Tuesday, February 17, 2009

Of Theorems, Conjectures And Me

Like I promised in my post on Fermat's Last Theorem, here is my post on my time as a Mathematics student. This is neither the first nor the last such post, just one of many.

I first heard of Fermat's Last Theorem when I was in class nine, I think. At that time, I read a little bit about it, but probably not enough to get me really interested in it. In class eleven, I happened to land up on something called the Beal Conjecture. The statement of this conjecture is on similar lines to Fermat's Last Theorem. Incidentally, until a statement is proved, it should be called a conjecture, not a theorem. Fermat's Last Theorem was always referred to as a theorem instead of a conjecture, for over three hundred years when it stood without a proof.

I was rather intrigued by the Beal Conjecture. I was in touch with a Professor from the University of North Texas over e-mail, doing some background research, and trying to figure out if I could attempt to actually prove it. I told him I wanted to study the proof for Fermat's Last Theorem, and asked him to suggest references. He pointed me in the right direction, but I guess I did not know enough Mathematics then to be able to figure it out.

As an undergraduate student of Mathematics, I attended a workshop where a Professor from Berkeley gave us an overview of the proof. He did it in a fraction of the time that Andrew Wiles spent at the Newton Institute for the same task, but the overview was enough for me to be interested and confident enough to make another serious attempt to figure it out. I did, to an extent, but was never able to grasp it fully, because of the sheer bulk of the thing, and I no longer remember any of it, except that it was based on elliptic curves. This I remembered before Simon Singh's book reminded me of it.

Somewhere along the line, I gave up Mathematics, and forgot all about Fermat and Beal. After reading this book, I do have a bit of renewed enthusiasm. Maybe I will take up that stuff all over again. It won't necessarily be fruitful, but it just might be fun.

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