Mathematical Writing Guide for All

Mathematical writing is not as popular in the academic sphere as other subjects but it still exists. To do it with flying colors, a student, expert or whoever needs to do it should know both math and communication. If you do not know how to communicate, there is a chance you will not know how to explain your mathematical paper correctly. So, learning to communicate effectively, whether speaking or writing, is not only a courtesy to your readership; it is also a practice of understanding and organizing your thinking. These criteria can be used as a starting point for writing good mathematical papers.

And if you are still wondering how math and writing are connected – remember, mathematicians also spend a significant amount of time writing. If a mathematician wishes to research anything in mathematics, they should be able to explain their ideas in a way that others can understand. As a result, writing clearly is just as vital as being able to solve mathematics.

Any mathematician can get promoted at their job by learning how to clearly present and explain mathematical ideas.

How to Use Technical Writing in Mathematics

The writers of technical documents should communicate information effectively, clearly, accurately, and succinctly.

Also, you should not mistake “presenting your work” for “writing in math”. You will be writing math papers to show how well you comprehend mathematical theories and concepts. If you just put down your equations and formulas with little context or mediocre explanation, that will only show that you have spent some time making calculations. The reader will not see that you understand your research topic. So, a list of plain calculations with no writing or explanation is not a work of mathematical writing.

When writing a paper in math, your goal is to express mathematical reasoning and ideas to your target audience clearly.

Integrating Mathematical Ideas into Writing

1. Structure your work.

It is easier to read a well-structured document than a messy one. There are a few typical methods for structuring a math paper. The introduction always comes first. The problem is usually stated in the beginning. Even if you are working on a well-known problem, do not simply replicate it! The problem must be rewritten in your own words.

A good introduction should also emphasize the problem’s importance and how your paper will contribute to the existing research. The main purpose of the introduction section is to give your readers a general idea of the rest of the work.

Before you start writing a mathematics paper, you might want to outline. Writing a plan will also assist you in thinking more clearly about the concepts and, as a result, in understanding the subject better.

2. Analyse your audience.

For writers, this is the key factor to consider. What do you know about the reader’s background? As an author of mathematical writing, your main goal is to explain maths concepts and ideas to your readers effectively. That is why you should take your time to review all the confusing terminology, style, and tone of your writing to make sure your readers can understand you without any misinterpretation.

You should not presume the reader is knowledgeable about the issue you are trying to solve. A good math writer knows how to give math help efficiently. While you do not need to get into unnecessary details, you should provide an overview of all essential aspects.

3. Use illustrations.

In your mathematical writing, you can and should use visual arguments. If you do incorporate an image, a graph, or other visual, mathematical evidence, make sure to state how it fits into your research clearly. Any graphs and pictures you add should be properly labeled.

Tips on Writing Mathematical Documents

It may be frustrating at first if you have not written much mathematics earlier. However, the only way to improve your writing skill in mathematics is practice. It may not be easy, but it will become easier with practice, and you will improve. Here are a few tips on writing a math paper:

• Use proper grammar and vocabulary.

Mathematical papers should be written in grammatically correct English. You should not assume that a text devoided of articles or riddled with grammatical errors is nevertheless readable; there are several examples to the opposite. Computers do not always detect grammatical mistakes, so you should review the math essay and edit it yourself.

• Keep it simple.

It is best not to use cliches, idioms, and slang in your work. Otherwise, you risk being criticized if you do not use clear and direct words. Every piece of mathematics should be written in full sentences. Even presented equations include punctuation that allows you to see where they fit into a bigger text.

Find relevant examples. If a difficult concept is backed by an example, it may be easier to understand. Choose one that is easy to follow but intriguing enough to keep the main points in mind. It is important in this case to know how to write proof. So, when you are writing proofs in math, an example could precede proof of a rather basic idea. 

• Use words and symbols correctly.

Knowing when to use symbols and when to use words is essential to be able to write mathematics well. Misusing the “=” symbol is a common occurrence.

When you mean “the next step is” or “implies,” do not use the equal symbol. Using arrows instead of equal signs improves things slightly, but it is still not ideal.  Words are the finest way to convey some things. On the other hand, other things are best stated using mathematical notation.

How Do You Explain a Math Problem in Writing?

You have figured out how to solve the math problems, which is excellent! However, you are not done yet. You must have the skill of clearly presenting your answer.

The essential step in good math writing is to make a quick plan of presenting your solution. Include the items you will need to define and the sequence in which you will write out the key elements of your solution.

The plan will assist you in making sure you do not forget anything and that your steps are in a logical order. This step will save you much time and unnecessary stress. Also, when writing down your solution, keep the following in mind:

• Do not try to pack algebra into a single paragraph.
• Equations, formulae, and visual support that you will use later should all be labeled appropriately.
• Choose the ideal strategy to express your ideas (e.g., use words, calculations, a diagram, or graph).
• Demonstrate/explain the steps involved in solving the problem.
• State your results in a logical and structured way.

Writing mathematics is not easy. However, do not be discouraged! If you follow all the tips mentioned here, your writing skill will eventually improve. The best way to become better at writing maths is to practice more!