Sunday, April 15, 2007
JSH: Galois Theory, so what's wrong?
I am sure there will be a lot of confusion about the significance of the result that I have showing a problem with use of the ring of algebraic integers.
It is such a huge problem in number theory that it's hard to grasp the full impact, but I can maybe help at least with Galois Theory.
The result shows that Galois Theory tells you nothing more about non-rationals than it does about rationals.
That is the succinct way to explain the impact there, and why I say it does not say Galois Theory is wrong, exactly, but it greatly limits its usefulness to number theorists as to taking it away for the most part as a meaningful tool.
And I want to emphasize that mathematically it just never was.
People just can make mistakes, and as time goes on those mistakes can be found and the truth learned. It is a process that has gone on for as long as there have been people.
We live. We learn.
It is such a huge problem in number theory that it's hard to grasp the full impact, but I can maybe help at least with Galois Theory.
The result shows that Galois Theory tells you nothing more about non-rationals than it does about rationals.
That is the succinct way to explain the impact there, and why I say it does not say Galois Theory is wrong, exactly, but it greatly limits its usefulness to number theorists as to taking it away for the most part as a meaningful tool.
And I want to emphasize that mathematically it just never was.
People just can make mistakes, and as time goes on those mistakes can be found and the truth learned. It is a process that has gone on for as long as there have been people.
We live. We learn.
# posted by James Harris @ 14:39 
