He quickly moved on. He found sufficient conditions for the existence of maxima, learned to determine the inflection points, drew tangents to all known curves of the second and third order. A few more years, and he finds a new purely algebraic method for finding quadratures for parabolas and hyperbolas of arbitrary order (that is, integrals of functions of the form y p = Cx q and y p x q \u003d C), calculates areas, volumes, moments of inertia of bodies of revolution. It was a real breakthrough. Feeling this, Fermat begins to seek communication with the mathematical authorities of the time. He is confident and longs for recognition.
In 1636 he wrote the first letter to His Reverend Marin Mersenne: “Holy Father! I am extremely grateful to you for the honor you have done me by giving me the hope that we will be able to talk in writing; ...I will be very glad to hear from you about all the new treatises and books on Mathematics that have appeared in the last five or six years. ... I also found many analytical methods for various problems, both numerical and geometric, for which Vieta's analysis is insufficient. All this I will share with you whenever you want, and, moreover, without any arrogance, from which I am freer and more distant than any other person in the world.
Who is Father Mersenne? This is a Franciscan monk, a scientist of modest talents and a wonderful organizer, who for 30 years headed the Parisian mathematical circle, which became the true center of French science. Subsequently, the Mersenne circle, by decree of Louis XIV, will be transformed into the Paris Academy of Sciences. Mersenne tirelessly carried on a huge correspondence, and his cell in the monastery of the Order of the Minims on the Royal Square was a kind of "post office for all the scientists of Europe, from Galileo to Hobbes." Correspondence then replaced scientific journals, which appeared much later. Meetings at Mersenne took place weekly. The core of the circle was made up of the most brilliant natural scientists of that time: Robertville, Pascal Father, Desargues, Midorge, Hardy and, of course, the famous and universally recognized Descartes. Rene du Perron Descartes (Cartesius), a mantle of nobility, two family estates, the founder of Cartesianism, the “father” of analytic geometry, one of the founders of new mathematics, as well as Mersenne’s friend and comrade at the Jesuit College. This wonderful man will be Fermat's nightmare.
Mersenne found Fermat's results interesting enough to bring the provincial into his elite club. The farm immediately strikes up a correspondence with many members of the circle and literally falls asleep with letters from Mersenne himself. In addition, he sends completed manuscripts to the court of pundits: “Introduction to flat and solid places”, and a year later - “The method of finding maxima and minima” and “Answers to B. Cavalieri's questions”. What Fermat expounded was absolutely new, but the sensation did not take place. Contemporaries did not flinch. They didn’t understand much, but they found unambiguous indications that Fermat borrowed the idea of the maximization algorithm from Johannes Kepler’s treatise with the funny title “The New Stereometry of Wine Barrels”. Indeed, in Kepler's reasoning there are phrases like "The volume of the figure is greatest if, on both sides of the place of the greatest value, the decrease is at first insensitive." But the idea of a small increment of a function near an extremum was not at all in the air. The best analytical minds of that time were not ready for manipulations with small quantities. The fact is that at that time algebra was considered a kind of arithmetic, that is, mathematics of the second grade, a primitive improvised tool developed for the needs of base practice (“only merchants count well”). Tradition prescribed to adhere to purely geometric methods of proofs, dating back to ancient mathematics. Fermat was the first to understand that infinitesimal quantities can be added and reduced, but it is rather difficult to represent them as segments.
It took almost a century for Jean d'Alembert to admit in his famous Encyclopedia: Fermat was the inventor of the new calculus. It is with him that we meet the first application of differentials for finding tangents.” At the end of the 18th century, Joseph Louis Comte de Lagrange spoke out even more clearly: “But the geometers - Fermat's contemporaries - did not understand this new kind of calculus. They saw only special cases. And this invention, which appeared shortly before Descartes' Geometry, remained fruitless for forty years. Lagrange is referring to 1674, when Isaac Barrow's "Lectures" were published, covering Fermat's method in detail.
