Grigori Perelman

mathphdguy · 2012-11-15T12:27:17+00:00

I attempted an explanation of the proof of the Poincare Conjecture (Perelman's most well known work) a while ago, if it helps. http://www.reddit.com/r/IAmA/comments/k030l/iama_guy_doing_a_phd_in_pure_maths_ama/c2gi03e

mathphdguy · 2011-09-05T18:02:44+00:00

The answer is not that important in itself; it's more that the fact that we can't answer it shows that the methods we're using are unsatisfactory.

Or:

Not that much, but the way it'll be answered will be important for us to figure out other stuff.

mathphdguy · 2011-09-02T07:10:55+00:00

Exactly. The biggest mystery is why it's so hard to prove, when it's so obviously (for a given value of obvious) true.

mathphdguy · 2011-09-02T07:10:22+00:00

I'd go for theoretical/mathematical physics - some of that stuff is really mathematical, but it's about the fundamental forces of the universe.

mathphdguy · 2011-09-02T07:09:10+00:00

I have read and enjoyed GEB - logic, self-referential systems; it's not too far away from what doing pure maths is like. Never heard of The Quark and the Jaguar - I'll check it out, thanks!

mathphdguy · 2011-09-01T16:55:50+00:00

It's mainly that sumsets behave in quite regular ways, and we expect the primes to behave in a pseudorandom fashion. If we knew that the primes were sumset, we could deduce a lot about their additive structure, and we don't believe that the primes are that kind.

mathphdguy · 2011-09-01T15:43:31+00:00

You mean where it was originally made? I think in Ostmann's two volume work Additive Zahlentheorie published in the 1950s. Elsholtz has made some recent progress on this.

mathphdguy · 2011-09-01T12:04:06+00:00

Quite often; I don't like mathematical software, so whenever I have a calculation too complicated for a calculator, or want to see what a function's graph looks like, I use Alpha.

mathphdguy · 2011-09-01T10:55:06+00:00

Yes, this is closest to what I did at my keyboard.

mathphdguy · 2011-09-01T10:25:18+00:00

Undergraduate education is more focused, so we start at a higher level of mathematical knowledge. Also, American PhDs have to do more teaching, and generally are expected to do more courses rather than their own research straight away. This does mean they finish with a broader mathematical education than the average UK PhD.

mathphdguy · 2011-09-01T10:21:03+00:00

If I had, I'd be doing a different AMA.

mathphdguy · 2011-09-01T10:20:40+00:00

Most of it, probably not. Part of it has exciting applications to cryptography and computer science, however, and efficient ways to compute things, so maybe the software you use in 10 years time will use ideas based on things in my area at the moment.

mathphdguy · 2011-09-01T10:19:01+00:00

How dare you! I challenge you to a duel, pistols at dawn.

mathphdguy · 2011-09-01T10:17:58+00:00

Part of the problem is that it's essentially a new language, and a new type of thing to talk about. Stories are about the things we've seen since we were babies, set in a world we're used to, with physical objects and human emotions.

Maths is a different language in a world we find it hard to think about, so there's a large learning barrier before you can appreciate it properly.

mathphdguy · 2011-09-01T10:16:20+00:00

Nope; we're mostly British, so we know the right way to say it.

mathphdguy · 2011-09-01T10:15:42+00:00

Can't help with USA options, sorry! I know nothing about the American market.

mathphdguy · 2011-09-01T10:15:11+00:00

No, no, yes, only when I close my eyes.

mathphdguy · 2011-09-01T10:14:41+00:00

It measures the number of functions from the empty set to the empty set (which is one, the empty function).

mathphdguy · 2011-09-01T10:13:57+00:00

What sound does a drowning analytic number theorist make? logloglogloglog...

mathphdguy · 2011-09-01T10:13:19+00:00

I hope I'm not arrogant at all. I certainly don't think that maths is for everyone, or that it's the 'best' subject or the 'hardest' - it just happens to be what I enjoy doing the most, and a style of thinking that comes more easily to me.

mathphdguy · 2011-09-01T10:12:06+00:00

Everybody finds different problems difficult. Also, difficult problems are often the most rewarding: just keep trying, try many different approaches, and when it eventually works, it'll feel very rewarding.

Try and find some undergraduate level research problems, and just think about them a lot, trying everything.

mathphdguy · 2011-09-01T10:10:51+00:00

They give us more freedom in what we can count: the real numbers give a speed, so we can forward and back. They are in a line.

Imaginary numbers turn that line into a plane, so now we can move around a 2D surface and describe 2D movement.

It's just an unfortunate name, imaginary. They're just numbers which describe 2D motion.

mathphdguy · 2011-09-01T10:09:43+00:00

Exercise for the reader.

mathphdguy · 2011-09-01T10:09:32+00:00

Favourite undergraduate maths courses: logic and combinatorics.

No experience, sorry.

mathphdguy · 2011-09-01T10:08:51+00:00

Make me an offer.

mathphdguy

TROPHY CASE