I'd like to add a little to the puzzle analogy. Not only is doing research like putting together a puzzle without an idea what the picture is, but the puzzle is irregularly shaped.
What is it like to be a mathematician?
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Re: What is it like to be a mathematician?
#12I did three years of Maths in University. Then, I swap to Computer Science because it was always 'my thing'. When I read this kind of posts I really miss Maths. It is beautiful. If you never tried, if your only experience is high school, go for it. Learn some Math. You will be happier.
Math is satisfying in that you can study it either for its own sake, or in order to better arm yourself to understand the world. To each his/her preference. I like both.
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Re: What is it like to be a mathematician?
#13On a related note, there's a good in-depth answer to the question "What is it like to understand advanced mathematics?" here:
http://www.quora.com/Mathematics/What-is-it-like-to-understa...
I'm not a mathematician, but was a theoretical physicist for more than a decade, and the Quora article accords well with my experience in understanding mathematics.
(Fairly) readable examples of some of the points made in the above article may be found in Terry Tao and Scott Aaronson's comments about how to think intuitively in high dimensions:
http://mathoverflow.net/questions/25983/intuitive-crutches-f...
Re: What is it like to be a mathematician?
#14From Edward Frankel also comes this wonderful excerpt on antisemitism in Russian higher education (that doesn't sound exciting now, but you'll like the article):
http://www.newcriterion.com/articles.cfm/The-Fifth-problem--...
Re: What is it like to be a mathematician?
#15Ed Frenkel made a film to convey the beauty of math - some nudity. http://www.imdb.com/title/tt1530994/
I am big fan of Ed Frenkel's lectures on youtube but this movie was one of the worst movies I've ever watched.
Re: What is it like to be a mathematician?
#16Same as to be a biologist, or a programmer or a doctor.
Not in my experience.
I've worked both as a research mathematician and as a programmer working on production software.
Even applied to the "same" types of problems, I've found them to be very different in day to day activities, goals, incentives ... really they are quite far apart.
Re: What is it like to be a mathematician?
#17Re: What is it like to be a mathematician?
#18When you're a mathematician, everything is black or white, but you get to define what those two words mean.
I think that's another misunderstood thing about math.
By the time you get into higher mathematics, you get to a place where nearly everything is unknown. I remember reaching the level of ordinary differential equations and realizing that "most" non-linear equations had no exact solution at all.
In ways, math and programming have this in common - as the size of the systems being studied increases, a randomly chosen example becomes harder and harder to deal and thus the "art" consists in choosing important and tractable examples out of a world of huge but intractable systems.
Re: What is it like to be a mathematician?
#19Earlier quoted context omitted.
As far as I can see, being a programmer has almost nothing in common with being a doctor...
Debugging.
Funny... that reminds me that in 'Programming Pearls' (http://netlib.bell-labs.com/cm/cs/pearls/) Jon Bentley recommends the book 'The Medical Detectives' by Berton Roueche, as both entertaining and instructive for the kind of lateral thinking needed to debug.
Re: What is it like to be a mathematician?
#20Same as to be a biologist, or a programmer or a doctor.
I've done some research in theoretical physics, and now I work as a programmer. And the two are very, very different in their reward structure.
In research it was usual to go for a few months without any relevant feelings of success (and not just me, many of my colleagues felt the same). In programming I usually get some positive feedback a few times a day, at the very least every few days.
That's a huge difference.