according to this model, a series of subcontexts including “goal”, “current capacity”, “problem”, “solution”, and “criteria for evaluation” have been described ( 6 ). The structure of this model could vary across disciplines ( 22 , 23 ).

Another popular model proposed is “creating a research space”, which mainly focuses on “the dark side” of the issue; this model, is usually known as CARS (create-a-research-space) model and follows three moves including establishing a territory (the situation), establishing a niche (the problem), and occupying a niche (the solution) ( 24 , 25 ). This model can be modified to a four-move model by expanding move 3 to include a “concluding step” when it is required to explain the structure of remaining parts of the paper ( 6 , 25 ).

4. A Typical Model of Introduction

In this paper, we focused on a typical model of introduction commonly used in biomedical papers. As shown in Figure 1 , the form of introduction is a funnel or an inverted pyramid, from large to small or broad to narrow ( 7 , 16 , 19 , 26 ). The largest part of the funnel at the top describes the general context/topic and the importance of the study; the funnel then narrows down to the gap of knowledge, and ends with the authors’ hypothesis or aim of the study and the methodological approach used to examine the research hypothesis ( 18 , 26 ). In fact, introduction presents research ideas flowing from general to specific ( 27 ). As given below, in hypothesis-testing papers, the introduction usually consists of 2 - 3 ( 28 ) and sometimes 4 paragraphs ( 16 ), including the known, the unknown (knowledge gap), hypothesis/question or specific topic, and sometimes the approach ( 16 , 19 ). Some authors end the introduction with essential findings of the paper ( 29 ). It has, however, been argued that the introduction should not include results or conclusion from the work being reported ( 2 , 16 , 20 ), as readers would then lose their interest in reading the rest of the manuscript ( 2 ). The introduction may also be expanded by including some uncommon parts like “future implications of the work” ( 30 ).

4.1. The Known

In this section, a brief summary of background information is provided to present the general topic of the paper ( 20 ). This section should arouse and build the audience’s attention and interest in the hypothesis/question or specific topic ( 29 ). This part may be considered the same as move 1 of the CARS model and includes “claiming importance”, “making topic generalizations”, and “reviewing items of previous research” ( 22 , 24 ).

Besides the different roles proposed for citation, its primary motive is believed to be “perceived relevance” ( 31 ). It is important that the review of literature be complete, fair, balanced ( 29 ), to the point ( 19 ), and directly related to the study ( 16 ); it should not be too long or contain a very detailed review of literature ( 7 , 28 ) or a complete history of the field ( 9 ). Depending on the audience ( 16 ), authors should include background information that they think readers need for following the rest of the paper ( 16 ).

Contrary to the current view that the introduction should be short and act as a prelude to the manuscript itself, another opinion, however, suggests this section provides a complete introduction to the subject ( 32 ). Sweeping generalizations (i.e., applying a general rule to a specific situation) should be avoided in the first (the opening) sentence of the introduction ( 8 ). The first three sentences of the first paragraph should present the issue that will be addressed by the paper ( 8 ). If the general topic be presented in the very first word of a very short sentence, the reader is able to immediately focus on and understand the issue ( 30 ).

4.2. The Unknown/Gap of Knowledge

The importance and novelty of the work should be stated in the introduction ( 19 ). This section describes the gaps in our present understanding of the field and why it is necessary that these gaps in data be filled ( 29 ). In this section, the author should present limitations of prior studies, needed (but currently unavailable) information, or an unsolved problem and highlight the importance of the missing pieces of the puzzle ( 16 ). This section provides information to justify the aim of the study, that is, it provides rationale for the readers to convince them ( 8 , 20 ); however, one-sided or biased views of controversial issues should be avoided ( 33 ).

The unknown section of the introduction is similar to “establishing a niche” and includes “counter-claiming” and “indicating a gap” ( 6 , 25 ). To develop a “counter-claiming” statement, the author needs to mention an opposing viewpoint or perspective or highlight a gap or limitation in current literature ( 24 ). “Counter-claiming” sentences are usually distinguished by a specific terminology, including albeit, although, but, howbeit, however, nevertheless, notwithstanding, unfortunately, whereas, and yet ( 24 ). This step toward or “continuing a tradition” part ( 6 , 25 ) is an extension of prior research to expand upon or clarify a research problem ( 24 ), and the connection is commonly initiated with the following terms: “hence,” “therefore,” “consequently,” or “thus” ( 24 ). An alternative approach for “counter-claiming” within the context of prior research is giving a “new perspective” without challenging the validity of previous research or highlighting their limitations ( 24 ).

