Youri Kraskov - The Wonders of Arithmetic from Pierre Simon de Fermat

The history did not preserve for us in writing everything that would be especially interesting to us, therefore, nothing remains, but to try to restore some events at that in a very unusual way what about we will also more tell. However, it is well known that this senator during his lifetime became famous for offering simple-looking arithmetic tasks to noble grandees, which for some reason no one could solve. But apparently, he didn't had time (or even perhaps he didn't want) to tell anyone about that wonderful and non-proven until now theorem therefore it is also often called the “the Fermat’s Last theorem”.

Especially curious is the fact that not a single piece of paper has been preserved from the manuscripts of his scientific works on arithmetic and even those that were published after his death. The only exceptions were letters collected from different respondents. This strange fact indicates that some amazing and even incredible course of events took place, which led to such a situation and the establishment of only this fact alone significantly changes the whole picture, which presented to researchers so far.

They even believed that Fermat could not have a proof of his Last theorem and justified it with all sorts of arguments. But then they needed to be consistent and insist that Fermat also could not solve all other his tasks since for his justification he has not left us any explanation. But if they were solved by such giants of science as, say, Euler or Gauss, well, then it is quite another thing and we could assume that Fermat also has solved them. But if even they failed, then science in no way cannot afford to trust words that look like bluster.

In our research we will go the other way and we will proceed from the fact that the proof of Fermat’s Last theorem, without any doubt, should have been written down on paper at least in a sketch version. But if this is so, then where could it have disappeared moreover along with all the other papers? The answer to this question can shed light on the healing of the above-mentioned misfortune, which led to the fact that for unknown reasons this very proof for as much as three and a half centuries has become not only an unsolvable problem, but also a real stumbling block for science.

The riddles that we now have to explore seem at first as an accidental collision of all kinds of large and small stories, but these seemingly intricate events have their own rather rigid logic. It so happened that Fermat’s life and activities coincided with a turning point in history when a slow and very painful transition to the Renaissance took place after a long period of terrifying oppression by the Inquisition, which did not tolerate advanced scientific thought and have organized in France mass destruction of Protestant-Huguenots by Catholics.

Taking into account this circumstance, it is possible to explain such facts and events that from the point of view of a later time look as very strange and not able to understand. In particular, it should be noted that in those times, especially for people of ignoble origin, it would be very dangerous to have at home even completely harmless notes with formulas and calculations that could be interpreted as a very dangerous for their owners’ recordings of heretical content.

Pierre's Father Dominique Fermat was a wealthy merchant, but did not have a noble title. In 1601 his son Pierre was born, about which there is an entry in the church book, but his mother Françoise Cazeneuve and her child died not having lived after giving birth to three years. If the child had survived, then without a noble origin, he would have no chance of becoming a senator let alone a great scholar. And when after the loss of his first wife, Dominique married Claire de Long having noble roots, then this ensured a very opportunity that the future celebrity would appear [16].

Pierre Simon de Fermat was born not in 1601 as it was believed until now, but in 1607 (or in 1608) [1] in the little town of Beaumont-de-Lomagne near Toulouse. From childhood he stood out for such talent that Dominique Fermat did not spare the funds for his education and sent him to study first in Toulouse (1620 – 1625) and then in Bordeaux and Orleans (1625–1631). Pierre did not only study well, but also showed brilliant abilities that together with his mother’s kinship and financial support from his father, gave him every opportunity to get a best education as a lawyer.

During his studies the young future Senator Pierre Fermat was very keen on reading scientific literature and was so inspired by the ideas of great thinkers that he also himself felt a desire for scientific creativity. In order to learn more about what particularly interested him, he had mastered five languages 4 4 On a preserved tombstone from the Fermat’s burial is written: “qui literarum politiforum plerumque linguarum” – skilled expert in many languages (see Pic. 93-94 in Appendix VI). and read with enthusiasm the works from the classics of that time. As a result, he deservedly received the highest education that just was possible in those times and deep down he cherished the dream of being able to continue work in the field of science.

If the support of Pierre Fermat’s career had ended on that, then there could be no question of a future senator since in those times even simple lawyer activity demanded the highest royal deigning. From this it becomes clear why the decisive step in Pierre’s parental care was his marriage in 1631 to Louise de Long, who was a distant relative (the fourth cousin) of his mother. It is clear that such a decision could not be spontaneous especially since such kindred marriages could be concluded only with the permission of the Pope of Rome. And once again the Dominic Fermat's money solved this not simple problem.

