What Do Math Grad Students Actually Do?

[ForMyThunder]

I've decided to major in mathematics but I need to know something: so, what exactly does a graduate student in mathematics do?

I assume a grad student in physics, chemistry, or biology will spend their academic time in class and performing experiments with there professors, but a mathematician has no experiments to perform.

 

[DarrenM]

That's kind of funny; I asked almost the exact same question back in October. Here's a link to that thread:

https://www.physicsforums.com/showthread.php?t=343271


fantispug gives a wonderful answer, however I've done quite a bit of reading (and studying) since then and I feel that there is one additional element that should be emphasized. fantispug touches on it when he says,

This is the hardest bit - you have to guess what tool you need. Often you just try different things with varying amounts of success.

However, Steven Krantz (A Mathematician's Survival Guide), Courant & Robbins (What Is Mathematics?), Ian Stewart (Letters To A Young Mathematician, as well as the introduction to the second edition of WIM?), come right out and say it, but I think it was best expressed in this (perhaps) apocryphal story about David Hilbert from Derbyshire's book Prime Obsession:

One of Hilbert's students stopped showing up to classes. On inquiring the reason, Hilbert was told that the student had left the university to become a poet. Hilbert replied, "I can't say I'm surprised. I never thought he had enough imagination to be a mathematician."

The point being, imagination and creativity are essential for (pure) mathematics research, a revelation that rather surprised me when I stumbled across it and one that is quite a bit removed from my previous misconception that it would only involve a great deal of number-crunching and calculating.

 

[Topher925]

I assume a grad student in physics, chemistry, or biology will spend their academic time in class and performing experiments with there professors, but a mathematician has no experiments to perform.

Its actually, quite a bit more boring than this. Most of my time is spent just doing homework and projects and helping other people with their homework and projects. Research is only done when I have free time which isn't very often.

Although I'm an engineering major, I would imagine mathematics wouldn't be that much different.