Pitfalls in this section include missing an important paper and overstating the novelty of the study ( 29 ).

4.3. Rationale of Research/Hypothesis/Question

Defining the rationale of research is the most critical mission of the introduction section, where the author should tell the reader why the research is biologically meaningful ( 34 ). In stating the rationale of the study, an author should clarify that the study is the next logical step in a line of investigations, addressing the limitations of previous works ( 8 ). This section corresponds to “occupying the niche” in the CARS model ( 6 ), where contribution of the research in the development of “novel” knowledge is stated in contrast to prior research on the topic ( 24 ). The question/hypothesis, something that is not yet proven ( 35 ), is placed at the tip of the inverted cone/pyramid ( 16 ), and it is usually last sentence of the last paragraph in the introduction that presents the specific topic, which is “ What was done in your paper ?” ( 7 , 8 , 19 ).

The main and secondary objectives should be clear and preferably comprise no more than two sentences ( 20 ). The question should be clearly stated as the most common reason for rejection of a manuscript is the inability to do this ( 8 ); it would be a bad start that reviewers/readers cannot grasp the research question of the paper ( 36 ).

5. Writing Tips

5.1. the length.

The introduction should be generally short ( 7 , 37 ) and not exceed one double-spaced typed page ( 37 ), approximately 250 - 300 words are typically sufficient and sometimes it may be longer (500 - 600 words) ( 19 , 38 ); however, depending on the audience and type of paper, the length of the introduction could vary ( 20 ); if it is more than two-thirds the length of the results section, it is probably too long ( 9 ). It has been recommended that the introduction should be no more than 10% to 15% of total manuscript excluding abstract and references ( 18 , 26 ). A long introduction may be used to compensate for the limited data given about the actual research, a pitfall that peer-reviewers are aware of ( 30 ).

5.2. Sentence and Paragraph

In a scientific paper, each paragraph should contain a single main idea ( 7 , 39 ) that stands alone and is very clear ( 7 ). The first sentence of a paragraph should tell the reader what to expect to get out of the paragraph ( 7 ). Flow is a critical element in paragraph structure, that is to say, every sentence should arise logically from the sentence before it and transition logically into the next sentence ( 7 ). It is suggested that length of a sentence in a scientific text should not exceed 25 - 30 words; maximum three to four 30-word sentences are allowed in a paper ( 40 ). The ideal size for a paragraph is 3 - 4 sentences (maximum five sentences) ( 39 ) or 75 - 150 words (ideally not exceeding 150 words) ( 30 ). The maximum length of a paragraph in a well-written paper should not exceed 15 lines ( 30 ).

To test readability of a paragraph or passage, the Gunning Fog scoring formula may be helpful. This index helps the author to write clearly and simply. Fog score is typically between 0 and 20 and estimates the years of formal education the reader requires to understand the text on the first reading (5, is very easy; 6 is easy to read; 14 is difficult; 16 is very difficult) ( 41 , 42 ). Fog score is calculated as follow:

Where a complex word is defined as a word containing three or more syllables ( 43 ). An online tool that calculates the Gunning Fog Index is available at http://gunning-fog-index.com/index.html.

Using the correct verb tense in scientific writing enables authors to manage time and establish a logical relation or “time framework” within different parts of a paper ( 44 ). Two tenses are mostly used in scientific writing, namely the present and the past ( 18 , 45 ); “present tense” is used for established general knowledge (general truths) and “past tense” for the results that you are currently reporting ( 11 , 39 , 45 ). Some authors believe that “present tense” better describes most observations in a scientific paper ( 5 , 7 ). To manage the time framework of the introduction, a transitional verb tense from “present simple” at the beginning (to describe general background) to “present perfect” (describing the problem over time), and again “present simple” at the end of introduction (to state the hypothesis and approach) is commonly recommended ( 30 ).

Although a review of the literature may recommend several tenses, using “present simple” or “present perfect” is more common ( 46 ); the use of “present tense” to refer to the existing research indicates that the authors believe the findings of an older research are still true and relevant ( 44 ). The “present perfect tense” may be adopted when authors communicate “currency” (being current), in both positive (asserting that previous studies have established a firm research foundation) and negative (asserting that not enough relevant or valid work has yet been done) forms ( 44 ).

