Prof. Chandrashekhar Khare and Fermat's last theorem

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. In a paper posted on the Mathematics Arxiv on the web in April 2005 and subsequently sent for publication to a leading mathematics journal, the 37-year-old mathematician based at the University of Utah has proved what is known to specialists in the field as the `level-1 case of the Serre conjecture.' In earlier work done with the French mathematician, J.P. Wintenberger, in December 2004, Dr. Khare outlined a two-part general strategy to prove the Serre conjecture fully. The present result is a first key step. Experts in the field emphasise that the attempt to prove the Serre conjecture — named after the eminent French mathematician, Jean-Pierre Serre, who originally formulated it in the early 1970s — has been the driving force behind many recent developments in number theory. As Professor Serre himself noted many years ago, his conjecture, if proved in generality, would imply the proof of Fermat's last theorem.Dr. Khare's work reaps the harvest of seeds sown by Andrew Wiles and his co-worker, Richard Taylor, en route to proving Fermat's last theorem. Speaking to this correspondent after outlining his results at a TIFR seminar, Dr. Khare recounted that little progress had been made towards the proof of the conjecture till Professor Wiles' great work, and the realisation by Dr. Taylor that their methods could be used to tackle the solution of this outstanding problem.