How to Successfully Write a Mathematics Research Paper | 5 Easy Steps

Good mathematical writing is like good mathematical thinking. It is an expertise that should be developed for perfect performance. This article aims to help young mathematicians write their first mathematics research paper.

The goal is not only to assist in developing research papers but also to support students to think about mathematical writing. That is why in this article we will tell you 5 easy tips to successfully write a mathematics research paper.

These tips are the following:

  • Formatting and structure
  • Conventions of mathematics
  • Good writing and logical construction
  • Use Grammarly and paraphrasing tool to reduce writing errors
  • Specific recommendations

Mathematical research papers are quite different from standard research papers, however, their guidelines are not so separate.These papers rely on logic and particular language including different symbols.

Formatting and structure

  • To communicate well, you need to consider both what you want to convey, and to whom you want to convey your work.
  • The main purpose of a mathematical research paper is to emphasize the truth of a mathematical statement, using only carefully prepared logical deductions.
  • Cautious readers do not believe that your work is well established; they must agree after reading your work.

There are two main structures of mathematical research papers:

Formal exposition

  • The definitions, logic, and theorem-proof format fall under formal exposition.
  • The writer should start with an outline that evolves the logical structure of the research paper.
  • It is necessary that each deduction and hypothesis flow in an order using formal notation.
  • Do not repeat proof or phrases that are different from the definitions already established in the paper.

Informal exposition

  • Informal exposition involves reasoning behind the proofs and theorems.
  • Equations, proofs, and figures do not speak for themselves, writers will have to show why their deductions and hypothesis are valid.
  • Examples and analogies belong to this type of style.

Conventions of mathematics

  • To write an efficient mathematics research paper, clarity is very important.
  • It means sticking to the rules of definitions, logic, theorems that are physically separate from the surrounding text, and using math notation and symbols following the protocol of mathematical language.


Logic is the context upon which every right mathematics research paper is constructed.

Theorems and equations

  • They must be physically separated from the surrounding text and they are used as reference points.
  • That is why they should have a proper beginning and end.

Clear definitions

  • To understand the writer’s work, definitions for notations and terms must fit at the beginning of the research paper.
  • It is suitable to add them in the portion of the introduction rather than adding them in a separate section.

Math symbols and notations

  • These aspects are standardized within the math literature and deviation from these principles will generate confusion for the reader.
  • That is why the writer must stick to guidelines for units, equations, and notations.

Good writing and logical construction

Regardless of the preparation method selected, the publication of this document is similar to any other academic research paper in which good writing is required.

The writer is responsible for applying a logical construct in this regard.

Here are some important aspects to consider:

  • Concept of the paper
  • Acknowledgment
  • List of authors
  • Title
  • Abstract
  • Introduction
  • Body of the essay
  • Conclusion
  • References
  • Appendix
  • Publication of the paper
  • Preprint archive
  • Choice of submission

The crucial aspects of a math research paper are logical constructs and fine writing that enable the reader to follow an obvious path to the author’s conclusions.

Use Grammarly and online calculators to solve math problems

For good writing, it is also essential to take care of the grammar and spelling mistakes.

These mistakes affect your mathematics research paper very badly.

That is why it is your responsibility to check and remove them immediately with the help of well-known Grammarly or any other grammar checker that is suitable for you.

Besides grammatical errors, it is also vital to find the duplication in your content and remove it to increase the authenticity in your work.

You can perform this action by using paraphrasing techniques that helps you to rephrase the lines and paragraphs in your paper.

Use online calculators to solve different math problems under question.

For example, if you are writing about linear equations and you want to prove different forms like point-slope form, slope-intercept form, perpendicular bisectors, etc.

You can consult with online calculators like and

These tools are free and easy-to-use with user friendly environment.

Specific recommendations

There are some particular recommendations that you must consider while writing this sort of document:

  • The structure must be easily visible with the help of punctuations and headings.
  • There must be a clear and obvious definition of the problem.
  • The title is the first thing that the reader will see, so it must be interesting to the readers.
  • Notations that have not been used in several paragraphs must have a reference.
  • All notations must be meaningful.
  • Never use the same symbol for more than one proof, for example, if you are using ‘x’ for one function, use ‘y’ for other functions.
  • Use small paragraphs so that they are easy to read.
  • Use words correctly; distinguish between a value and a function.
  • Add counterexamples to show the importance of the condition on the theorem.

Last words

By following these 5 guidelines you can successfully write an effective and easy-to-read math research paper.

We hope this guide can be beneficial for you when you are about to start writing your first mathematics research article.