As seen in Table 1 , much of the introduction emphasizes on previously established knowledge, hence using the present tense ( 11 , 37 ). If you give the author’s name non-parenthetically, present or past tense could be used for the verb that is linked to the author; however, scientific work itself is given in the present tense; for instance, Smith (1975) showed that streptomycin inhibits growth of the organism ( 11 ).

5.4. Citation

Reference section is a vital component of papers ( 51 ). Peer-reviewed articles are preferred by scientific journals ( 51 ). Be cautious never to cite a reference that you have not read ( 51 ) and be sure to cite the source of the original document ( 18 ). The number of references in the introduction should be kept to a minimum ( 19 ) according to the International Committee of Medical Journal Editors (http://icmje.org). Only directly pertinent references should be selected, but do not miss important previous works ( 9 , 20 ). A common error in the writing of an introduction is the struggle to review all evidence available on the topic, which confuses the readers and often buries the aim of the study in additional information ( 26 , 52 ). If there are many references, select the first, the most important, the most elegant, the most pertinent, and the most recent ones ( 18 , 19 ). References should be selected from updated papers with higher impact factors ( 5 ). In addition, select original rather than review articles ( 2 , 53 ), as this is what most editors/reviewers expect ( 18 ). In the presence of newer references, older ones are usually used if considered as being an influential work ( 16 ).

Unnecessary overlap of introduction and discussion is a problem for both sections, therefore, it has been strongly recommended to cite the references where it makes most sense ( 16 ). No reference needs to be made for accepted facts such as double-helical structure of DNA ( 9 ). There is usually no need to list standard text books as references and if this has been done, specify the place in the book ( 32 ). Some authors believe that referring to papers using author names should be avoided, as it slows the pace of writing ( 8 ).

6. Common Pitfalls in Writing Introduction

The most common pitfalls that occur during writing the introduction include: ( 1 ) Providing too much general information, ( 2 ) going into details of previous studies, ( 3 ) containing too many citations, ( 4 ) criticizing recent studies extensively, ( 5 ) presenting the conclusion of the study, except for studies where the format requires this, ( 6 ) having inconsistency with other sections of the manuscript, ( 7 ) including overlapping information with the discussion section, and ( 8 ) not reporting most relevant papers ( 2 ). In Table 2 , most do’s and don’ts for writing a good introduction are summarized; examples of the principles for writing an introduction for a scientific paper can be found in the literature ( 16 , 19 ).

7. Conclusion

The introduction of scientific original papers should be short but informative. Briefly, the first part of a well-written introduction is expected to contain the most important concisely cited references, focused on the research problem. In the second part, the problem and existing solutions or current limitations should be elaborated, and the last paragraph should describe the rationale for the research and the main research purpose. The introduction is suggested be concluded with a brief paragraph that describes the organization of the rest of the paper. Overall, a good introduction should convince the readers that the study is important in the context of what is already known.

Acknowledgments

The authors wish to acknowledge Ms Niloofar Shiva for critical editing of English grammar and syntax of the manuscript.

Introductions

What this handout is about.

This handout will explain the functions of introductions, offer strategies for creating effective introductions, and provide some examples of less effective introductions to avoid.

The role of introductions

Introductions and conclusions can be the most difficult parts of papers to write. Usually when you sit down to respond to an assignment, you have at least some sense of what you want to say in the body of your paper. You might have chosen a few examples you want to use or have an idea that will help you answer the main question of your assignment; these sections, therefore, may not be as hard to write. And it’s fine to write them first! But in your final draft, these middle parts of the paper can’t just come out of thin air; they need to be introduced and concluded in a way that makes sense to your reader.

Your introduction and conclusion act as bridges that transport your readers from their own lives into the “place” of your analysis. If your readers pick up your paper about education in the autobiography of Frederick Douglass, for example, they need a transition to help them leave behind the world of Chapel Hill, television, e-mail, and The Daily Tar Heel and to help them temporarily enter the world of nineteenth-century American slavery. By providing an introduction that helps your readers make a transition between their own world and the issues you will be writing about, you give your readers the tools they need to get into your topic and care about what you are saying. Similarly, once you’ve hooked your readers with the introduction and offered evidence to prove your thesis, your conclusion can provide a bridge to help your readers make the transition back to their daily lives. (See our handout on conclusions .)

