What exactly is mathematical research?

[ezperkins]

I am a high school senior now and I would love to pursue a career in math.

I have been doing some research on the track from undergrad to grad school to tenure, and there's one thing I don't quite understand: research.

I understand what research might be for life sciences or social studies, but what exactly does pure mathematical research consist of?

Please be specific.

Thanks in advance.

 

[Pengwuino]

No one is sure. They do not let us into their secret world.

Or maybe they're trying to prove that pi = 3.

 

[Shackleford]

No one is sure. They do not let us into their secret world.

Or maybe they're trying to prove that pi = 3.

Or that it terminates.

 

[unscientific]

I love to say this, and I shall say this again.

If you know what you're doing, then it wouldn't be called research!

 

[Caramon]

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[Caramon]

This scenario consists of 3 Mathematics Professors:
Researcher A, Researcher B, and Researcher C.

1) Researcher A constructs a shortcut proof that a 3-hyperbola convex cone is compact.
2) Researcher A shows his friend Researcher B and they get very excited and begin to giggle.
3) Researcher C shows that the 5th step in the proof is a non sequitur in light of the 2nd premise.
4) Researcher B publishes the entire story in the CJM.
5) They all continue to make minimum wage.

 

[HallsofIvy]

"Mathematical research" consists primarily of proving theorems, finding ways of solving difficult differential equations or other problems. You don't say if you are at a college or university now. If you are, go over to the school library and look at some of the mathematics journals where such research is published.

 

[Astronuc]

If one is interested in pursuing mathematics, then one should check these societies.

http://www.siam.org/

http://www.ams.org/home/page

Mathematics Research Communities
http://www.ams.org/programs/research-communities/mrc

Journals - http://www.ams.org/journals


One aspect of applied math is exploring more computationally efficient algorithms, which are particularly important for systems of time-dependent differential equations - and particularly nonlinear systems.

 

[mathwonk]

It is simply problem finding and problem solving. Sometimes this requires generating new methods of solution. Thus it is merely an enhanced version of what you have been doing in all your math classes. To improve, start trying to generate further problems based on the problems you are asked to solve in your courses.

check out this blog, by an eminent researcher: http://terrytao.wordpress.com/career-advice/

 

[PETER.PHIL]

Try the Dyscalculia website and forum
Source(s)

 

[mathwonk]

E.g. in my own case, once I gave a talk on simplified approaches to a certain well known theorem and developed a simple set of hypotheses that allowed a general proof. It was traditional to assume a little more than I did, and also to conclude a little more. But with my own simpler hypotheses in mind, I noticed that there was another more general situation where my smaller set of hypotheses still held, but not the usual larger set. This mindset of most other people, of assuming they needed more assumptions, had prevented them from proving an analogous theorem in the new situation, but allowed me to prove one, only slightly weaker than in the classical situation. This was not a shocking result and some experts had probably thought of it as well, but not published it. Still it was publishable new research, and it led me to conjecture some stronger and better results later proved by other people.

So learning thoroughly some good existing work, and then thinking about how to use that understanding in a new situation, is one type of research work.

 

[kramer733]

I have another question

How much more knowledge does a new phd graduated math person have in math compared to a person who just graduated from a 4 year math program?

 

[Vanadium 50]

How much more knowledge does a new phd graduated math person have in math compared to a person who just graduated from a 4 year math program?

Six.

Seriously, what kind of answer would answer that question?

 

[Shackleford]

I have another question

How much more knowledge does a new phd graduated math person have in math compared to a person who just graduated from a 4 year math program?

A lot more.

 

[jtbell]

Six.

Really? I would have thought 42.

 

[Sankaku]

Six.

Really? I would have thought 42.

Same answer, just different units...

 

[dkotschessaa]

awww c'mon. It wasn't that bad a question, just badly phrased. I think the poster would like to know what we could say generally about the expectation of grad students in math vs. someone with a bachelor's degree. I've heard that encountering grad school classes for the first time can be a bit of shock.

-DaveKA