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How to write Mathematics papers


It is rare that we write a mathematics paper; many students are not familiar with the norms and conditions of writing a mathematics paper. The word mathematics was derived from a Greek word, 'mathemas', that combines the notions of perception, cognition, knowledge, and understanding. Eventually, the term mathematics is all about the ideas. In university life, the complexity that is encountered during new ideas and concepts increases. The college mathematics will include some concepts that cannot be expressed using the equations and expressions only. To shift the mathematics onto the paper, we will need writing of sentences and paragraphs along with the formulas and equations.

In reality, to write, a mathematician needs to spend quite a time. If someone is contributing to the scientific body of mathematics, they must be able to express their ideas hastily to others. So writing in clear words is as much as important as mathematical skills. When a person pursues his studies in mathematics after college or during college, he or she develops a higher sense of mathematics. Whenever there is a need to discuss the mathematical issue with your boss or a colleague, there is a big possibility that they have less mathematical knowledge than you do. So you have to use simpler terms so we can well understand your perspective. This will enhance your chances to prosper in your career.

You observe that whenever you write, you will end up increasing your knowledge and understanding of the ideas related to mathematics. To transfer your idea on the paper requires some careful thoughts and focused attention. Hence the mathematics written more carefully is more likely to be accurate.

Indicators of Good mathematical writing

In writing a mathematical paper, it is more important to justify the answer than just to write the answer down. Like if the author describes why he is writing the novel rather than just writing it. One should never confuse oneself with writing mathematics meaning "showing your work". You do not write the mathematical paper to show what you have done, but to tell how well you understand the topic and the concept. A text full of calculations with no explanation or background shows you have spent some handsome amount of time in computations, and this text is independent of any idea. The actual meaning of mathematics is ideas, so any text that is just composed of computational calculation with no explanation and ideas is no math at all.

Similarly, writing the conclusion in a text will not be enough for a mathematics paper. When you are writing a mathematical paper, the goal is to communicate using mathematical reasoning and concepts with another person. Some basic guidelines which we follow while writing a simple paper, must also be followed while writing a mathematics paper.

Basic: Combination of Equations and words

The Grammatical Rules

The good writers always follow the grammatical rules. This also applies to the writing of mathematical papers. In the mathematical paper, we expect to use proper grammar and spellings. Be professional and clear. Avoid usage of irregular abbreviations or any short forms which are not standard conventions of writing. We write mathematics paper along with the sentences in the paragraphs. Yes, the paragraphs are very important. It is not comfortable reading a three-page paper containing only one paragraph.

There is an element that is used in mathematical writing, which is not there in other writing, called the formulas. Formulas and equations also follow standard grammatical rules. The symbols of mathematics relate to different parts of the speech. For example, we describe a perfectly good complete sentence as below;

1 + 3 = 4

The symbol '=' represents a verb, which means equal to. We describe more examples below;

6xy < -8

7z > R

9-k = J

We can identify the verbs from the examples; similarly, the expressions look like;

6x +3y

It is not a complete sentence; no verb is there. So we can say that we take such an expression as a noun. So we can also point at the nouns in the previous examples.

It requires the equations and the formulas to be in a complete sentence with the use of proper punctuation.

For example;

The total funds are the budget made from selling watches, is B.


Where ('s') is the price at which they sell each watch and (t) is the total number of watches sold. From experience, we know that when the watches are at a price of 20 dollars each, they sold 3000 watches. We also know that by increasing (x) dollars, the number of watches sold becomes 150 less. Hence using the equation to tell that the impact made by (x) dollars’ increase in the price.

B=(20+x) *(3000-150x)

B=150x^2 - 2700x +6000.

You can notice the way each of equation follows punctuation. A period should follow the computation, which is ending a sentence. Those computations which do not come at the end of the sentence are followed by the commas.

A better way of enhancing your mathematical writing skills is by reading your writing, including the equations and the expressions, loudly. Sometimes your ears can catch the grammatical errors and the fragments in the sentence better than your eyes. Whenever you find that the sentences are not right, you will rewrite the sentences and equations.

In mathematical writings, some other important things are to be observed from the above examples. Notice how the term "we" is used. In the mathematical paper, it is common to use the first person, so don't hesitate while using the word "we" while writing a mathematical paper. Also, notice that the long formulas and the important ones are to be written on separate lines. The mathematical writings can be made easier to read if we place the formula on its own line.

For example, in the below paragraph, it is hard to pick the formulas which are important.

If, ‘Y’ is the distance in meters from the ground and Jack, then d=500-7y, where Y is the number of seconds after Jack's task is activated. So if we solve for Y in the above equation. 500 - 7y = 0, we find that Y =71.4. So Jack will hit the ground exactly after 71.4 seconds.