Note that what constitutes a good introduction may vary widely based on the kind of paper you are writing and the academic discipline in which you are writing it. If you are uncertain what kind of introduction is expected, ask your instructor.

Why bother writing a good introduction?

You never get a second chance to make a first impression. The opening paragraph of your paper will provide your readers with their initial impressions of your argument, your writing style, and the overall quality of your work. A vague, disorganized, error-filled, off-the-wall, or boring introduction will probably create a negative impression. On the other hand, a concise, engaging, and well-written introduction will start your readers off thinking highly of you, your analytical skills, your writing, and your paper.

Your introduction is an important road map for the rest of your paper. Your introduction conveys a lot of information to your readers. You can let them know what your topic is, why it is important, and how you plan to proceed with your discussion. In many academic disciplines, your introduction should contain a thesis that will assert your main argument. Your introduction should also give the reader a sense of the kinds of information you will use to make that argument and the general organization of the paragraphs and pages that will follow. After reading your introduction, your readers should not have any major surprises in store when they read the main body of your paper.

Ideally, your introduction will make your readers want to read your paper. The introduction should capture your readers’ interest, making them want to read the rest of your paper. Opening with a compelling story, an interesting question, or a vivid example can get your readers to see why your topic matters and serve as an invitation for them to join you for an engaging intellectual conversation (remember, though, that these strategies may not be suitable for all papers and disciplines).

Strategies for writing an effective introduction

Start by thinking about the question (or questions) you are trying to answer. Your entire essay will be a response to this question, and your introduction is the first step toward that end. Your direct answer to the assigned question will be your thesis, and your thesis will likely be included in your introduction, so it is a good idea to use the question as a jumping off point. Imagine that you are assigned the following question:

Drawing on the Narrative of the Life of Frederick Douglass , discuss the relationship between education and slavery in 19th-century America. Consider the following: How did white control of education reinforce slavery? How did Douglass and other enslaved African Americans view education while they endured slavery? And what role did education play in the acquisition of freedom? Most importantly, consider the degree to which education was or was not a major force for social change with regard to slavery.

You will probably refer back to your assignment extensively as you prepare your complete essay, and the prompt itself can also give you some clues about how to approach the introduction. Notice that it starts with a broad statement and then narrows to focus on specific questions from the book. One strategy might be to use a similar model in your own introduction—start off with a big picture sentence or two and then focus in on the details of your argument about Douglass. Of course, a different approach could also be very successful, but looking at the way the professor set up the question can sometimes give you some ideas for how you might answer it. (See our handout on understanding assignments for additional information on the hidden clues in assignments.)

Decide how general or broad your opening should be. Keep in mind that even a “big picture” opening needs to be clearly related to your topic; an opening sentence that said “Human beings, more than any other creatures on earth, are capable of learning” would be too broad for our sample assignment about slavery and education. If you have ever used Google Maps or similar programs, that experience can provide a helpful way of thinking about how broad your opening should be. Imagine that you’re researching Chapel Hill. If what you want to find out is whether Chapel Hill is at roughly the same latitude as Rome, it might make sense to hit that little “minus” sign on the online map until it has zoomed all the way out and you can see the whole globe. If you’re trying to figure out how to get from Chapel Hill to Wrightsville Beach, it might make more sense to zoom in to the level where you can see most of North Carolina (but not the rest of the world, or even the rest of the United States). And if you are looking for the intersection of Ridge Road and Manning Drive so that you can find the Writing Center’s main office, you may need to zoom all the way in. The question you are asking determines how “broad” your view should be. In the sample assignment above, the questions are probably at the “state” or “city” level of generality. When writing, you need to place your ideas in context—but that context doesn’t generally have to be as big as the whole galaxy!

