Pierre De Fermat was one of the greatest mathematicians of all time. He was born on August 20, 1601, in the town of Beaumaont-de-Lomagne in southwest France. His father, Dominique Fermat, was a wealthy leather merchant, and so Pierre was fortunate enough to enjoy a privileged education at the Franciscan monastery of Grandselve, followed by a stint at the University of Toulouse….
Pressure from his family steered Fermat toward a career in the civil service, and in 1631 he was appointed conseiller au Parlement de Toulouse, a councillor at the Chamber of Petitions.
Sir Kanelm Digby, an English mathematician, who tried to visit Fermat, wrote in a letter to John Wallis, another mathematician, that the Frenchman had been occupied with pressing judicial matters, thus excluding the possibility of a meeting:
“It is true that I had exactly hit the date of the displacement of the judges of Castres to Toulouse, where he (Fermat) is the Supreme Judge to the Sovereign Court of Parliament; and since then he has been occupied with capital cases of great importance, in which he has finished by imposing a sentence that has made a great stir; it concerned the condemnation of a priest, who had abused his functions, to be burned at the stake. This affair has just finished and the execution has followed.”
Fermat corresponded regularly with Digby and Wallis. …Fermat’s judicial responsibilities occupied a great deal of his time, but what little leisure he had was devoted entirely to mathematics.
…Fermat noticed that 26 is sandwiched between 25 and 27, one of which is a square number and the other is a cube number. He searched for other numbers sandwiched between a square and a cube but failed to find any, and suspected that 26 might be unique. After days of strenuous effort he managed to construct an elaborate argument that proved without any doubt that 26 is indeed the only number between a square and a cube. His step-by-step proof established that no other numbers could fulfill this criterion.
Fermat announced this unique property of 26 to the mathematical community, and then challenged them to prove that this was the case. He openly admitted that he himself had a proof; the question was, however, did others have the ingenuity to match it? Despite the simplicity of the claim the proof is fiendishly complicated, and Fermat took particular delight in taunting the English mathematicians Wallis and Digby, who eventually had to admit defeat.
From : Fermat’s Enigma by Simon Singh
Gp: the philosophical question here is : is our number system (of Natural Numbers) an intrinsic part of the Universe or a product of Man’s mind?