Among other things, it quickly became clear that Fermat was more inclined to formulate new problems than to humbly solve the problems proposed by the meters. In the era of duels, the exchange of tasks between pundits was generally accepted as a form of clarifying issues related to chain of command. However, the Farm clearly does not know the measure. Each of his letters is a challenge containing dozens of complex unsolved problems, and on the most unexpected topics. Here is an example of his style (addressed to Frenicle de Bessy): “Item, what is the smallest square that, when reduced by 109 and added to one, will give a square? If you do not send me the general solution, then send me the quotient for these two numbers, which I chose small so as not to make you very difficult. After I get your answer, I will suggest some other things to you. It is clear without any special reservations that in my proposal it is required to find integers, since in the case of fractional numbers the most insignificant arithmeticist could reach the goal. Fermat often repeated himself, formulating the same questions several times, and openly bluffed, claiming that he had an unusually elegant solution to the proposed problem. There were no direct errors. Some of them were noticed by contemporaries, and some of the insidious statements misled readers for centuries.
Mersenne's circle reacted adequately. Only Robertville, the only member of the circle who had problems with the origin, maintains a friendly tone of letters. The good shepherd Father Mersenne tried to reason with the "Toulouse impudent". But Farm does not intend to make excuses: “Reverend Father! You write to me that the posing of my impossible problems angered and cooled Messrs. Saint-Martin and Frenicle, and that this was the reason for the termination of their letters. However, I want to object to them that what seems impossible at first is actually not, and that there are many problems that, as Archimedes said...” etc.
However, Farm is disingenuous. It was to Frenicle that he sent the problem of finding a right-angled triangle with integer sides whose area is equal to the square of an integer. He sent it, although he knew that the problem obviously had no solution.
The most hostile position towards Fermat was taken by Descartes. In his letter to Mersenne dated 1938 we read: “because I found out that this is the same person who had previously tried to refute my “Dioptric”, and since you informed me that he sent it after he had read my “Geometry ” and in surprise that I did not find the same thing, i.e. (as I have reason to interpret it) sent it with the aim of entering into rivalry and showing that he knows more about it than I do, and since more of your letters, I learned that he had a reputation as a very knowledgeable geometer, then I consider myself obliged to answer him. Descartes will later solemnly designate his answer as “the small trial of Mathematics against Mr. Fermat”.
It is easy to understand what infuriated the eminent scientist. First, in Fermat's reasoning, coordinate axes and the representation of numbers by segments constantly appear - a device that Descartes comprehensively develops in his just published "Geometry". Fermat comes to the idea of replacing the drawing with calculations on his own, in some ways even more consistent than Descartes. Secondly, Fermat brilliantly demonstrates the effectiveness of his method of finding minima on the example of the problem of the shortest path of a light beam, refining and supplementing Descartes with his "Dioptric".
The merits of Descartes as a thinker and innovator are enormous, but let's open the modern "Mathematical Encyclopedia" and look at the list of terms associated with his name: "Cartesian coordinates" (Leibniz, 1692), "Cartesian sheet", "Descartes ovals". None of his arguments went down in history as Descartes' Theorem. Descartes is primarily an ideologist: he is the founder of a philosophical school, he forms concepts, improves the system of letter designations, but there are few new specific techniques in his creative heritage. In contrast, Pierre Fermat writes little, but on any occasion he can come up with a lot of witty mathematical tricks (see ibid. "Fermat's Theorem", "Fermat's Principle", "Fermat's method of infinite descent"). They probably quite rightly envied each other. The collision was inevitable. With the Jesuit mediation of Mersenne, a war broke out that lasted two years. However, Mersenne turned out to be right before history here too: the fierce battle between the two titans, their tense, to put it mildly, polemic contributed to the understanding of the key concepts of mathematical analysis.
Fermat is the first to lose interest in the discussion. Apparently, he spoke directly with Descartes and never again offended his opponent. In one of his last works, "Synthesis for refraction", the manuscript of which he sent to de la Chaumbra, Fermat mentions "the most learned Descartes" through the word and in every possible way emphasizes his priority in matters of optics. Meanwhile, it was this manuscript that contained the description of the famous "Fermat's principle", which provides an exhaustive explanation of the laws of reflection and refraction of light. Curtseys to Descartes in a work of this level were completely unnecessary.
