Case Converter Significance of Mathematics Mathematics is a study of the measurement, quantity numbers and symbolsproperties, structure, space and change. It is used for plenty of goals, such as formulating and supporting conjectures, define whether a certain conjecture is true or false, study natural processes and predict the possible phenomena, etc. Mathematics may have several different definitions. A broad and old discipline, which is growing its value and impact on society.

It has happened many times in the past, and I know of several cases today. I don't have time to offer a lot of personal advice and guidance, but I figured I'd post some general advice here. I've aimed it at people who think they've already solved famous problems, since those are the sort that typically write, but it should be equally useful for people with more modest aspirations.

I focus on the mechanics of how to do literature searches, write papers, and publish them, because I have less to say about the deeper issue of how to do research.

None of this advice is specific to amateurs, but professionals already learn all these things from their advisors. Develop a track record If you appear out of nowhere claiming to have solved a famous open problem, nobody will pay any attention.

In principle you might be right, but many people claim to have done this and virtually all of them are wrong.

If you want anyone to take your work seriously, you need to develop a track record that separates you from the cranks. The easiest way to do this is to publish some other papers.

They don't have to be deep or profound, just to show that you can make a serious, uncontroversial contribution to an area some other mathematicians care about. If you can't in fact do this, and all you can do is write controversial papers, then you should start worrying that you're deluding yourself about the quality of your papers.

One common misconception is that other researchers have an obligation to evaluate your work, and that it's unprofessional and unfair of them to ignore it.

There's a kernel of truth in that, since once you've got a good track record and are circulating a clear manuscript your work shouldn't be entirely ignored it might still be reasonable to dismiss it as nonsense, if that happens to be the case. However, it's ridiculous to argue that all proposed solutions to famous problems must either be accepted as true or be refuted to the satisfaction of the author.

The mathematical community couldn't function under such a constraint. Along the way to developing a convincing track record you'll most likely realize that your purported solution was incorrect or incomplete, but that's another side benefit.

Use standard terminology and language It's amazing how many people introduce their own terminology or notation, on the grounds that it's better than the existing options.

That's usually debatable, but even when it's objectively true doing this will just make it less likely that anyone will actually read your work.

If you must introduce new notation, explain clearly how it is related to the standard notation. It's a database of virtually every published mathematical paper from the last fifty years, with brief reviews.

Unfortunately a subscription is required, but you can access it at any college or university library. They will likely have it on paper too, but that is harder to search.

Using MathSciNet you can look up reviews of specific papers the reviews typically summarize the contentsfind all papers by a given author, search by topic, find papers whose titles or reviews include a certain word or phrase, find all reviews that refer to a certain paper, etc.Section 2.

Before you write: Structuring the paper. The purpose of nearly all writing is to communicate. In order to communicate well, you must consider both what you want to communicate, and to whom you hope to communicate it.

This is no less true for mathematical writing than for any other form of writing. The primary goal of mathematical writing is to assert, using carefully constructed logical deductions, . Having just refereed my first paper, I'll try to say a few of meaningful things.

(1) Don't obfuscate with formally correct notation where a general idea -- simply expressible in English with perhaps a few mathematical symbols -- will suffice.

(2) Be consistent with notations/conventions.

A Guide to Writing Mathematics Dr. Kevin P. Lee Introduction This is a math class! Why are we writing? When you write a paper in a math class, your goal will be to communicate a math paper.

Just make sure that your mathematical notation is legible. If you do.

A math essay about a concept looks similar to essays in other classes; it is, in fact, an expository essay. For this, you investigate a mathematical concept, develop further ideas about the theory based on research and make a claim in the form of a thesis statement.

Advice for amateur mathematicians on writing and publishing papers There's no reason why amateurs can't make worthwhile research contributions in mathematics. Advice for amateur mathematicians on writing and publishing papers It's a database of virtually every published mathematical paper from the last fifty years, with brief reviews.

you should do a professional job of it. If possible, you should write your paper using LaTeX (the TeX users group has information). That's not necessary, but it.

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soft question - How to write a good mathematical paper? - Mathematics Stack Exchange