Monday, September 27, 2010
JSH: Better as a puzzle?
I'm kind of excited at the idea of presenting what I claim is a major number theory issue as a puzzle.
And it kind of makes sense to do it that way versus trying to explain it in detail—which I've been doing for years—as it could be more fun that way for those who wish a massive intellectual challenge. After all, the problem has stood for over a hundred years!
Back-story as well is that I faced it as a puzzle years ago. As back in 2002 I had what I thought was a proof of Fermat's Last Theorem using equations that followed from what I call tautological spaces. YEARS of effort but I kept being called on the ring. Posters would bug me about the ring, and for a while I'd even talked about a "flat ring" as I needed a ring without fractions.
Well one poster says that what I really wanted was the ring of algebraic integers, and I said, ok, as they sounded fine, and went on about my way, except with this latest arguments posters noted my result contradicted with the ring of algebraic integers.
I was floored! It was like, uh oh, not good. And I began to puzzle it out. After some time I figured out the puzzle!
And I discovered the object ring.
It IS a puzzle.
Presumably the smartest math people can just figure it out! Which can keep me from having to keep trying to explain, but a major benefit is emerging already in the thread I created presenting the puzzle as some very obsessive posters just fail outright, and badly.
I'm re-thinking how I look at various posters based on responses in that thread. Surprisingly to me, I may have given some of them too much benefit of the doubt as to their, um, mathematical abilities.
That puzzle is a breaker. It will break anyone but the best. And responses to it, are crystal clear as to basic math ability.
Either you have it, or you don't.
And it kind of makes sense to do it that way versus trying to explain it in detail—which I've been doing for years—as it could be more fun that way for those who wish a massive intellectual challenge. After all, the problem has stood for over a hundred years!
Back-story as well is that I faced it as a puzzle years ago. As back in 2002 I had what I thought was a proof of Fermat's Last Theorem using equations that followed from what I call tautological spaces. YEARS of effort but I kept being called on the ring. Posters would bug me about the ring, and for a while I'd even talked about a "flat ring" as I needed a ring without fractions.
Well one poster says that what I really wanted was the ring of algebraic integers, and I said, ok, as they sounded fine, and went on about my way, except with this latest arguments posters noted my result contradicted with the ring of algebraic integers.
I was floored! It was like, uh oh, not good. And I began to puzzle it out. After some time I figured out the puzzle!
And I discovered the object ring.
It IS a puzzle.
Presumably the smartest math people can just figure it out! Which can keep me from having to keep trying to explain, but a major benefit is emerging already in the thread I created presenting the puzzle as some very obsessive posters just fail outright, and badly.
I'm re-thinking how I look at various posters based on responses in that thread. Surprisingly to me, I may have given some of them too much benefit of the doubt as to their, um, mathematical abilities.
That puzzle is a breaker. It will break anyone but the best. And responses to it, are crystal clear as to basic math ability.
Either you have it, or you don't.
# posted by James Harris @ 20:31 