What happened? Why did Fermat, putting aside pride, went to reconciliation? Reading Fermat's letters of those years (1638 - 1640), one can assume the simplest thing: during this period, his scientific interests changed dramatically. He abandons the fashionable cycloid, ceases to be interested in tangents and areas, and for a long 20 years forgets about his method of finding the maximum. Having great merits in the mathematics of the continuous, Fermat completely immerses himself in the mathematics of the discrete, leaving the hateful geometric drawings to his opponents. Numbers are his new passion. As a matter of fact, the entire "Theory of Numbers", as an independent mathematical discipline, owes its birth entirely to the life and work of Fermat.
<…>After Fermat's death, his son Samuel published in 1670 a copy of Arithmetic belonging to his father under the title "Six books of arithmetic by the Alexandrian Diophantus with comments by L. G. Basche and remarks by P. de Fermat, Senator of Toulouse." The book also included some of Descartes' letters and the full text of Jacques de Bigly's A New Discovery in the Art of Analysis, based on Fermat's letters. The publication was an incredible success. An unprecedented bright world opened up before the astonished specialists. The unexpectedness, and most importantly, the accessibility, democratic nature of Fermat's number-theoretic results gave rise to a lot of imitations. At that time, few people understood how the area of a parabola was calculated, but every student could understand the formulation of Fermat's Last Theorem. A real hunt began for the unknown and lost letters of the scientist. Until the end of the XVII century. Every word of his that was found was published and republished. But the turbulent history of the development of Fermat's ideas was just beginning.
Unsolvable problems are 7 most interesting mathematical problems. Each of them was proposed at one time by well-known scientists, as a rule, in the form of hypotheses. For many decades, mathematicians all over the world have been racking their brains over their solution. Those who succeed will be rewarded with a million US dollars offered by the Clay Institute.
Clay Institute
This name is a private non-profit organization headquartered in Cambridge, Massachusetts. It was founded in 1998 by Harvard mathematician A. Jeffey and businessman L. Clay. The aim of the Institute is to popularize and develop mathematical knowledge. To achieve this, the organization gives awards to scientists and sponsors promising research.
At the beginning of the 21st century, the Clay Mathematical Institute offered a prize to those who solve problems that are known as the most difficult unsolvable problems, calling their list Millennium Prize Problems. From the "Hilbert List" it included only the Riemann hypothesis.
Millennium Challenges
The Clay Institute list originally included:
- the Hodge cycle hypothesis;
- equations of quantum theory Yang-Mills;
- the Poincaré hypothesis;
- the problem of equality of classes P and NP;
- the Riemann hypothesis;
- on the existence and smoothness of its solutions;
- Birch-Swinnerton-Dyer problem.
These open mathematical problems are of great interest because they can have many practical implementations.
What did Grigory Perelman prove
In 1900, the famous philosopher Henri Poincaré suggested that any simply connected compact 3-manifold without boundary is homeomorphic to a 3-sphere. Its proof in the general case was not found for a century. Only in 2002-2003, the St. Petersburg mathematician G. Perelman published a number of articles with a solution to the Poincaré problem. They had the effect of an exploding bomb. In 2010, the Poincaré hypothesis was excluded from the list of "Unsolved Problems" of the Clay Institute, and Perelman himself was offered to receive a considerable remuneration due to him, which the latter refused without explaining the reasons for his decision.
The most understandable explanation of what the Russian mathematician managed to prove can be given by imagining that a rubber disk is pulled onto a donut (torus), and then they try to pull the edges of its circumference into one point. Obviously this is not possible. Another thing, if you make this experiment with a ball. In this case, a seemingly three-dimensional sphere, resulting from a disk, the circumference of which was pulled to a point by a hypothetical cord, will be three-dimensional in the understanding of an ordinary person, but two-dimensional from the point of view of mathematics.
