Thursday, December 10, 1998
JSH: Afterword
Wanted to mention a few housecleaning things. For one thing, my FLT proof draft 12 post doesn't consider the case where two of the roots for 'f' are rational. That was covered, in my draft 11 post by a nifty subproof that I really liked but thought I didn't need. I'm happy to realize now that I do need it.
I've also come up with (I hope) a better way to handle the problem of defining f. Instead of the complex field I'm certain that I can define it as a complex irrational. Undoubtably not the correct terminology so I'll describe: Something like sqr(3)i+2 or sqr(sqr(5)+2i)+sqr(5)i, or (5)^{1/3}i. As I'm dealing with a polynomial of finite degree and rational coefficients I figure this is safe but I'm not totally sure so this post.
It does seem to me this offers the weird consideration that at infinite p, maybe my proof doesn't apply, but that sounds sort of metaphysical.
Finally, it's been quite a bit of fun throwing ideas out and bouncing them off of the mathematicians of the world. I've gotten quite a bit of criticism for not being precise. I've tried to counter somewhat by noting that mathematics is a language (whether everyone excepts it or not) and like any language, initial ideas and arguments tend to be imprecise.
That's why authors do drafts. My public drafts allowed me to absorb a large number of ideas and opinions quickly. Now it's time for that information to incubate. Of course, the drafts would have stopped sooner if I had a complete proof sooner! I'm just lucky enough (or destined?) that I did stumble (bumble?) upon it eventually.
Incubations are over when you know they're over so there's no time frame here. I'm an impatient lad so I've given the figure of six months, hoping that it'll be much sooner. I will undoubtably email a select group during that time with questions but I will not post further on FLT, unless I see an important reply to one of my previous posts that I need to answer (hint, hint, if you hate my posting don't reply!).
Happy holidays to every body out there! Try not to think too hard or take yourself too seriously!
And goodbye 1998! You're end can't come soon enough as far as I'm concerned. Here's to the New Year! A year when I plan to "party like it's 1999!"
I've also come up with (I hope) a better way to handle the problem of defining f. Instead of the complex field I'm certain that I can define it as a complex irrational. Undoubtably not the correct terminology so I'll describe: Something like sqr(3)i+2 or sqr(sqr(5)+2i)+sqr(5)i, or (5)^{1/3}i. As I'm dealing with a polynomial of finite degree and rational coefficients I figure this is safe but I'm not totally sure so this post.
It does seem to me this offers the weird consideration that at infinite p, maybe my proof doesn't apply, but that sounds sort of metaphysical.
Finally, it's been quite a bit of fun throwing ideas out and bouncing them off of the mathematicians of the world. I've gotten quite a bit of criticism for not being precise. I've tried to counter somewhat by noting that mathematics is a language (whether everyone excepts it or not) and like any language, initial ideas and arguments tend to be imprecise.
That's why authors do drafts. My public drafts allowed me to absorb a large number of ideas and opinions quickly. Now it's time for that information to incubate. Of course, the drafts would have stopped sooner if I had a complete proof sooner! I'm just lucky enough (or destined?) that I did stumble (bumble?) upon it eventually.
Incubations are over when you know they're over so there's no time frame here. I'm an impatient lad so I've given the figure of six months, hoping that it'll be much sooner. I will undoubtably email a select group during that time with questions but I will not post further on FLT, unless I see an important reply to one of my previous posts that I need to answer (hint, hint, if you hate my posting don't reply!).
Happy holidays to every body out there! Try not to think too hard or take yourself too seriously!
And goodbye 1998! You're end can't come soon enough as far as I'm concerned. Here's to the New Year! A year when I plan to "party like it's 1999!"
# posted by James Harris @ 23:30 
