How Do You Write a Research Paper in Mathematics?

[drake]

Hi :)
What are the basic steps of writing an article, doing a research on math?
The one study a specific topic or topics, then you make some claims and try to prove them? Thanks :)

 

[Simon Bridge]

Welcome to PF;
You usually don't actually start writing a paper until after you have a body of research to draw from.
Then you assess what you have done to see if there is anything worth publishing. Do the research first.
The research part is where you try to figure things out.

The paper is basically you talking about what you have done and if you think you've found anything out.

A paper may present the results of experiment, describe some observations, present a model (a new one for preference or an examination of an existing one), or may attempt to demonstrate some sort of relationship (like Fermats last theorem) ... in the last case you'd be expected to prove the mathematical relationship holds or aught to hold... then it will be up to the experimentalists to disprove the relationship in Nature.

You are specifically asking about a maths paper. If it is math maths, i.e. not a science thing, then you will mostly be trying to prove that relations hold or showing some clever use of an existing relation or something like that. The details depend on the exact area you are writing in - mathematics is a big field.
http://www.ams.org/profession/career-info/math-work/math-work

The actual paper writing is pretty much like doing an academic essay assignment or a report - read the guidelines for your target journal to see what standard to work to. Also read other papers in the same field and discuss the subject with your colleagues working in the same or overlapping fields.

Most people write their first paper in collaboration with others and/or under the aegis of an experienced supervisor.

 

[drake]

I want to start a maths paper for a long time. However, I just can't take the first step. I don't know what is the reason behind it - probably I am too lazy- . I hope I can start soon. Thanks :)

 

[Simon Bridge]

You mean you want to write a maths paper but you have not done any maths research?

 

[drake]

The topic I want to do a research is Number theory or Analytic NT. I know most of the topics in NT but that knowledge is not enough to find something new in that area. So I guess I need to learn some ANT.
p.s: I haven't done any research

 

[Simon Bridge]

Have you had a look at the open questions in Number Theory?
http://www.openquestions.com/oq-ma001.htm

You would not expect to solve them, but researching them can lead to other insights.
The other way is to look for new applications somewhere that may benefit from a number-theoretic description.

Don't expect to think up new maths by yourself.
Have you read papers by other people?

 

[drake]

I've checked some papers from journals and their topics were very very specific.

'Like Number Theory>Prime Numbers>... Primes>Some results in ... Primes'

And the open problems are not a piece of cake for me, I can't solve/prove them in a few weeks etc. :) Consider Fermat's Last Thm., the theorem looks very simple, but it stayed unsolved for more than 2 hundred years. Moreover, its proof is 100+ pages (I don't know the exact number).

Ah I just realized that you don't want me to try to solve them :)

Anyway, as you pointed out, my will is that to find something new in a specific topic like the ones I mentioned above.
I know I have to study a lot and a lot and a lot on that topic. But I want to know that what else do I need to write a paper? I think working a lot is not enough to write a paper.

 

[Simon Bridge]

I think you should not expect to solve one of the open problems, but I would certainly like you to try.
Most mathematicians will attempt some of these sometime in their career. Actually solving one would be a major contribution though.

You cannot expect that maths worthy of a paper will be "a piece of cake".

Immersing yourself in a field and actively working on the problems of that field is exactly the way to end up with something to write a paper about. Academics manage to publish fairly often - getting in touch with work in a field is part of what college education is for.

The fastest track to publication, and the one that most people use, is to join a post-grad program at a University.
What is your education level BTW?

 

[drake]

The fastest track to publication, and the one that most people use, is to join a post-grad program at a University.
What is your education level BTW?

I liked that part, I'm a impatient guy. I would like to write a paper asap :)
I'm studying maths at a college and I finished my 2nd year last week.

 

[micromass]

I liked that part, I'm a impatient guy. I would like to write a paper asap :)
I'm studying maths at a college and I finished my 2nd year last week.

Why are you not contacting a prof about undergrad research? That's your best chance on a paper.

 

[drake]

Yes I can find a mentor from our department. But I wonder the process, how should I study, how can I get ambition? How can I make my research keeps me awake, makes me to forget eating, sleeping etc. like in the 'movie' A Beautiful Mind?

P.s: Sorry if my grammar confused you

 

[micromass]

Yes I can find a mentor from our department. But I wonder the process, how should I study, how can I get ambition? How can I make my research keeps me awake, makes me to forget eating, sleeping etc. like in the 'movie' A Beautiful Mind?

P.s: Sorry if my grammar confused you

Find an advisor in your department. He will explain the process to you.

Also, Nash in 'A beautiful mind' had a severe mental illness, not sure why you would want that.

 

[drake]

I don't want any mental illnesses. I only want the ambition that accelerate my writing process.

 

[Choppy]

Forget about a "fast track" to publication. (a) There isn't one. (b) In pusuing one as a student you're likely to develop a lot of bad habits that will hinder you from doing any good research. (c) If you are impatient, research is likely not a good thing to get involved in.

To be published, a research paper generally has to meet three criteria. First, it has to provide a novel advancement on particular problem. Second, that problem and the advancement that's presented has to be of interest to scientific community (or at least the readership of the particular journal). Third, the work has to be in a presentable form (well-written, concise but not omit any important details, accessible to the journal readership, etc.)

To start this process, you need to start working on a problem. Before even starting the research, you have to understand the field. You need to know what's been done, why certain problems are relevant, what other people are working on, and what work is likely to yield a novel advancement. Usually this is what graduate students struggle with over their first couple years of graduate school under the mentorship of a superviser. Then you start doing the actual research. Then, once you've found something, you start writing the paper.

Undergraduates will usually involve themselves in the process by helping out with an existing, and ongoing project and as they do, learn about both the field and develo their own set of research skills.

It's very very rare for an undergraduate to have the background knowledge to embark on a research project successfully without guidance.

 

[drake]

So, to sum up, I have to learn the topic. Then I have to look at some papers and try to improve a result or create something new.