At its core, a mathematical paper is no different from any other research paper. It follows the same outline starting with an introduction, discussing the problem, and offering a conclusion.
However, good mathematical writing is a bit more different from anything else. You can compare it to mathematical thinking, a skill that is refined and polished with practice. Yet, you should present your thoughts in a way that can make any mathematical problem understood by others.
A well-written paper is what communicates your thought process well. You need to convey it effectively for others to appreciate and comprehend the core ideas. Your goal is not to merely make a readable text, but a good paper that reads well. We consulted some experts. We looked at a large number of Literature Study Guides For Teens. And we understand if you have any problems, please contact the essay writing services. Here you can see for yourself in which direction you are going to go further. What kind of service can help you?
Strive for Clarity
One would think it is obvious and easy to do. Yet, clarity in phrasing is often a challenge for mathematical papers.
Achieving clarity is a slow process, and it might require you to go through numerous drafts. However, it will help others to understand your paper better. If someone is skimming through your article to see if it’s useful for their research, would you want them to lay it aside because they are getting confused? Even with clear results and certain proofs, a clear presentation is the only thing that will give your paper a competitive advantage over others.
Read Mathematical Literature
If you have no clue where to start, the right place would be to look for guides. A case in point is not writing guides like this one. Look for famous essays by accomplished mathematicians.
For instance, John Milnor is not only an excellent mathematician. His works, such as the Characteristic Classics and Topology from the differentiable viewpoint, can offer great insights into writing as well. There are also others to refer to – J.P. Serre, Michael Spivak, Steven Krantz, to name a few. The works by these authors can give you an idea of mathematical writing and instill some inspiration.
Read Specialized Literature
If writing is not your strong suit, allocate some time to understand what writing is all about and how to approach it. Thankfully, this topic has been discussed vastly, so you will not have much trouble finding the right books.
On Writing by Stephen King or Willian Zissner’s writing guides would be great places to start. These are also engaging readings, so you won’t get bored. Here are all the famous writers https://www.isliptown.org/top-6-most-famous-writers-of-our-time/. This will be of help to you when you encounter difficulties.
Structure Your Papers
For a while now, mathematical papers have been reflecting a similar paper structure as those of other subjects. This framework gives your thoughts a certain flow. It helps you in asserting arguments and takes the readers through a logical flow of ideas. Your math paper’s first goal is to convince the audience that your research is well-versed in all aspects.
You cannot merely achieve this goal without supporting your research with evidence. In other words, you have to see the paper through the eyes of the reader and structure it accordingly.
One way to do this is by considering what questions might come to the reader’s mind and answering them in your paper. Remember that anything you have to support your argument has to be in there.
You also have to explain how your work fits into the bigger picture. It doesn’t matter how small you think your contribution is; you never know how or when it may lead to some insight. Structuring is essential for organizing your thoughts to help both the writer and the reader.
Formal and Informal Exposition
At this point, you should consider both the formal or informal exposition in your mathematical writing. A formal exposition or structure would consist of standard definitions, theorems, proofs. You can find a lot of useful information by finding a tutor.
In this case, the author has little room to deviate from the established terms within the paper. An informal exposition, on the other hand, offers reasoning and mathematical explanations. It will constitute analogies, examples, and motivations.
Both these approaches should run side-by-side to enable your reader to understand what your paper is all about.
When you know how to structure a paper, you are ready to plan the outline. The format for mathematical papers is more or less the same as for any other piece of academic writing. The standard sections are as follows:
- Table of Contents;
- Final Remarks;
The body of the paper would vary depending on what you are writing. Usually, it is presented with several subsections. Here are some of the points you need to cover:
- Why should one read this paper?
- What are you hoping to achieve in this paper?
- What is the problem, and how did you come to it?
- Is it a current issue in the field?
- What makes it interesting to the author?
You need to establish the background at first so that the reader will know what knowledge is required to understand the paper. You will also need to discuss the consequences and importance of your work. By the time you reach the final remarks, you should be able to answer every possible question posed by the reader.
Citing your paper is of equal importance as writing it. From the author’s part, though it might be time-consuming, it is your responsibility to acknowledge the materials you have referred to while working on the paper.
Most importantly, as you are well aware, math symbols and notations follow a standardized pattern. You cannot deviate from this, as it would only confuse readers. The same applies to protocols as well. If you are looking for guidelines, the American Mathematical Society has published a manual for your reference.
When you are planning the paper, be considerate enough to leave some time in the end. Get feedback from your professor or peers, be sure to address the comments.
They might have insights to help articulate your research and thoughts better. Logical flow and good writing are as important as your discovery in constituting an excellent mathematical paper.