In the clear form we should write the above example as:

If (d) is the Jack's distance above the ground in units feet, then

d = 500 - 7y

Where Y denotes the number of seconds right after Jack's task is activated.

So if we solve for Y from the equation;

500 - 7y = 0

We found that the value of Y comes 71.4, so concluding that Jack will hit the ground after 71.4 seconds of his task.

Words and Symbols

Using the words and symbols is very important in writing the mathematical or any other paper. Mathematical writing is an art of knowing when to use the symbol itself and when to use the word for it. You should not use mathematical symbols when you are meaning something else. The most common mistake is the use of the symbol "=". For example;

4-2x=-1 = 4-2x+1 = 0 =

(4+1) - 2x = 0 = 5-2x = 0 = 5/2 = x

Never use the sign of equality when you mean to say "the next step is" or "result". The above equation is stating that 1 is equal to 0 and 5/2. Which is not what actually the writer wants to say. A slightly better but not desired way of saying this is by using arrows instead of the sign of equality.

With the sequence of steps, it is the best way to place the equation in a separate line.


4-2x+1 = 0

(4+1) - 2x = 0

5-2x = 0

5/2 = x

In case of a difficult calculation, when there is a doubt that the reader might not properly follow each step, we can include the words to clarify the steps we take. For example;

Here the aim to calculate the X from the equation below,


Rewriting the equation by bringing all non-zero terms on one side of the equation.

4-2x+1 = 0

Simplifying the equation

(4+1) - 2x = 0

More simplification

5-2x = 0

Solving for x,

5/2 = x

Make sure you write the paper in a single flow; avoid using the two-column method while explaining the calculation. For example, avoid the method described below;

4-2x = -1

4-2x+1 = 0 Simplifying the equation

(4+1) - 2x = 0 More simplification

5-2x = 0 Solving for x,

5/2 = x

It is hard to read through, this style is also bad.

Sometimes words are the best way of expressing something and sometimes the symbols and mathematical terms do describe the idea more properly, for example reading the term below is harder;

We know that Y plus three is smaller than ten.

In such cases, the mathematical notation is way more appropriate,

We know that Y + 3 < 10.

Miscellaneous Commenting

Start no sentence with a formula. It may be correct grammatically but gives a strange feeling.

x=8 when w=300, so we will not add..........

adding just a single word or two will solve these issues

X = 8 when W = 300 we will not add….

Converting Ideas into writing

Organize the paper

It is easy to read organized papers than the ones that are not organized. Luckily, we have some standards to organize a mathematical essay.

First, there should be an introduction, which usually states the problem and the context of the problem. Even when you are answering just a question from the book, you must start by introducing the issue. We should not assume that the reader will be familiar with the textbook, etc. Never just copy-paste the question, always try to rewrite it in your own words. A healthy introduction should discuss the importance of the problem; it requires you to hook the reader in the introduction part. To catch the attention by previewing the result of the question in the introduction is a good idea.

Audience Importance

While writing most of the mathematical papers, we assume that the reader will have the same level of mathematical knowledge that we have. Most of the time you are not writing for your professor. You write the paper for a common person with basic knowledge of mathematics. So you have to be simple and descriptive while writing for them.

Defining Formulas and Variables

We should represent the functions and quantities with letters. The letter chosen is arbitrary, you can explicitly mark any letter with any quantity or function, and then that letter will start representing that quantity or the function. For example;

Either K or k+1 is even

What is K? If the value of K is 8.5 then will the above statement be true or not? A better way of saying that is,

For any whole number K, either K or the k+1 will be even.

A mostly used phrase in mathematics is "let".

Let T represents time in seconds.

Let P become the population of the United States.

Pictures in the Paper

A better way of elaborating your findings in a mathematical paper is by introducing some pictures into the paper. These pictures can be of many types; these can be graphs and charts. These visual arguments, when introduced, should be explained fully, how these visual arguments fit with the representation of your work. The graphs should be well labeled and titled properly. The important points on the graphs should be marked, and the trend line should be drawn accordingly. The independent variable should lie on the x-axis while the dependent one on the y-axis.


Mathematics is not just numbers and computations; it is as descriptive as any other technical or non-technical field. We usually don’t write a mathematical paper. So when we have to write one, we make certain mistakes. There are some norms and rules we have to follow while writing the mathematical paper. By following these rules, the writer can deliver his thoughts much better. The paper should be written with proper explanations and at a level of the reader you are expecting. Most of the errors occur due to the formulas and equations. By following the rules, a mathematician can avoid these misunderstandings. So we should be more careful while writing the mathematics paper.

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