On 11 November 2002, 10 March 2003 and 17 July 2003 Trianri Perelman posted three remarkable preprints on Ae website arXiv which claimed, among other things, to nrnvP the Pninr.re Conjecture, Perelman's method of communi-citing hfs ideas waTmost unorthodox but it was the contents of the filt iner eslecidlv that aroused and astounded those math-emackns who were"experts in this field. The arguments, partic-rlyTthrfcUwo papers, were eoncrse, sketchy, incomplete even and not entirely free from error However, subsequent work has shown that sueh imperfections were not fundamental and have since been rectified usually by methods introduced by Perelman himself: Indeed it is now accepted by the mathematical community that Perelman's claims were fully justified; refine-ments of some of his arguments have already appeared, [There wThe LZoverlap between what follows and the contents of mm in the FT?2005 issue of Mathematics Today].
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