Otherwise known as the Heine-Borel Theorem.
Otherwise known as the Heine-Borel Theorem.
There are certain things that I will find myself slowing down with, but only because I don't use this particular set of skills that often. But with other skills that I use on a daily basis, I am just as fast as ever. And I am 46. I am very good, for instance, and doing fractions in my head, because I do this all day long in the course of working out more complex problems.
When working with my own kids with long division once, I had to think about what I was doing, because it had been years since I had done this. I suppose that I could become fast at long division if I tried, but who cares? Being good at math is more about insight than speed, however. I believe there were only two great mathematicans that were exceptionally fast: Gauss and Euler.
At age 46 I can pick up just about any undergraduate math-related text and figure out a chapter in a 1/2 hour or so. I have done this countless times with former students. This insight comes from years of experience.
Einstein once said that most discoveries are made by young scientists. I believe he was refering to gigantic discoveries like relativity, etc., that are made about once each generation or two. I also believe his reasoning was that such gigantic discoveries take a genius with a fresh, unbiased view of things. I don't think this applies to the rest of us who are content to be merely good at math and science.
former math student wrote:
Please prove that if a space is closed and bound that it is compact.
This is only true in metric spaces. Consider a closed subspace of R-omega, which can be bounded, but not compact.
Any topology nerds out there that can produce this closed subspace of R-omega that is bounded but not compact?
so really, the original poster's question has two answers:
whiz-in-terms-of-business: absolutely
whiz-in-terms-of-fields medal: HIGHLY doubtful, but the math landscape is sprinkled with exceptions to the rule
of course, its not about the fields medal, you mathematical dick!