Try writing your introduction last. You may think that you have to write your introduction first, but that isn’t necessarily true, and it isn’t always the most effective way to craft a good introduction. You may find that you don’t know precisely what you are going to argue at the beginning of the writing process. It is perfectly fine to start out thinking that you want to argue a particular point but wind up arguing something slightly or even dramatically different by the time you’ve written most of the paper. The writing process can be an important way to organize your ideas, think through complicated issues, refine your thoughts, and develop a sophisticated argument. However, an introduction written at the beginning of that discovery process will not necessarily reflect what you wind up with at the end. You will need to revise your paper to make sure that the introduction, all of the evidence, and the conclusion reflect the argument you intend. Sometimes it’s easiest to just write up all of your evidence first and then write the introduction last—that way you can be sure that the introduction will match the body of the paper.

Don’t be afraid to write a tentative introduction first and then change it later. Some people find that they need to write some kind of introduction in order to get the writing process started. That’s fine, but if you are one of those people, be sure to return to your initial introduction later and rewrite if necessary.

Open with something that will draw readers in. Consider these options (remembering that they may not be suitable for all kinds of papers):

• an intriguing example —for example, Douglass writes about a mistress who initially teaches him but then ceases her instruction as she learns more about slavery.
• a provocative quotation that is closely related to your argument —for example, Douglass writes that “education and slavery were incompatible with each other.” (Quotes from famous people, inspirational quotes, etc. may not work well for an academic paper; in this example, the quote is from the author himself.)
• a puzzling scenario —for example, Frederick Douglass says of slaves that “[N]othing has been left undone to cripple their intellects, darken their minds, debase their moral nature, obliterate all traces of their relationship to mankind; and yet how wonderfully they have sustained the mighty load of a most frightful bondage, under which they have been groaning for centuries!” Douglass clearly asserts that slave owners went to great lengths to destroy the mental capacities of slaves, yet his own life story proves that these efforts could be unsuccessful.
• a vivid and perhaps unexpected anecdote —for example, “Learning about slavery in the American history course at Frederick Douglass High School, students studied the work slaves did, the impact of slavery on their families, and the rules that governed their lives. We didn’t discuss education, however, until one student, Mary, raised her hand and asked, ‘But when did they go to school?’ That modern high school students could not conceive of an American childhood devoid of formal education speaks volumes about the centrality of education to American youth today and also suggests the significance of the deprivation of education in past generations.”
• a thought-provoking question —for example, given all of the freedoms that were denied enslaved individuals in the American South, why does Frederick Douglass focus his attentions so squarely on education and literacy?

Pay special attention to your first sentence. Start off on the right foot with your readers by making sure that the first sentence actually says something useful and that it does so in an interesting and polished way.

How to evaluate your introduction draft

Ask a friend to read your introduction and then tell you what they expect the paper will discuss, what kinds of evidence the paper will use, and what the tone of the paper will be. If your friend is able to predict the rest of your paper accurately, you probably have a good introduction.

Five kinds of less effective introductions

1. The placeholder introduction. When you don’t have much to say on a given topic, it is easy to create this kind of introduction. Essentially, this kind of weaker introduction contains several sentences that are vague and don’t really say much. They exist just to take up the “introduction space” in your paper. If you had something more effective to say, you would probably say it, but in the meantime this paragraph is just a place holder.

Example: Slavery was one of the greatest tragedies in American history. There were many different aspects of slavery. Each created different kinds of problems for enslaved people.

2. The restated question introduction. Restating the question can sometimes be an effective strategy, but it can be easy to stop at JUST restating the question instead of offering a more specific, interesting introduction to your paper. The professor or teaching assistant wrote your question and will be reading many essays in response to it—they do not need to read a whole paragraph that simply restates the question.

Example: The Narrative of the Life of Frederick Douglass discusses the relationship between education and slavery in 19th century America, showing how white control of education reinforced slavery and how Douglass and other enslaved African Americans viewed education while they endured. Moreover, the book discusses the role that education played in the acquisition of freedom. Education was a major force for social change with regard to slavery.

3. The Webster’s Dictionary introduction. This introduction begins by giving the dictionary definition of one or more of the words in the assigned question. Anyone can look a word up in the dictionary and copy down what Webster says. If you want to open with a discussion of an important term, it may be far more interesting for you (and your reader) if you develop your own definition of the term in the specific context of your class and assignment. You may also be able to use a definition from one of the sources you’ve been reading for class. Also recognize that the dictionary is also not a particularly authoritative work—it doesn’t take into account the context of your course and doesn’t offer particularly detailed information. If you feel that you must seek out an authority, try to find one that is very relevant and specific. Perhaps a quotation from a source reading might prove better? Dictionary introductions are also ineffective simply because they are so overused. Instructors may see a great many papers that begin in this way, greatly decreasing the dramatic impact that any one of those papers will have.

