Problem Solving and Professional Mathematics

[philosophking]

Hi, I was wondering what the "big" math people here think about a correllation between recreational problems and performance in professional math fields. I hope this isn't too much of a stupid question. But this is what I was thinking.

I was wondering if people who do well on the AIME, USAMO, IMO, Putnam are the only people who can *really* succeed in the professional math world? Or can there be mathematicians who may not be so good at these problem solving competitions but still do very well in their respective field?

I've been fighting with this problem quite a bit, because I'm a little scared of how I stack up with other math majors out there. Will it end up hurting me in the end if I don't do well on the Putnam? Are there other ways to display my mathematical abilities, aside from classes?

 

[HallsofIvy]

My impression is that people who do well in mathematics are also people who like to solve puzzles. Of course, it doesn't follow that the converse is true!

 

[matt grime]

Almost all of the good mathematicians I know who were brought up in the UK do cryptic crossword puzzles (some even set them). Doing cryptic crosswords doesn't mean you can do maths.

 

[fourier jr]

Hi, I was wondering what the "big" math people here think about a correllation between recreational problems and performance in professional math fields. I hope this isn't too much of a stupid question. But this is what I was thinking.

I was wondering if people who do well on the AIME, USAMO, IMO, Putnam are the only people who can *really* succeed in the professional math world? Or can there be mathematicians who may not be so good at these problem solving competitions but still do very well in their respective field?

i don't think there's much connection between the two. like any other area of math, there are many textbooks full of techniques/tricks that can be learned. in a calculus text you'd learn different ways to differentiate/integrate stuff; in those problem books you learn about working backwards & other things, etc. maybe there's a bit of a connection in that the people who are interested in the putnam, etc are the ones who like math enough to do extra stuff like contests. (ie the people who do the contests is a subset of the people who really like doing math)

 

[philosophking]

Yeah, I wonder that too. I also wonder whether or not there is a lack of creativity that is outside of that subset but still in the main set (to go along with your illustration) that can have significant contributions to mathematics.