Poincaré suggested that a three-dimensional sphere is the only three-dimensional "object" whose surface can be contracted to a single point, and Perelman was able to prove this. Thus, the list of "Unsolvable problems" today consists of 6 problems.
Yang-Mills theory
This mathematical problem was proposed by its authors in 1954. The scientific formulation of the theory is as follows: for any simple compact gauge group, the quantum spatial theory created by Yang and Mills exists, and at the same time has a zero mass defect.
Speaking in a language understandable to an ordinary person, the interactions between natural objects (particles, bodies, waves, etc.) are divided into 4 types: electromagnetic, gravitational, weak and strong. For many years, physicists have been trying to create a general field theory. It should become a tool for explaining all these interactions. Yang-Mills theory is a mathematical language with which it became possible to describe 3 of the 4 main forces of nature. It does not apply to gravity. Therefore, it cannot be considered that Yang and Mills succeeded in creating a field theory.
In addition, the nonlinearity of the proposed equations makes them extremely difficult to solve. For small coupling constants, they can be approximately solved in the form of a series of perturbation theory. However, it is not yet clear how these equations can be solved with strong coupling.
Navier-Stokes equations
These expressions describe processes such as air flows, fluid flow, and turbulence. For some special cases, analytical solutions of the Navier-Stokes equation have already been found, but so far no one has succeeded in doing this for the general one. At the same time, numerical simulations for specific values of speed, density, pressure, time, and so on can achieve excellent results. It remains to be hoped that someone will be able to apply the Navier-Stokes equations in the opposite direction, that is, calculate the parameters with their help, or prove that there is no solution method.
Birch-Swinnerton-Dyer problem
The category of "Unsolved Problems" also includes the hypothesis proposed by English scientists from the University of Cambridge. Even 2300 years ago, the ancient Greek scientist Euclid gave a complete description of the solutions to the equation x2 + y2 = z2.
If for each of the prime numbers to count the number of points on the curve modulo it, you get an infinite set of integers. If you specifically “glue” it into 1 function of a complex variable, then you get the Hasse-Weyl zeta function for a third-order curve, denoted by the letter L. It contains information about the behavior modulo all prime numbers at once.
Brian Burch and Peter Swinnerton-Dyer conjectured about elliptic curves. According to it, the structure and number of the set of its rational solutions are related to the behavior of the L-function at the identity. The currently unproven Birch-Swinnerton-Dyer conjecture depends on the description of 3rd degree algebraic equations and is the only relatively simple general way to calculate the rank of elliptic curves.
To understand the practical importance of this task, it is enough to say that in modern cryptography a whole class of asymmetric systems is based on elliptic curves, and domestic digital signature standards are based on their application.
Equality of classes p and np
If the rest of the Millennium Challenges are purely mathematical, then this one is related to the actual theory of algorithms. The problem concerning the equality of the classes p and np, also known as the Cooke-Levin problem, can be formulated in understandable language as follows. Suppose that a positive answer to a certain question can be checked quickly enough, i.e., in polynomial time (PT). Then is the statement correct that the answer to it can be found fairly quickly? Even simpler it sounds like this: is it really not more difficult to check the solution of the problem than to find it? If the equality of the classes p and np is ever proved, then all selection problems can be solved for PV. At the moment, many experts doubt the truth of this statement, although they cannot prove the opposite.
Riemann hypothesis
Until 1859, no pattern was identified that would describe how prime numbers are distributed among natural numbers. Perhaps this was due to the fact that science dealt with other issues. However, by the middle of the 19th century, the situation had changed, and they became one of the most relevant that mathematics began to deal with.
The Riemann Hypothesis, which appeared during this period, is the assumption that there is a certain pattern in the distribution of prime numbers.
Today, many modern scientists believe that if it is proven, then many of the fundamental principles of modern cryptography, which form the basis of a significant part of the e-commerce mechanisms, will have to be revised.
According to the Riemann hypothesis, the nature of the distribution of prime numbers may differ significantly from what is currently assumed. The fact is that so far no system has been discovered in the distribution of prime numbers. For example, there is the problem of "twins", the difference between which is 2. These numbers are 11 and 13, 29. Other prime numbers form clusters. These are 101, 103, 107, etc. Scientists have long suspected that such clusters exist among very large prime numbers. If they are found, then the stability of modern crypto keys will be in question.