Example: Webster’s dictionary defines slavery as “the state of being a slave,” as “the practice of owning slaves,” and as “a condition of hard work and subjection.”

4. The “dawn of man” introduction. This kind of introduction generally makes broad, sweeping statements about the relevance of this topic since the beginning of time, throughout the world, etc. It is usually very general (similar to the placeholder introduction) and fails to connect to the thesis. It may employ cliches—the phrases “the dawn of man” and “throughout human history” are examples, and it’s hard to imagine a time when starting with one of these would work. Instructors often find them extremely annoying.

Example: Since the dawn of man, slavery has been a problem in human history.

5. The book report introduction. This introduction is what you had to do for your elementary school book reports. It gives the name and author of the book you are writing about, tells what the book is about, and offers other basic facts about the book. You might resort to this sort of introduction when you are trying to fill space because it’s a familiar, comfortable format. It is ineffective because it offers details that your reader probably already knows and that are irrelevant to the thesis.

Example: Frederick Douglass wrote his autobiography, Narrative of the Life of Frederick Douglass, An American Slave , in the 1840s. It was published in 1986 by Penguin Books. In it, he tells the story of his life.

And now for the conclusion…

Writing an effective introduction can be tough. Try playing around with several different options and choose the one that ends up sounding best to you!

Just as your introduction helps readers make the transition to your topic, your conclusion needs to help them return to their daily lives–but with a lasting sense of how what they have just read is useful or meaningful. Check out our handout on  conclusions for tips on ending your paper as effectively as you began it!

Works consulted

We consulted these works while writing this handout. This is not a comprehensive list of resources on the handout’s topic, and we encourage you to do your own research to find additional publications. Please do not use this list as a model for the format of your own reference list, as it may not match the citation style you are using. For guidance on formatting citations, please see the UNC Libraries citation tutorial . We revise these tips periodically and welcome feedback.

Douglass, Frederick. 1995. Narrative of the Life of Frederick Douglass, an American Slave, Written by Himself . New York: Dover.

You may reproduce it for non-commercial use if you use the entire handout and attribute the source: The Writing Center, University of North Carolina at Chapel Hill

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The Mathematician Who Finds the Poetry in Math and the Math in Poetry

January 12, 2024

Philipp Ammon for Quanta Magazine

Introduction

Sarah Hart has always had an eye for the covert ways mathematics permeates other fields. As a child, she was struck by the ubiquity of the number 3 in her fairy tales. Hart’s mother, a math teacher, encouraged her pattern-seeking, giving her math puzzles to pass the time.

Hart went on to earn a doctorate in group theory in 2000 and later became a professor at Birkbeck, University of London. Hart’s research probed the structure of Coxeter groups, more general versions of structures that catalog the symmetries of polygons and prisms. In 2023, she published Once Upon a Prime , a book about the ways math appears in fiction and poetry. “Since we humans are part of the universe, it is only natural that our forms of creative expression, literature among them, will also manifest an inclination for pattern and structure,” Hart wrote. “Mathematics, then, is the key to an entirely different perspective on literature.”

Since 2020, Hart has been the professor of geometry at Gresham College in London. Gresham has no traditional courses; instead, its professors each deliver several public lectures per year. Hart is the first woman to ever hold the 428-year-old position, which was occupied in the 17th century by Isaac Barrow, famous for teaching another Isaac (Newton). More recently, it was held by Roger Penrose, a mathematician who won the 2020 Nobel Prize in Physics. Hart spoke with Quanta about how mathematics and art influence one another. The interview has been condensed and edited for clarity.

Why did you choose to write your book about the links between math and literature?

These links are less explored and less known than those between math and, say, music. The connections between mathematics and music have been celebrated since at least as far back as the Pythagoreans. However, though there has been writing and academic research about specific books, authors or genres, I hadn’t seen a book for a general audience about the broader connections between mathematics and literature.

Video : Sarah Hart, the professor of geometry at Gresham College, sees symmetry everywhere.

Video: Christopher Webb Young and Emily Buder/ Quanta Magazine ; Photo: Philipp Ammon for Quanta Magazine

How should people in the arts think about math?

