Pic. 10. Blaise Pascal

For Fermat everything was happened so that he had no opportunity to solve this problem otherwise as by his direct participation in the preparation of the royal decree on the creation of the French Academy of Sciences. This is indicated by his correspondence with Mersenne and Pierre de Carcavy who was involved in the preparation of this decree. Fermat received a desired noble title only after 17 years of diligent service becoming in 1648 a member of Edicts House, which met regularly in the little town of Castres near Toulouse. But this promotion only increased his workload and further limited his opportunity for science activity.

But paradoxically in this life drama is distinctly seen a truly divine providence having lay a special mission to Senator Pierre de Fermat aimed at saving science from destruction. At that early age the science was still seemed as a beautiful tree, which by growing became more and more valuable and attractive. But with the development of science the features of perfection and harmony inherent in it, began to fade and the image of the beautiful creation of the mind more and more resembled a helpless little freak.

Pic. 11. Pierre de Carcavy

These first signs of trouble were noticed else by Fermat since controversies in his correspondence with colleagues appeared almost on empty place. It became clear that this tree has almost no roots. This means that science does not have a sufficiently strong foundation and for it there is a threat of the fate of the Pisa Tower. Then, in order for this magnificent building of science to serve its intended purpose, all creative forces will have to be used not for development, but for preventing its complete collapse.

For Fermat this theme was going past the limits of his physical possibilities and he considered it only from the point of view of generalizing methods for solving various arithmetic problems. It is so, because arithmetic is not some separate science, but the basis for all other sciences. If we have no arithmetic, then we have no any science generally. In this sense, the arithmetic tasks proposed by Fermat are of peculiar importance. Their peculiarity is that they teach people to think in general categories i.e. to find methods regulating the possibilities of computations for solving a wide range of tasks.

And here is an amazing paradox. About Diophantus who gave solutions to nearly two hundred completely not simple arithmetic tasks, now, if anyone remembers of him, then only in connection with the name of Fermat. But about Fermat himself, who did not leave any single (!!!) proof of his theorems,5 all and sundry are constantly discussing for the fourth century in a row! Very few of those who were able to solve although one Fermat’s tasks, secured for themselves world-wide fame, but countless number of people who suffered fiasco, cannot find for this any rational explanation and they have no other choice, but only simply to ignore this very fact.

But how could such an amazing phenomenon appear in the history of science when a man, who was not even a professional scientist, became so famous? To see here only an accidental combination of circumstances, would be clearly unwise. It is much more logical to proceed from the fact that at some stage in his life, Fermat began to realize that if his plans for publishing his research were carried out, the fate of Diophantus, which was already then almost forgotten, awaits him at best. If about Fermat anyone will also remember, then only against the background of derogatory and even caricature opinions of the “experts”.