Hodge Cycle Hypothesis
This hitherto unsolved problem was formulated in 1941. Hodge's hypothesis suggests the possibility of approximating the shape of any object by "gluing" together simple bodies of higher dimensions. This method has been known and successfully used for a long time. However, it is not known to what extent the simplification can be made.
Now you know what unsolvable problems exist at the moment. They are the subject of research by thousands of scientists around the world. It remains to be hoped that in the near future they will be resolved, and their practical application will help humanity enter a new round of technological development.
Sometimes a diligent study of the exact sciences can bear fruit - you will become not only known to the whole world, but also rich. Awards are given, however, for nothing, and in modern science there are a lot of unproven theories, theorems and problems that multiply as science develops, take at least Kourovka or Dniester notebooks, sort of collections with unsolvable physical and mathematical, and not only, tasks. However, there are also truly complex theorems that have not been solved for more than a dozen years, and for them the American Clay Institute has put up an award in the amount of 1 million US dollars for each. Until 2002, the total jackpot was 7 million, since there were seven "millennium problems", but the Russian mathematician Grigory Perelman solved the Poincare conjecture by epically abandoning a million, without even opening the door to US mathematicians who wanted to give him his honestly earned bonuses. So, we turn on the Big Bang Theory for the background and mood, and see what else you can cut a round sum for.
Equality of classes P and NP
In simple terms, the equality problem P = NP is as follows: if a positive answer to some question can be checked fairly quickly (in polynomial time), then is it true that the answer to this question can be found fairly quickly (also in polynomial time and using polynomial memory)? In other words, is it really not easier to check the solution of the problem than to find it? The bottom line here is that some calculations and calculations are easier to solve algorithmically rather than brute-force, and thus save a lot of time and resources.
Hodge hypothesis
Hodge's conjecture, formulated in 1941, is that for particularly good types of spaces called projective algebraic varieties, the so-called Hodge cycles are combinations of objects that have a geometric interpretation - algebraic cycles.
Here, explaining in simple terms, we can say the following: in the 20th century, very complex geometric shapes were discovered, such as curved bottles. So, it was suggested that in order to construct these objects for description, it is necessary to use completely puzzling forms that do not have the geometric essence “such terrible multidimensional scribbles-scribbles” or you can still get by with conditionally standard algebra + geometry.
Riemann hypothesis
It is quite difficult to explain here in human language, it is enough to know that the solution of this problem will have far-reaching consequences in the field of distribution of prime numbers. The problem is so important and urgent that even the derivation of a counterexample of the hypothesis is at the discretion of the academic council of the university, the problem can be considered proven, so here you can also try the “from the opposite” method. Even if it is possible to reformulate the hypothesis in a narrower sense, even here the Clay Institute will pay out a certain amount of money.
Yang-Mills theory
Particle Physics is one of Dr. Sheldon Cooper's favorite topics. Here the quantum theory of two smart uncles tells us that for any simple gauge group in space there is a mass defect other than zero. This statement has been established by experimental data and numerical simulations, but so far no one can prove it.
Navier-Stokes equations
Here, Howard Wolowitz would certainly help us if he existed in reality - after all, this is a riddle from hydrodynamics, and the foundation of the foundations. The equations describe the motions of a viscous Newtonian fluid, are of great practical importance, and most importantly describe turbulence, which cannot be driven into the framework of science in any way and its properties and actions cannot be predicted. Justification for the construction of these equations would allow not to point a finger at the sky, but to understand turbulence from the inside and make aircraft and mechanisms more stable.
Birch-Swinnerton-Dyer hypothesis
True, here I tried to pick up simple words, but there is such a dense algebra that one cannot do without deep immersion. Those who do not want to scuba dive into the matan need to know that this hypothesis allows you to quickly and painlessly find the rank of elliptic curves, and if this hypothesis did not exist, then a sheet of calculations would be needed to calculate this rank. Well, of course, you also need to know that the proof of this hypothesis will enrich you by a million dollars.
