Mathematicians are people who make creative work on the development of world mathematics, and apply their knowledge to their work (especially solving mathematical problems).Mathematicians focus on numbersdata、aggregate、structure、space、change。
Focus on solvingPure mathematicsMathematicians of problems outside the field are called applied mathematicians. They use their special knowledge and professional methods to solve many outstanding problems in the scientific field.Because it focuses on problems in a wide range of fields, theoretical systems, and fixed-point structures.Applied mathematicians often study and formulatemathematical model 。
Chinese name
mathematician
Foreign name
Mathematician
Specific population
People who have done creative work on the development of world mathematics
Early mathematicians were rich in their own families, or attached to the rich and powerful who were interested in research. They studied mathematics more out of interest.In modern times, the profession of mathematician has gradually formed.Their work includes teaching mathematics courses in schools at all levels, guiding graduate students, conducting research in specific fields, and publishing papers and reports.
Mathematical research is not only to understand and sort out known results, but also to create new mathematical achievements and theories.Many people misunderstand that mathematics is a field that has been studied. In fact, there are many unknown fields and problems to be solved in mathematics, and a large number of new mathematical achievements have been published.Some of these mathematical achievements are new mathematical knowledge, and some are new applications.Therefore, mental arithmetic and abacus cannot be regarded as mathematicians, and mathematicians may not be able to make various calculations quickly.People engaged in mathematics related work, such as teaching and science popularization, but not engaged in mathematics research, can be called "mathematics workers" in a broad sense.
It is generally believed that the earliest mathematicians that can be tested in history areancient GreekOfThales。
publish one’s thesis
The main purpose of publishing papers is to facilitate communication between researchers and allow peers to evaluate their own research achievements, which later became the basis for judging the originality and ownership of research achievements (mainly the time sequence).Early academic exchanges could only be conducted orally.Later, scholars began to use letters and manuscripts instead of oral communication.The rise of printing and publishing makes academic works more widely spread.The first work on arithmetic to go to press was published by Treviso in Italy in 1478.EuclidOf《Geometric primitives》It was first published in 1482.
In the 17th century, special academic journals appeared in Europe, such asLeibnizaboutCalculusHis paper was first published in the magazine "ACTA ERUDITORUM" in 1686, as early as 1687NewtonPublish his《Mathematical Principles of Natural Philosophy》。The first special journal of mathematics appeared in 1810 in the French magazine Annals of Pure and Applied Mathematics.So far, there are thousands of mathematical journals in the world, among which the four most famous and authoritative journals includePrinceton UniversityandPrinceton Institute for Advanced StudiesAnnual Journal of Mathematics（Annals of Mathematics），American Mathematical SocietyJournal of the American Mathematical Society,Springer Publishing GroupInventions mathematicae under SPRINGER and ACTA MATHEMATICA sponsored by MITTAG-LEFTER Research Institute in Sweden.
It is generally believed that the more authoritative the magazine, the higher the academic value of the articles published.Mathematics journals (especially pure mathematics) are not very suitable for“Influencing factors”This indicator often appears in journals of other disciplines.As for the order of signatures between collaborators, the mathematical world does not distinguish“First author”, "Second author"“Corresponding author”In general, the authors are listed in alphabetical order of Latin names.
The second largest number of books and papers in history are mathematicians in the 17th centuryEulerHis records were not recognized by Hungarian mathematicians until the 20th centuryPaul Erdos Break.
The International Congress of Mathematicians (ICM) is a quadrennial gathering of the international mathematical community.First meeting in Switzerland in 1897ZurichAt that time, only about 200 people attended.Since then, it has generally been held once every four years, except for a pause during the First and Second World Wars.
Stamps in memory of the International Mathematical Congress
The agenda of the International Conference of Mathematicians is organized byInternational Mathematical UnionAccording to the major achievements and progress in the international frontier work of mathematical science in the past four years, the designated program committee composed of several world famous mathematicians decided to invite a group of mathematicians to give an hour's academic report at the General Assembly and a 45 minute academic report at the group meeting of the discipline group, which enjoyed a high honor in the international mathematical community.
In addition, those who have registered can sign up for a 15 minute special report, which will be arranged by the General Assembly.In 2002, 1114 people made 15 minute group reports and posted 93 posters. The total number of reports (including posters) exceeded 1400.
