Abstract
The goal of this book is to give a brief description of the steps leading to the solution of a problem which was first raised by Pierre de Fermat in the margin of his copy of Bachet de Meziriac's translation of Diophantus' Arithmetica. Diophantus' methods were ad hoc, although they were very clever methods nonetheless. This chapter explores Fermat's last theorem, which is the only one of Fermat's many theorems that remained unproven. Diophantus is one of the great names of the “Silver Age” of Greek mathematics, and it is thought that he lived in Alexandria, together with other scholars such as Pappus and Proclus, between about 250 and 350 A.D. The chapter is interested in Fermat as an amateur mathematician of such extraordinary talent that professionals of the time bowed to his superior knowledge. In geometry, one of his very first results was to reconstruct the planar loci of ApoUonius according to Pappus' analysis: his first book on the subject appeared before 1629, and the second book appeared in 1636.
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