It should be noted that in almost every area there are already advances, and even proven cases for individual examples. Therefore, do not hesitate, otherwise it will turn out like with Fermat's theorem, which succumbed to Andrew Wiles after more than 3 centuries in 1994, and brought him the Abel Prize and about 6 million Norwegian kroner (50 million rubles at today's exchange rate).
Often, when talking with high school students about research work in mathematics, I hear the following: "What new things can be discovered in mathematics?" But really: maybe all the great discoveries have been made, and the theorems have been proven?
On August 8, 1900, at the International Congress of Mathematicians in Paris, mathematician David Hilbert outlined a list of problems that he believed were to be solved in the twentieth century. There were 23 items on the list. Twenty-one of them have been resolved so far. The last solved problem on Gilbert's list was Fermat's famous theorem, which scientists couldn't solve for 358 years. In 1994, the Briton Andrew Wiles proposed his solution. It turned out to be true.Following the example of Gilbert at the end of the last century, many mathematicians tried to formulate similar strategic tasks for the 21st century. One such list was made famous by Boston billionaire Landon T. Clay. In 1998, at his expense, the Clay Mathematics Institute was founded in Cambridge (Massachusetts, USA) and prizes were established for solving a number of important problems in modern mathematics. On May 24, 2000, the institute's experts chose seven problems - according to the number of millions of dollars allocated for prizes. The list is called the Millennium Prize Problems:
1. Cook's problem (formulated in 1971)
Let's say that you, being in a large company, want to make sure that your friend is also there. If you are told that he is sitting in the corner, then a fraction of a second will be enough to, with a glance, make sure that the information is true. In the absence of this information, you will be forced to go around the entire room, looking at the guests. This suggests that solving a problem often takes more time than checking the correctness of the solution.
Stephen Cook formulated the problem: can checking the correctness of a solution to a problem be longer than getting the solution itself, regardless of the verification algorithm. This problem is also one of the unsolved problems in the field of logic and computer science. Its solution could revolutionize the fundamentals of cryptography used in the transmission and storage of data.
2. The Riemann Hypothesis (formulated in 1859)
Some integers cannot be expressed as the product of two smaller integers, such as 2, 3, 5, 7, and so on. Such numbers are called prime numbers and play an important role in pure mathematics and its applications. The distribution of prime numbers among the series of all natural numbers does not follow any regularity. However, the German mathematician Riemann made an assumption regarding the properties of a sequence of prime numbers. If the Riemann Hypothesis is proven, it will revolutionize our knowledge of encryption and lead to unprecedented breakthroughs in Internet security.
3. Birch and Swinnerton-Dyer hypothesis (formulated in 1960)
Associated with the description of the set of solutions of some algebraic equations in several variables with integer coefficients. An example of such an equation is the expression x2 + y2 = z2. Euclid gave a complete description of the solutions to this equation, but for more complex equations, finding solutions becomes extremely difficult.
4. Hodge hypothesis (formulated in 1941)
In the 20th century, mathematicians discovered a powerful method for studying the shape of complex objects. The main idea is to use simple "bricks" instead of the object itself, which are glued together and form its likeness. The Hodge hypothesis is connected with some assumptions about the properties of such "bricks" and objects.
5. The Navier - Stokes equations (formulated in 1822)
If you sail in a boat on the lake, then waves will arise, and if you fly in an airplane, turbulent currents will arise in the air. It is assumed that these and other phenomena are described by equations known as the Navier-Stokes equations. The solutions of these equations are unknown, and it is not even known how to solve them. It is necessary to show that the solution exists and is a sufficiently smooth function. The solution of this problem will make it possible to significantly change the methods of carrying out hydro- and aerodynamic calculations.
6. Poincare problem (formulated in 1904)
If you stretch a rubber band over an apple, then you can slowly move the tape without leaving the surface, compress it to a point. On the other hand, if the same rubber band is properly stretched around the donut, there is no way to compress the band to a point without tearing the band or breaking the donut. The surface of an apple is said to be simply connected, but the surface of a donut is not. It turned out to be so difficult to prove that only the sphere is simply connected that mathematicians are still looking for the correct answer.
