can someone tell me some recent famous mathematican, and the major works...
Do a google search on Fields medalalists.
How about Andrew Wiles (correct spelling I think) - Solved Fermat's Last Theorem.
Wiles is brilliant, but that one accomplishment was based closely on the work of many others. Not as bad as using a computer to solve the four-color map theorem, though. Have you see the movie The Beautiful Mind about John Nash? We'll never again have a mathematician with the talents of Ramanujan, Gauss, Euler, Fermat...
Why would you say that?
I think the problem nowadays is that math has grown so much that it would be really hard for a mathematician to make significant contributions in multiple fields. However, I don't see why we would not have now people as talented as any old-time mathematician.
I would also mention Ed Witten as one of the best mathematicians ever. IIRC, besides being one of the fathers of string theory, he is a Field medalist.
Yes, from what I understand, Witten is a mentor and math genius. The talents of modern mathematicians incline more toward popularizing their field, and less toward generalization than those of old.
What is this four color theorem, and how was a computer used to solve it?
What is the minimum number of colors needed for arbitrary regions covering a (two-dimensional) map, such that no two regions of the same color adjoin?
And the computer proof went as follows:
Using traditional mathematics, you can prove that there exists some finite set of maps with the property that if you know how to 4-color all of those maps, you can find a way to 4-color any map.
From there, you use a computer to compute the entire set of maps and to compute a 4-coloring for each map. I can't remember if the actual number of maps was in the thousands or tens of thousands... it certainly wasn't a task doable by hand.
Since then, more advanced arguments have reduced the number of maps to consider, but to my knowledge haven't reduced the problem to something an individual could expect to do himself in any reasonable amount of time.
The peculiar thing is that the optimal n-coloring was long since known for EVERY other two dimensional topological surface aside from the sphere, for which the problem is equivalent to the plane, and the proof really isn't that difficult.
i remember reading there was some problem with using a computer to do mathematical proof, can some one explain that to me?
Separate names with a comma.