There are feelings between people, between people and animals, and some numbers also have feelings for mathematicians. The following is a mathematician love story I prepared for you. I hope you like it!

One: The Story of Galois

Galois * * *? Varistegolois * * *,/kloc-One of the greatest mathematicians in France in the 9th century, and the only one I call a "gifted mathematician". 16 years old to take the entrance examination of Paris Institute of Technology. As a result, the examiner didn't know what to say because there were too many steps to solve the problem during the interview, and finally he failed.

In the history of mathematics, Galois is undoubtedly the most legendary and romantic mathematician, and there is no "one". /kloc-at the age of 0/8, galois beautifully solved the number one problem in mathematics at that time: why there was no general solution to polynomial equations of degree five or above. He submitted this research result to the French Academy of Sciences, which was reviewed by the great mathematician Cauchy-Louis Cauchy. But Cauchy suggested that he go back and polish it carefully. * * * Before, he always thought that Cauchy had lost his paper or hid it privately. Recently, the archives research of French Academy of Sciences made Cauchy * * * * *. Later, Galois handed the paper to the secretary of the Academy of Sciences, Fourier Joseph Fourier, but Fourier died a few days later, so the paper was lost. 183 1 year, galois submitted for the third time. The reviewer at that time was Poisson. He thought Galois's paper was difficult to understand and refused to publish it.

Because of some extreme political acts, Galois was arrested and imprisoned. Even in prison, he continued to develop his own mathematical theory. He met a doctor's daughter in prison and soon fell in love. But the good times didn't last long, and their feelings soon broke down. The second month after his release from prison, Galois decided to fight for his beloved girl and one of her political opponents. Unfortunately, he was shot and died in the hospital the next day. Galois's last words were to his brother Alfred: "Don't cry, I need enough courage to die at the age of 20."

As if a presentiment of his own death, the night before the duel, Galois stayed up all night and wrote down all his mathematical thoughts, together with three papers, to his good friend Chevalier * * * * At the end of the letter, Galois left a will, hoping that Chevally would give the manuscript to two great German mathematicians at that time, Jacoby * * * Karl Gustav Jacob * * and Gauss * * * * *.

Chevalier followed Galois's wishes and sent the manuscript to jacoby and Gauss, but they didn't receive any reply. It was not until 1843 that the mathematician joseph liouville * * * joseph liouville * * recognized Galois' research results and published them in his own Journal of Pure and Applied Mathematics * * Journal de Mathé matiques Pures et Appliqué es * *. People summarized Galois' whole set of mathematical thoughts as "Galois Theory". Galois made a unique analysis of the structure of solutions of algebraic equations by means of group theory. A series of algebraic equations, such as the roots of polynomial equations and the impossibility of drawing rulers, can be solved simply and perfectly by using Galois theory. Galois theory played a decisive role in the development of algebra in the future.

Second: the story of the Szekeres couple.

1933, Hungarian mathematician George sekres * * * george szekeres * * was only 22 years old. At that time, he often discussed mathematics with his friends in Budapest, Hungary. There is also a Hungarian-born math geek-erd?s· Parr * * * Paul Elder in this group? It's a great god. But at that time, Ordos was only 20 years old.

At a math party, a beautiful classmate named * * ***EstherKlein*** * came up with a conclusion: draw five points * * * on a plane and any three of them are not * * * lines * * *, then there must be four points, and these four points form a convex quadrilateral. Szekeres and Erdos thought for a long time, but they didn't know how to prove it. So, the beautiful girl proudly announced her proof that the convex of these five points covered the smallest convex polygon of the whole point set, which can only be pentagons, quadrilaterals and triangles. The first two cases need not be discussed, but for the third case, if two points in a triangle are connected into a straight line, then two of the three vertices of the triangle must be on the same side of the straight line, and these four points form a convex quadrilateral.

There are three positions of five points on the plane.

Everyone shouted brilliantly. After that, Erdos and Sai Keres were still obsessed with this problem, so they tried to popularize it. Finally, they published a paper in 1935, which successfully proved a stronger conclusion: for any positive integer n ≥ 3, there is always a positive integer m, so as long as there are m * * * straight lines on the plane and any three points are not * * *, then a convex N polygon can be found. Ordos named this problem "happy ending problem" * * *, because of this problem, a spark broke out between Jeangeorges Szekeres and beautiful classmate Esther Klein, and they got closer and closer, and finally got married on June 1937.

For a given n, we might as well write down the minimum number of points needed as f***n***. Finding the exact value of f***n*** is a great challenge. Since a triangle can be determined by three points of any line on a plane, f***3*** = 3. Esther Klein's conclusion can be simply expressed as f***4*** = 5. Using some slightly complicated methods, it can be proved that f***5*** is equal to 9. In 2006, with the help of computers, people finally proved that f***6*** = 17. What is the value of f * * * n * * for a larger n? Is f * * * n * * accurately expressed? This is one of the unsolved problems in mathematics. After decades, the problem of happy ending is still active in mathematics.

Anyway, the final outcome is really happy. After nearly 70 years of marriage, they have been to Shanghai and Adelaide, and finally settled in Sydney, and they have never been apart. On August 28th, 2005, George and Esther died less than an hour apart.