7. Yang-Mills equations (formulated in 1954)
The equations of quantum physics describe the world of elementary particles. Physicists Yang and Mills, having discovered the connection between geometry and elementary particle physics, wrote their own equations. Thus, they found a way to unify the theories of electromagnetic, weak and strong interactions. From the Yang-Mills equations, the existence of particles followed, which were actually observed in laboratories all over the world, therefore the Yang-Mills theory is accepted by most physicists, despite the fact that within this theory it is still not possible to predict the masses of elementary particles.
I think that this material published on the blog is interesting not only for students, but also for schoolchildren who are seriously involved in mathematics. There is something to think about when choosing topics and areas of research.
Lev Valentinovich Rudy, the author of the article “Pierre Fermat and his “unprovable” theorem”, after reading a publication about one of the 100 geniuses of modern mathematics, who was called a genius due to his solution of Fermat’s theorem, offered to publish his alternative opinion on this topic. To which we readily responded and publish his article without abbreviations.
Pierre de Fermat and his "unprovable" theorem
This year marks the 410th anniversary of the birth of the great French mathematician Pierre de Fermat. Academician V.M. Tikhomirov writes about P. Fermat: “Only one mathematician has been honored with the fact that his name has become a household name. If they say "fermatist", then we are talking about a person obsessed to the point of insanity by some unrealizable idea. But this word cannot be attributed to Pierre Fermat (1601-1665), one of the brightest minds in France, himself.
P. Fermat is a man of amazing destiny: one of the greatest mathematicians in the world, he was not a "professional" mathematician. Fermat was a lawyer by profession. He received an excellent education and was an outstanding connoisseur of art and literature. All his life he worked in the civil service, for the last 17 years he was an adviser to the parliament in Toulouse. A disinterested and sublime love attracted him to mathematics, and it was this science that gave him everything that love can give a person: intoxication with beauty, pleasure and happiness.
In papers and correspondence, Fermat formulated many beautiful statements, about which he wrote that he had their proof. And gradually there were fewer and fewer such unproven statements and, finally, only one remained - his mysterious Great Theorem!
However, for those interested in mathematics, Fermat's name speaks volumes regardless of his Grand Theorem. He was one of the most insightful minds of his time, he is considered the founder of number theory, he made a huge contribution to the development of analytic geometry, mathematical analysis. We are grateful to Fermat for opening for us a world full of beauty and mystery” (nature.web.ru:8001›db/msg.html…).
Strange, however, "gratitude"!? The mathematical world and enlightened humanity ignored Fermat's 410th anniversary. Everything was, as always, quiet, peaceful, everyday ... There was no fanfare, laudatory speeches, toasts. Of all the mathematicians in the world, only Fermat has "honored" such a high honor that when the word "fermatist" is used, everyone understands that we are talking about a half-wit who is "madly obsessed with an unrealizable idea" to find the lost proof of Fermat's theorem!
In his remark on the margin of Diophantus's book, Fermas wrote: "I have found a truly amazing proof of my assertion, but the margins of the book are too narrow to accommodate it." So it was "the moment of weakness of the mathematical genius of the 17th century." This dumbass did not understand that he was “mistaken”, but, most likely, he simply “lied”, “cunning”.
If Fermat claimed, then he had proof!? The level of knowledge was no higher than that of a modern tenth grader, but if some engineer tries to find this proof, then he is ridiculed, declared insane. And it is a completely different matter if an American 10-year-old boy E. Wiles "accepts as an initial hypothesis that Fermat could not know much more mathematics than he does" and begins to "prove" this "unprovable theorem." Of course, only a “genius” is capable of such a thing.