Louise's father was an adviser to the Toulouse Parliament and being in the service of King Louis XIII, received a noble title, so Pierre had no problems with employment. But it would be a delusion to expect that also further everything will go on easily and smoothly. After the end of the study, marriage and the beginning of work, the reality seemed to Pierre as at all not so rosy. The gray days of the hustle and bustle of earning money for daily bread went day after day and did not leave any hopes to be engaged in science. And then it was still a very great good to have within the framework of lawyer activity the ability to support though not a luxurious, but still a well-off life in those difficult times for France.

A new danger for Pierre appeared unexpectedly. The next plague epidemic claimed the life of his father-in-law and this could have a very bad effect on his fate. However, by that time he had already managed to establish friendly relations with other senators what opened for him the way to parliament and as a result it made possible to turn the misfortune in his favor. With the help of a fair amount of money, he still managed to take the vacant position of an official in charge of receiving complaints in the cassation chamber of the Toulouse parliament.

The biographers of Pierre Fermat rate his career as simply brilliant, but at that they lose sight of one very significant detail. Exactly such a career tightly closes him all even the slightest opportunities to be engaged in science. They did not take into account the fact that there is a royal directive forbidding the posts of councilors of parliament for the people engaged in scientific research that may contradict the Holy Scriptures. But since Pierre became a senator, this will put a big fat cross on his dreams of being engaged in science on a professional basis. He will carry this cross for the rest of his life.

Moreover, as a Catholic he should not commit any mortal sin and is obliged to confess regularly once a year about the pardonable sins committed by him. As such a pardonable sin Pierre reports at confession about his moderate idleness after reading the books by Diophantus of Alexandria “Arithmetic” and “Tasks undertraining and pleasant, related to numbers”.

Pic. 6. Diophantus of Alexandria

The risk of falling into disfavor by such a sin fall was small because the book was published by Claude Gaspard Bachet de Méziriac a flawless in every respect a high-ranking linguist and future member of the French Academy established by Cardinal Richelieu in 1635. Here of course, there will be a question about the secret of confession. But if even in our time with respect to the Catholic Church this question looks very naïve, then what is to say about the times when the supreme executors of the royal power were cardinals. All priests were obliged to inform the authorities about what their parishioners live and especially officials in government posts. Information from the priests was also controlled, for which authorized inspectors were sent to the places.

Pic. 7. Bachet de Méziriac

It is understandable that Pierre could not expect anything good from meeting with such an inspector, but he had no choice and was ready to put up the complete impossibility of his dream. But then of course, he could not have known that he was destined to another fate and it was to decide at that very moment. It is even difficult to imagine his amazement when an arrived inspector turned out to be the priest Marin Mersenne … a passionate lover and connoisseur of mathematics!!!

Pic. 8. Marin Mersenne

Pierre took it as the supreme wonder bestowed on him from heaven by the Almighty. And how else could this be understood since Reverend Father Mersenne managed miraculously to organize for him the possibility of correspondence with René Descartes himself as well as with other elite representatives of the French creative aristocracy what about he could not ever to dream. Pierre went through the test brilliantly when he was able to solve several problems at the request of Mersenne and in particular quickly calculate some of the so-called perfect numbers moreover, also those that were previously unknown. Hardly anyone else could to solve or at least somehow cope this task.

Historians in their studies see only pure randomness in the coincidence of interest to the numbers of Mersenne and Fermat, and Mersenne himself in their presenting is a weirdo acting on his whim. However, in real history so does not happen and there should be a more reasonable explanation of events. In this sense, it would be much more logical to believe that Mersenne was no more than a performer of some instruction from above, and since he came from church nobility, only one person could give such an instruction to him – it was no one other as Cardinal Armand-Jean du Plessis Duc de Richelieu!

Pic. 9. René Descartes

This implies the activity of the association of learned nobility created by Mersenne, could not be just his initiative, but was sanctioned by the highest authorities of that time, otherwise this activity could not be deployed or it would curtail after the death of Mersenne in 1648. However, his brainchild continued to function for a long time and successfully until the creation of the French Academy of Sciences in 1666.