Hermit

French mathematician

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synonym Ermett (Hermit) generally refers to Hermit

Charles Hermite (1822-1901) was a French mathematician. Paris Polytechnic School Graduation. Former post College de France 、 Paris Normal University Professor, University of Paris. Academy of France academician. stay Function theory 、 Advanced Algebra 、 differential equation And other aspects.^[1]

Chinese name: Hermit
Foreign name: Charles Hermite
Nationality: France
date of birth: December 24, 1822
Date of death: January 14, 1901

University one is graduated from: Paris Polytechnic School
Occupation: mathematician
Key achievements: Hermite polynomial
one's native heath: Dijoz
Belief: Catholicism
Representative works: Elliptic Function Theory

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Hermit, French mathematician. Born in Jeez, Lorraine. Studying in Paris Engineering University 。 Successively served as tutor of Paris University of Technology Paris Normal University Lecturer Sorbonne University Advanced Algebra Professor. still Royal Society Members French Academy of Sciences academician. He devotes himself to the research of elliptic function theory and its application. The fifth order is established by using elliptic function Solution of the equation ； Effectively studied orthogonality polynomial One of the classes in - Hermite polynomials (also known as Chebyshev polynomials), the similarity between polynomials and multivariable numbers, and the algebraic representation of integers; It is proved that the transcendence I of the number e introduces a special Bilinear form (Hermite type). There are many more Mathematical concept The sum theorem is named after Hermit. E.g. matrix operator , tensor, space, cluster, etc. In addition, classical mathematical analysis Complex function theory , differential and integral equation Theory and geometry are also studied. Author of Elliptic Function Theory《 Analysis Tutorial 》And nearly 200 papers.^[2]

Life experience

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Elmet's father, Ferdinand Hermite, was a person with strong artistic tendencies. He learned engineering At the one not far from Dijoz Salt mine After working for a while, he accepted the invitation of one of his in laws to leave the salt mine to engage in cloth trade, and then left the business to his wife to manage, so that his artistic hobbies could be freely developed. Hermite is the sixth of his seven children. Hermite had a disability in his right leg when he was born. He was lame all his life and had to walk with a cane.

Hermit accepted it from his parents elementary education In 1829, Hermit and his family moved to Nanxi 。 Here, because business activities occupy almost all the time of parents, they send several children to Nanxi Public secondary schools Be a boarder. After graduating from middle school, Hermit went to Paris to continue his studies. He first studied at Henry IV College, and in 1840, he transferred to Louis Grande College, where he applied for the exam Paris Polytechnic School Prepare. This college is where E. Galois read books. Professor Richard, who taught mathematics to Hermit, taught Galois just 15 years ago. Hermit did not prepare for the examination course seriously, but was keen on reading various books. He also studied the famous works of C.F. Gauss very carefully《 Disquisitiones Arithmeticae 》And really mastered it, no matter at that time or later, only a few people really mastered this book; He also read and understood J.L Lagrange (Lagrange) About algebraic equation The works of algebraic solution. He later said, "It was from these two books that I learned algebra." Examination results Professor Richard could not help saying to his father that Hermit was "a young Lagrange" because of his poor but rich mathematical knowledge.

Hermit's first two papers were published in the French New Mathematical Yearbook in 1842, and were written by him when he was studying at the Louis Grande Institute. The first one is Guan Yu Conic curve Of analytic geometry An exercise that did not show creativity; The second chapter shows extraordinary creativity Quintic equation In his paper on the discussion of algebraic solution, he did not know P Ruffini (Ruffini) and N.H Abel (Abel) Radical solution of equation This article was later included in his anthology.

In 1842, Hermit was awarded a lower score of 68th in the total score Paris Polytechnic School Although he was already a mathematician at that time, he was even a mathematician who was much better than some people who tested him. Hermit had only been in the comprehensive engineering school for one year, but he was expelled from the school because of the disability of his right leg. At this time, he was already a little famous in the mathematical world, and had close contacts with J.W. Alexander and J.L.F. Bertrand. He hopes to find a teaching career as a base where he can make a living and continue to engage in research. But this requires a degree, so when he was 24 years old, he had to stop his research work to master those things that he was not interested in. In 1847, he passed the examination and obtained a bachelor's degree.

During this period, his mathematical level has been greatly improved. He has learned about A.L Cauchy (Cauchy) and J Liouville (Liouville) et al General function And familiar with C.G.J Jacobian (Jacobi) About elliptic function And hyperelliptic functions. Hermit combined the above two fields and showed a high degree of mathematical talent. His preliminary work in this field confirmed his position in the mathematical world. In the words of G. Darboux, Hermit was now among the top mathematicians. Hermit's main mathematical work during this period was expressed in his six letters to Jacobi (between 1843 and 1850), and Jacobi published the abstracts of these letters in Crail Magazine and included them in his own works, and also in P.G.L Dirichlet (Dirichlet) later edited in volume 2 of Jacobi's works. Throughout his life, Hermit's correspondence with other mathematicians had a tremendous scientific impact.

Hermit's achievements in mathematics attracted the attention of the academic community. In 1848, he was appointed Paris Polytechnic School Of the entrance examination committee. He was very active in the following 10 years. In 1852, he was elected as an academician of the Paris Academy of Sciences vote 40 of them were obtained.

In 1862, L Pasteur (Pasteur). The Paris Integrated Engineering School has set up a position of teacher director for Ermett. The next year, he was appointed as the examiner of the school. He held this position until 1867, when he succeeded J.M.C. Duhamel as the examiner of the Paris Comprehensive Engineering School Analytics Professor position, and he also became a professor of the Paris Institute of Sciences Algebra Later, he taught analysis. His lecture notes on analysis are famous at home and abroad. In 1876, Hermit resigned from his position in the Paris Comprehensive Engineering School, and in 1897, he resigned from his position in the Paris Institute of Science and retired. He is an honorary member of the academies and societies of many countries and has received many medals. On his 70th birthday in 1892, the European scientific community paid tribute to him. It is said that this is a rare honor for a mathematician.

Elmett's wife is J.L.F. Bertrand's sister, Lonise Bertrand. They have two daughters, one of whom becomes E. Picard's wife. In Paris, Hermit and the famous linguist E. Bournoff is the neighbor, which makes Hermit have Opportunity research Sanskrit Hegu Persia Literature. In 1856, Hermit suffered a serious smallpox Influenced by A.L. Cauchy during his illness, he converted to Catholicism and later became a devout catholic 。 His collection of works was later sorted out by Pickup and published between 1905 and 1917.^[3]

Main contributions

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Hermit's research on pure mathematics and applied mathematics Have conducted a lot of research, including Function theory He has published about 200 books and papers on general theory, special function theory, number theory, algebraic theory and mechanical problems. His main achievements lie in elliptic function theory and its applications. In 1892, he wrote: "I can't leave the elliptical field, where goats are tied, they must eat grass." He created elliptic function He studied the connection with number theory and applied ellipse Modular function Solved the general Quintic equation And the mechanical problems including this function are dealt with. He also proved e's Transcendence And introduction Hermite polynomial And famous all over the world.

In Classic mathematical analysis 、 Complex function theory , differential equation theory and geometry On the other hand, Hermit has also studied. In addition to Hermite polynomials, there are many mathematical concepts and theorems, such as matrices operator , tensors, spaces, clusters, etc., are also named after Hermite.^[4]

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