By chance, I came across a site (works.tarefer.ru›50/100086/index.html), where a student of the Chita State Technical University Kushenko V.V. writes about Fermat: “... The small town of Beaumont and all its five thousand inhabitants are unable to realize that the great Fermat was born here, the last mathematician-alchemist who solved the idle problems of the coming centuries, the quietest judicial hook, the crafty sphinx who tortured humanity with its riddles , a cautious and virtuous bureaucrat, a swindler, an intriguer, a homebody, an envious person, a brilliant compiler, one of the four titans of mathematics ... Farm almost never left Toulouse, where he settled down after marrying Louise de Long, the daughter of an adviser to parliament. Thanks to his father-in-law, he rose to the rank of adviser and acquired the coveted prefix "de". The son of the third estate, the practical offspring of wealthy leather workers, stuffed with Latin and Franciscan piety, he did not set himself grandiose tasks in real life ...
In his turbulent age, he lived thoroughly and quietly. He did not write philosophical treatises, like Descartes, was not the confidant of the French kings, like Viet, did not fight, did not travel, did not create mathematical circles, did not have students and was not published during his lifetime ... Having found no conscious claims to a place in history, The farm dies on January 12, 1665."
I was shocked, shocked... And who was the first "mathematician-alchemist"!? What are these “idle tasks of the coming centuries”!? “A bureaucrat, a swindler, an intriguer, a homebody, an envious person” ... Why do these green youths and youths have so much disdain, contempt, cynicism for a person who lived 400 years before them!? What blasphemy, blatant injustice!? But, not the youngsters themselves came up with all this!? They were thought up by mathematicians, "kings of sciences", that same "humanity", which Fermat's "cunning sphinx" "tortured with his riddles".
However, Fermat cannot bear any responsibility for the fact that arrogant, but mediocre descendants for more than three hundred years knocked their horns on his school theorem. Humiliating, spitting on Fermat, mathematicians are trying to save their honor of uniform!? But there has been no “honor” for a long time, not even a “uniform”!? Fermat's children's problem has become the greatest shame of the "selected, valiant" army of mathematicians of the world!?
The “kings of sciences” were disgraced by the fact that seven generations of mathematical “luminaries” could not prove the school theorem, which was proved by both P. Fermat and the Arab mathematician al-Khujandi 700 years before Fermat!? They were disgraced by the fact that, instead of admitting their mistakes, they denounced P. Fermat as a deceiver and began to inflate the myth about the “unprovability” of his theorem!? Mathematicians have also disgraced themselves by the fact that for a whole century they have been frenziedly persecuting amateur mathematicians, "beating their smaller brothers on the head." This persecution became the most shameful act of mathematicians in the entire history of scientific thought after the drowning of Hippasus by Pythagoras! They were also disgraced by the fact that, under the guise of a "proof" of Fermat's theorem, they slipped enlightened humanity the dubious "creation" of E. Wiles, which even the brightest luminaries of mathematics "do not understand"!?
The 410th anniversary of the birth of P. Fermat is undoubtedly a strong enough argument for mathematicians to finally come to their senses and stop casting a shadow on the wattle fence and restore the good, honest name of the great mathematician. P. Fermat “did not find any conscious claims to a place in history,” but this wayward and capricious Lady herself entered it in her annals in her arms, but she spat out many zealous and zealous “applicants” like chewed gum. And nothing can be done about it, just one of his many beautiful theorems forever entered the name of P. Fermat in history.
But this unique creation of Fermat has been driven underground for a whole century, outlawed, and has become the most contemptible and hated task in the entire history of mathematics. But the time has come for this "ugly duckling" of mathematics to turn into a beautiful swan! Fermat's amazing riddle has earned its right to take its rightful place in the treasury of mathematical knowledge, and in every school of the world, next to its sister, the Pythagorean theorem.
Such a unique, elegant problem simply cannot but have beautiful, elegant solutions. If the Pythagorean theorem has 400 proofs, then let Fermat's theorem have only 4 simple proofs at first. They are, gradually there will be more of them!? I believe that the 410th anniversary of P. Fermat is the most appropriate occasion or occasion for professional mathematicians to come to their senses and finally stop this senseless, absurd, troublesome and absolutely useless "blockade" of amateurs!?
