There is also the proof of inequality in the series. You have no sense of direction. We all know the general conversion methods, but even if you know the methods, you don't know how to convert and where to convert. There are countless directions. If you are not sensitive to numbers, you can't figure it out at all. (Of course, there are only a few routines in the college entrance examination. To sum up, most people can do it, but this is because the routine is rigid and few people can do it outside the routine. There is also the probability problem in permutation and combination, which mainly examines your understanding and sensitivity to numbers. If it is difficult, you can't solve it with those permutation and combination formulas, but you must rely on abstract numerical equivalence ability to solve it. There are many mathematical geniuses who are sensitive to numbers, such as Gauss and Pascal.
But I want to introduce the following Indian genius, a poor boy who was born in a rural area in southern India. He himself has deduced more than 1000 theorems, many of which have been proved in Europe, and many of them have not yet been proved. And he deduced this theorem by intuition rather than logic. He is a brahmin, and he thinks that these intuitions are given to him by God. . The most important thing is that he proved that1+2+3+4+5+... =-112, which really subverts my three views. The sum of all natural numbers is actually equal to a negative value. . . In the infinite world, there are many wonderful unknown secrets waiting for us to explore, thanks to a mathematical genius like Lamanukin who led us to explore the unknown. The following content comes from Baidu Encyclopedia.
Srinivasa Ramanujan is one of the most famous mathematicians in Indian history. He has no formal higher mathematics education and is addicted to number theory, especially the summation formula involving π, prime numbers and other mathematical constants, as well as integer division. I'm used to deriving formulas by intuition (or by leaps and bounds), and I don't like proof (he is often proved right afterwards). The unconfirmed formula he left behind triggered many later studies. 1997 founded Ramanukin Journal and published a research paper on "Mathematics Influenced by Ramanukin". Ramanukin was born in Geraud, Tamil Nadu, southeast India. 1898, when he was ten years old, he entered a middle school in Gombogonan, where he seemed to be exposed to formal mathematics for the first time. 1 1 years old, he had mastered the mathematics knowledge of the tenants living in his house. They are students of public universities. /kloc-When he was 0/3 years old, he mastered the knowledge borrowed from Advanced Trigonometry. His biographer said that his genius began to appear at the age of 14. He not only won honorary certificates and scholarships when he was a student, but also helped the school handle the logistics of distributing 1200 students (with different needs) to 35 teachers. He even finished the test in half the given time, which has shown his proficiency in infinite series. His classmates at that time later recalled: "We, including teachers, seldom understood him and stayed away from him.".
However, Ramanujin was unable to concentrate on other subjects and failed the high school exam. At this time of his life, he was also poor and often went hungry. Adult work in India's adult stage, because married, so I want to find a job. With his mathematical calculation ability, he looked for a job as a scribe everywhere in Chennai (formerly known as Madras). Finally, he got a job and contacted researchers in Cambridge at the suggestion of an Englishman. As an employee of Chennai's chief accounting firm, Lamanukin hopes to devote himself to mathematics without doing other work. He appealed to influential Indians for support, and published some papers in Indian mathematical magazines, but failed to find financial support.
At this time, Sir AshutoshMukherjee is trying to support his cause. 19 13, Lamanukin sent a series of complicated theorems to three Cambridge scholars, H.F. Baker, E.W. Hobson and G.H. Hardy, an academician of Trinity College, only noticed the genius shown in Lamanukin's theorem. Reading a sudden letter from an unknown and untrained Indian mathematician, Hardy and his colleague J.E.Littlewood commented: "No theorem can be put into the highest mathematics exam in the world." Although Hardy was a famous mathematician at that time and an expert in several fields written by Ramanukin, he still said many theorems: "Beat me completely" and "I have never seen anything like it."
As an example of his achievements, Lamanukin gave a beautiful continued fraction: the golden section. In his later years, Lamanukin was seriously ill and Hardy went to visit him. Hardy said, "I came by taxi, and the license plate number is 1729. This number is really boring. I hope this is not a bad sign. " Ramanukin replied: "No, this is an interesting number. 1729 is the smallest number that can be expressed by the sum of two cubes and has two expressions. " (i.e.1729 =13+123 = 93+103. Later, this figure was called the number of taxis. In response to this anecdote, Littlewood said, "Every integer is a friend of Ramanukin." Personality achievement? Including Lamanukin's own discovery and the theorem developed and proved in cooperation with Hardy, the properties of high composite number, integer partition function and its asymptote, Lamanukin θ function.
He also made great breakthroughs and discoveries in the following fields: Galerkin function, modular form, divergent series, hypergeometric series and prime number theory.
Although many propositions can be called Lamanukin conjecture, there is one that is particularly suitable for this title and has great influence in the follow-up work. Ramanukin conjecture is an assertion about the coefficient of τ-function, and it is a typical peak form in modular form theory. This proved to be a result of Weil's conjecture several decades later, and the reduction steps were very complicated. Character evaluation? Ramanukin is a super mathematician born in India in the last thousand years. His intuitive leap even puzzled today's mathematicians. More than 70 years after his death, the secrets buried in his papers are still being excavated. The theorem he discovered was applied to fields that he could hardly imagine when he was alive.