There’s a lot of common ground between mathematics and, shall I say, the other arts. In literature, as well as music and art, you don’t ever start with nothing at all. If you’re a poet, you are choosing: Will I have a haiku with its very precise numerical constraints, or will I write a sonnet which has a certain number of lines, a certain rhyme scheme, a certain meter? Even something that doesn’t have a rhyme scheme will have line breaks, a rhythm. There will be constraints that inspire creativity, that help to focus you.

In mathematics, we have the same thing. We have some ground rules. Within that, we can explore, we can play, and we can prove theorems. What mathematics can do for the arts is help find new structures, show what the possibilities are. What would a piece of music look like that doesn’t have a key signature? We can think about the 12 tones and arranging them differently, and here are all the ways you can do that. Here are different color schemes you can devise, here are different forms of poetic meter.

What’s one example of how math has been affected by literature?

Thousands of years ago in India, poets were trying to think about the possible meters. In Sanskrit poetry, you have long and short syllables. Long is twice as long as short. If you want to work out how many there are that take a length of time of three, you can have short, short, short, or long, short, or short, long. There are three ways to make three. There are five ways to make a length-four phrase. And there are eight ways to make a length-five phrase. This sequence you’re getting is one where every term is the sum of the previous two. You exactly reproduce what we nowadays call the Fibonacci sequence. But this was centuries before Fibonacci.

Hart is interested in the mathematical language found on this Babylonian cuneiform tablet, one of the earliest records of humans doing math.

How about math’s influence on literature?

A quite simple sequence, but it works very, very powerfully, is Eleanor Catton’s book The Luminaries , which came out in 2013. She used the sequence that goes 1,1/2, 1/4, 1/8, 1/16. Every chapter in that book is half the length of the one before. It creates this really fascinating effect, because the pace is picking up, and the characters’ choices are being more constrained. Everything hurtles toward its conclusion. By the end, the chapters are extremely short.

Another example of a slightly more complicated mathematical structure is what’s called orthogonal Latin squares. A Latin square is kind of like a sudoku grid. In this case, it’d be a 10-by-10 grid. Every number appears exactly once in each row and in each column. Orthogonal Latin squares are formed by overlaying two Latin squares so there is a pair of numbers in each space. The grid formed by the first number in each pair is a Latin square, and so is the grid formed by the second number in each pair. Furthermore, in the grid of pairs, no pair appears more than once.

These are very useful in all sorts of ways. You can make error-correcting codes out of them, which are useful for sending messages along kind of noisy channels. But one of the great things about these particular ones, size 10, is that one of the greatest mathematicians of all time, Leonhard Euler, thought they couldn’t exist. It was one of the very few times when he made a mistake; that’s why it was so exciting. A long time after he made this conjecture that these things couldn’t exist for particular sizes, it was refuted, and squares of this size were found in 1959. It was on the cover of Scientific American that year.

Hart has been making mathematical patterns since she was a young child.

Years after that, a French writer, Georges Perec, was looking for a structure to use for his book Life: A User’s Manual . He chose one of these orthogonal Latin squares. He set his book in a Paris apartment block, which had 100 rooms, a 10-by-10 square. Every chapter was in a different room, and every chapter had its unique flavor. He had lists of 10 things — various fabrics, colors, that kind of thing. Every chapter would use a unique combination. It’s a really fascinating way to structure the book.

You clearly value good writing. What do you think of the quality of writing in math research papers?

It’s very variable! I know we prize brevity, but I think sometimes that is taken too far. There are too many papers that don’t have any useful examples.

What we actually prize is an ingenious argument that, because it covers all the cases at once so cleverly, is also brief and elegant. That is not the same as squashing your long argument into a smaller space than it needs by covering the page with arcane sigils that you’ve created to make the notation briefer, but which not only the reader but probably you yourself will have to unpack laboriously again in order to make any sense of what’s going on.

We don’t give enough thought to helpful notation which reminds the reader what is meant. The right notation can absolutely transform a piece of mathematics, and can make space for generalizations as well. Think of the transition, historically, from writing an unknown, its square and its cube with three different letters, and how much more likely, and even possible, it is to start thinking about  when you have started writing ,  and  instead.

Hart works from her home office, which sits in her back garden.

Do you see evolution in the links between math and art?

