The history of solving equations

Do not underestimate this seemingly ordinary topic, the problem of the solution of the one-dimensional algebraic equation directly leads to the birth of abstract mathematics today.

The solution formula of the one-yuan two-th equation is given by the Arabic mathematician Khwarizmi in the eight or nine century. The nine-chapter arithmetic of China also gives the numerical solution of two-times equation. Of course, in this top foreigner is far ahead: the foreigner gives the analytic solution, the Chinese give the numerical solution, the gap is not a little bit. After a long period of time the discussion of equation was blank, and people never found a solution to the three-dimensional equation. It was not until Europe in the 16th century that people once again hit on the problem.

Start with Tartaglia (Tartaglia). Tartaglia, formerly known as Niccolòfontana, was injured in clashes with the invading French army, leading to unclear speech. Tartaglia is the call of the people to his banter, the literal translation comes to the stuttering person. In any case, the label was set for him. Tartaglia was a poor engineer, librarian, and a self-taught mathematician, who also translated Archimedes and Euclid's manuscripts. The 16th century Renaissance University of Bologna (the oldest university in the world) is known for its open mathematical contests. Through these competitions, university faculty members can gain fame and opportunity to get a promotion. And Tartaglia is in this big environment rise. 1530 Tartaglia claimed to be able to solve a single-element three-time equation for the first time. This is going to get out of the way, because it was a superb technology at the time, just as you claim you are the first martial arts master in Central Plains. Others must not obey. In fact, 20 years ago, Professor Filo of Mister Pollan University found a solution to the three-time equation that was missing two times and passed to his student Fiore before he died. More and more like China's martial arts, two master each hold a half of the cheats, and together can cultivate to the highest, but at the same time who also suspected that the other side kung fu really so high. So in 1535, young, Fiore, challenged Tartaglia in the maths contest at Bologna University. Before the challenge, Tartaglia was prepared, and some even said that he had found the solution of the universal three-time equation that was not missing. So Tartaglia won the game without any difficulty. After that, tartaglia his solution deeply in a poem ... This is no different from the Chinese martial arts world.

At that time a mathematician card when is writing an algebra monograph, hears the news that Tartaglia wins, invites Tartaglia to come to the guest. Cadan repeatedly begged and vowed to secrecy, tartaglia the solution told him. Cadan The general solution of three-time equation and its proof are given. Cadan later published these results in the 1545 Magna ARS, which led him and his students to long debates with the tower. Cadan is a plagiarism, but it cannot be said that there is no credit at all. Card when a smart student called Ferrari, that's right, after seeing the solution of the three-time equation, the solution of the four-time equation was introduced. Ferrari, of course, did not miss the opportunity to fame, he challenged Tartaglia, Tartaglia accepted the challenge, but failed to attend (perhaps know that will lose), Ferrari naturally won the victory (others say that Tartaglia participated in the game and the three-time equation solved faster, But Ferrari accused the other side will not solve the four-time equation, away combat Tartaglia naturally fell to a disadvantage. After that, Tartaglia also lost his job. Tartaglia was penniless when he died. Of course, Ferrari rise, accumulated a lot of wealth. Top three men standing at the pyramid of the three/four equation: Tartaglia, Carlo, Ferrari three people have given an important concept in the human thinkers: imaginary. Don't forget, equation is a virtual root. I am not aware of the height of the three people's conclusions about imaginary numbers. It was not until 1560 that the Italian mathematician Bombelli systematically discussed the general nature of the complex numbers. This is the height of Western thought.

Say two sentences to two people: Bombelli----points out that the problem of the three-angle can be transformed into the three-order equation problem of irreducible condition, which is the basis of the theory to prove that the problem of the ruler-gauge drawing is impossible. Bombelli, known as the last mathematician of the Renaissance, was highly praised by Leibniz. Card when —--illegitimate child, from childhood discrimination and abuse, personality quirks, he in mathematics, philosophy, physics and medicine have a considerable success, but also addicted to astrology and gambling, he predicted (horoscope) September 21, 1576 died, and the day he was still very healthy, so ... Suicide, yes suicide.

17th century ago, the four-time equation solved the problem, what about the five-time equation? Let's start with a paragraph about China. is also involved in China's own cultivation of the top mathematician Hua. Hua's debut was based on the article "Su Jia's five-time formula solution could not be established," Su Jia in the age of information occlusion is not known 100 years ago this problem has been solved. As for Hua Hua's method is not this 100 years ago the method I do not know. A small algebraic equation, involving two top mathematical problems (equation solution, tri-angle), is also quite unexpected. Although these two problems have been solved, it is said that there are still a lot of "civil branch" trying to overthrow, it is really a waste of food.

So the five-time equation has no formula solution, a: No. There are only two genius in this story: Abel and Gamma MabThera. Abel lived 27 years old and destitute. The 19-year-old has proved that more than five times the equation does not exist, because he proposed the "group theory" too leading time, almost no one to talk to him, and finally out of the pocket, only to get the opportunity to fame. But in the end, it was premature to die after a major illness (not knowing that money could not be cured at the time). Two days after his death, the notice came to tell him that he had obtained a position at a university in Berlin. Gamma MabThera is a general theorem for the determination of solutions to algebraic equations. The abelian group theory lays the foundation for the theory of Gamma MabThera. The two are also known as the founders of modern group theory. The theory of gamma MabThera not only proves that there is no formula for the five-time equation, but also proves that there is no solution to the three major mathematical problems in ancient Greece. These problems are: (1) The rules of the three equal arbitrary angle, (2) the circle as a square: that is, make a square, so that it and know the circle area; (3) Cubic: Make a cube, its volume is twice times the known cube. Gamma MabThera This person is more radical and keen on political movements. The first exam university, unprepared, not admitted, the second preparation is full, but somehow still did not. There are legends, he problem-solving ideas too jumping, the examiner can not keep up, resulting in his anger. His revised paper was sent to the Poisson review in 1831. Poisson's careful review of the conclusion is "incomprehensible". "We have done our best to study the proof of Gamma MabThera, and his reasoning is very unclear," he said in a report to the Academy of Sciences. We can't even figure out his proof of mind. "In March 1832, the arrest of Gamma MabThera in political activity was transferred to a private hospital where he fell in love with the Doctor's daughter. He was released one months later. But the doctor's daughter had an ex-boyfriend, so the two men were going to fight. The first night of the duel, he knew he was going to die, because he was a sharpshooter, and he tidied up his manuscript all Night long: "I have no time" on the side of the manuscript. Aged 21 years. This argument is too romantic for a general historian to take seriously. Friends in accordance with his wishes, the paper sent to the great God Gauss and Jacob, all the Liouville, until the final confirmation of the correctness of the results.

This time no formula, all happy, ready to write a second sequel, there will be a formula.

The history of solving equations