I had seen Simon Singh on Book-TV some years back talk about this book, Fermat's Enigma regarding the quest to solve Fermat’s Last Theorem (FMT) but though its been at the back of my mind, I never read up more about it till yesterday when I found a great website, Larry Freeman‘s blog on the subject.
The blog is a great site for amateur readers like me to read about ‘the story behind FMT and Wiles' proof in a way accessible to the mathematical amateur.’ You can also read about the intrigue and excitement that caught even the fancy of the media when Andrew Wiles, with the help of Richard Taylor, proposed that he had a solution to FMT in 1995. (If you insist on reading it, here are the papers, all 129 pages of it – most mathematicians also do not follow it – so, do not say you were not forewarned!)
In 2006, another mathematician, Chandrashekhar Khare (previously at TIFR and now Associate Prof at University of Utah), has provided a very significant result (here is the paper) that builds on the work done by Wiles.
The Slashtdot entry on this says:"An Indian mathematician, Chandrashekhar Khare, is poised to make a significant breakthrough in the field of number theory with his solution of part of a major outstanding problem in algebraic number theory. He is currently an associate professor in Mathematics Department of University of Utah. "
Actually, Khare does not provide another proof of the FMT but proved what is known to experts as the ‘level-one Serre conjecture’. This conjecture was posed in 1972 by the Fields medallist Jean-Pierre Serre, and belongs to the field of Arithmetic Algebraic Geometry.
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