Descartes' story
17th century French philosopher rene descartes? I once put forward the philosophy of "I think, therefore I am". It has the title of "the father of modern philosophy". Descartes' contribution to mathematics is also indispensable. The plane rectangular coordinate system that everyone learned in middle school is called Cartesian coordinate system. It is said that Descartes once went to Sweden and met the beautiful Swedish princess Christina. Descartes found that Princess Christina was very clever, so he became the princess's math teacher, and they were completely immersed in the world of mathematics.
When the king learned about this, he thought Descartes was not good enough for his daughter. Not only did he forcibly separate them, but he didn't receive all the letters Descartes wrote to the princess. Later Descartes contracted the Black Death and sent the last letter to the princess before he died. This letter contains only one line (r=a( 1-sinθ).
The king and ministers naturally didn't understand what this meant, so they had to return it to the princess. The princess established a polar coordinate system on paper, traced the points of the equation on it with a pen, and finally solved the secret of this line-this is the beautiful heart line. It seems that mathematicians have their own romantic ways.
A= 1
In fact, Descartes and Christina did have a friendship. However, Descartes came to Sweden on 16491October 4 at the invitation of Christina, who had already become the queen of Christina. And Descartes and Christina are mainly talking about philosophical issues. It is recorded that Descartes can only discuss philosophy with Queen Christina at five o'clock in the morning because of her tight schedule. Cold weather and overwork made Descartes unfortunately suffer from pneumonia, which is the real cause of Descartes' death.
Whether the story of the heart line is true or not is left to everyone to judge for themselves.
The story of Galois
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, and the great mathematician Augustine-Louis Cauchy was responsible for reviewing the manuscript. But Cauchy advised him to go back and polish it carefully (he always thought Cauchy had lost or hidden his paper, and the recent archives research of French Academy of Sciences only rehabilitated Cauchy). Later Galois handed the paper to Joseph Fourier, secretary of the Academy of Sciences, 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 he had a premonition of his own death, the night before the duel, Galois stayed up all night and wrote down all his mathematical thoughts, together with three manuscripts, to his friend Chevalier. At the end of the letter, Galois left a will, hoping that Sheva would give the manuscript to Karl Gustav Jacob Jacobi and C.F.Gauss, two great German mathematicians at that time, so that they could publicly express their views on these mathematical theorems and let more people realize the importance of this mathematical theory.
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 mathematician joseph liouville recognized Galois's research results and published them in his own journal Pure and Applied Mathematics. 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.
The story of the Sikes
At a math party, a beautiful classmate named Esther Klein came to the conclusion that if you draw five points on a plane (any three of which are not lines), 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, this beautiful student proudly announced her proof that the convex hull of these five points (the smallest convex polygon covering the whole point set) can only be pentagon, quadrilateral and triangle. 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.
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 points on the plane (and any three points are not * * * lines), 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. F(3) = 3 because any three points on the plane can determine a triangle. Esther Klein's conclusion can be simply expressed as f(4) = 5. With some slightly more 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 there an exact expression for f(n)? 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.