There are new things all the time. Fractals were everywhere in the 1990s. On every student dorm room wall, there was a picture of the Mandelbrot set or something like this. Everyone was like, “Oh, this is exciting, fractals.” You get, for example, musicians, composers, who are using fractal sequences in their compositions.

When I was about 16, there were these new things called graphics calculators. Very exciting. And a friend of my mother’s gave me this program that could draw a Mandelbrot set on one of these little graphics calculators. It had about, I don’t know, 200 pixels. You program this thing in, and then I had to leave it for 12 hours. It would plot these 200 points at the end of it. So even mere schoolchildren could engage with this in the late ’80s and early ’90s, and produce these pictures for themselves.

Even when you were in school, you were already very interested in hardcore math, it sounds like.

  I think I’ve been interested since before I even knew that meant I was mathematical. Like, I just always was making patterns from when I was a tiny, weeny child.

When I was quite little, my favorite toy was some very simple wooden painted tiles. They came in all different colors. I would make them into patterns, and then I’d look at it proudly for a day or so, and then I’d make another one.

Hart with her bird, Coco, at her home in northeast London.

When I got a bit older, I would play with numbers and look at patterns. Mum would be the one I would go to and say, “I’m bored.” And then she’d say, “Well, can you work out what the pattern is of the number of points you need to make a triangle?” or whatever it was. She’d have me rediscover the triangular numbers or something, and I’d be very excited.

My poor mother, the number of amazing inventions that I would go to my mother with. “I’ve developed a whole new way of doing something!” And she’d say, “OK, that’s very nice. But, you know, Descartes thought of that centuries ago.” And then off I’d go; I’d come up with another amazing idea a few days later. “That’s lovely, dear. But the ancient Greeks had that one.”

Do you recall any particularly satisfying moments from your math research career?

The moments when you finally understand what the pattern is that you are seeing is always satisfying, as well as when you work out how to complete a proof you’ve been wrestling with. My strongest memories of those feelings of delight, probably because they were the first times I’d felt them, are from the start of my research career. But it’s still a lovely feeling to get that “aha,” when you finally understand what’s going on.

Very early on I was trying to prove something about infinite Coxeter groups. I’d resolved some of the cases, and in looking at the rest I came up with a technique that would work if a specific criterion was satisfied. You can write these relationships in a graph, so I started putting together a collection of the graphs for which my technique could be applied. This was over Christmas one year.

“Doing mathematics feels like discovery,” Hart said. “If we were inventing the mathematics, it surely wouldn’t be so hard to prove things! Sometimes we desperately want something to be true, and it isn’t.”

After a while, my set of pictures started to look like a particular set of graphs that were listed in a book about Coxeter groups that was in my office, and I began to hope that it was this exact set of graphs. If it was, then that would fill in the hole in my proof, and my theorem would be finished. But I couldn’t check for sure until I got back into the university after Christmas — this was before you could just Google everything. I think the anticipation of having to wait to confirm my hunch made it even better when I got to the book and compared my handwritten set of diagrams with the ones in the book, and they were indeed a match.

What do you think about the question of whether math is created or discovered? Almost nobody would argue that any of the novelists you write about in your book “discovered” their novels. Is this a fundamental difference between math and literature or not?

It probably is, though there are still some resonances.

Doing mathematics feels like discovery. If we were inventing the mathematics, it surely wouldn’t be so hard to prove things! Sometimes we desperately want something to be true, and it isn’t. We can’t avoid the consequences of logic, I suppose.

It all feels like discovery when you are doing it. Some choices mirror what we experience in the real world, like the axioms of geometry we work with, which are chosen because that seems to be roughly what reality is like — though even there, there’s no such thing as a “point” or a “line” (because we can’t draw something that takes up no space, and a line in geometry has no breadth and extends infinitely far).

To some extent, there are parallels to this continuum in literature. Once you define the rules of a sonnet, you will be hard-pressed to write one whose first line ends with “orange” or “chimney.”

But I can’t resist sharing something J.R.R. Tolkien said about writing The Hobbit : “It all began when I was reading exam papers to earn a bit of extra money. … Well, one day I came to a blank page in an exam book and I scribbled on it. ‘In a hole in the ground there lived a hobbit.’ I knew no more about the creatures than that, and it was years before his story grew. I don’t know where the word came from.”

Hobbits — did he create them or discover them?

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