posted on Apr, 27 2006 @ 11:53 PM
If you have the desire, learn as much mathematics as you can. Calculus/Analysis, Abstract Algebra, and Number Theory are all interesting things to
Good mathematics allows you to understand complex in such a way that it is simple. Most areas of mathematics have fundamental theorems, which often
describe those areas of mathematics. However, there is often a complicated process to go through in deriving those theorems, and you don't really
understand fundamental theorems, unless you can derive them.
However, for problems where there are no easy ways to apply fundamental, the problems are really hard. The same is true if you don't know the
Professional mathematician often work on problems that require understanding lots of related areas, just so you can understand the problem. Since they
are unsolved, they are often in areas, where fundamental have not yet been proved, which further complicates understanding them. This makes it hard to
understand what various mathematicians are working on.
Even the greatest mathematicians, can't solve certain problems. Many of the greatest mathematicians attempted to solve FLT, and many probably died
trying. Even for Andrew Wiles, it took him years of work. One of the oldest problems concerns perfect numbers. Perfect numbers were even mentioned by
Euclid over 2000 years ago. A number is perfect if the sum of its factors equals the number.
6 has factors 2,3,1 and 2+3+1=6.
28 has factors 1,2,4,7,14 and 1+2+4+7+14=28. Are there any odd perfect numbers? Nobody has ever found an odd perfect number, but nobody knows if there
are any. Can you prove there are no odd perfect numbers?