International Congress of MathematiciansIssued at the opening ceremonyFields Medal It devotes its life to mathematical researchFieldsName the professor.Since its establishment in 1936, the Fields Prize has been awarded by the head of state of the host country every four years at the opening ceremony of the General Assembly. It is only awarded to mathematicians under the age of 40 to recognize important contributions in mathematics.Issued by the International Congress of Mathematicians since 1982Nevanlinna Prize , reward the most outstanding mathematical achievements in the mathematical field of computer science (such as computer science, programming language, algebraic analysis);Issued since 2006Gauss Award, reward important achievements in applied mathematics;Issued from Hyderabad, India in 2010Chern Medal , in recognition of mathematicians with outstanding lifelong achievements in the field of mathematics.[1-3]
Former President Jiang Zemin presented awards to the winners of the Fields Prize[4]
The 2002 International Conference of Mathematicians (ICM2002 for short) was held in Beijing from August 20 to 28, 2002.More than 4000 mathematical workers from all over the world attended the world's highest level mathematical event.The conference received the care of the party and state leaders, the guidance and support of relevant government ministries, and the support of many mathematicians at home and abroad. This conference is the largest international mathematicians conference in history.A total of 4157 mathematics workers from 104 countries and regions attended the meeting, including 1965 mathematics workers from the mainland of China.Former President Jiang Zemin attended the opening ceremony with more than 5000 people.This is the first time that the International Conference of Mathematicians has been held in a developing country, which is of great significance.The success of the conference fully shows the improvement of China's comprehensive national strength, and shows that China's mathematical research level has made great progress after the reform and opening up.[3]
Mathematics Award
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Scientific Breakthrough Award
Founder of Alibaba Group in 2013Jack MaAnd his wife, a famous Russian investorYuri Milner , Chairman of AppleArthur Levinson, andSergey BrinCouples,Mark ZuckerbergCouples and other well-known industrialists funded the establishment of the Science Breakthrough Award.In 2014, the Science Breakthrough Award was awarded its first mathematics award in San Francisco, USA.British mathematician working in the Institute for Advanced Research of Princeton UniversityRichard Taylor , Imperial College LondonSimon Donaldson Maxim Koncevich of the French Institute of Advanced Science, Jacob Lurie of Harvard University, and Australian Chinese mathematician of the University of California, Los AngelesTao ZhexuanProfessors received awards, and each received a prize of up to $3 million.This is the highest prize in the field of science in the world at present, more than double the Nobel Prize of 1.2 million dollars.[5-6]
Millennium Award
Millennium Prize Problems, also known asSeven major mathematical problems in the world, is seven by the United StatesCray Institute of Mathematics(Clay Mathematics Institute, CMI) published the mathematical conjecture on May 24, 2000.According to the rules set by Cray Institute of Mathematics, as long as the solution of any conjecture is published in a mathematical journal, and after a two-year verification period, the solver will be awarded a $1 million prize.
Note: Russian mathematiciansPerelmanIn 2003, the third conjecture was solved: "Poincare conjecture". In 2010, the Clay Institute of Mathematics finally released that Perelman was the first to win the Millennium Prize, but Perelman refused the Millennium Prize and the $1 million prize.
abel prize
Abel(Abel) Award is aNorwayAn award given by the royal family to outstanding mathematicians once a year.In 2001, in memory of the famous Norwegian mathematician in 2002Niels Henrik AbelThe bicentennial birthday,norwegian government Announce that such bonuses will begin to be awarded.One of the reasons for the establishment of this prize is that there is no mathematics prize in the Nobel Prize, and the mathematics prize is established.Issued once a year.Since 2003, a committee composed of five mathematicians from the Norwegian Academy of Natural Sciences and Arts has been responsible for announcing the winners.The bonus is NOK 6 million (about US $1 million), which has been awarded annually since 2003. The bonus is roughly the same asNobel Prizeclose.
In 2003, an Abel Prize for mathematicians with a prize amount of nearly 800000 dollars will be held in NorwayOsloPresented by the professor of the Department of Mathematics of Oslo University who is here today to attend the Congress of the Member States of the International Mathematical UnionStomerThe news was announced.Stomer is one of the five members of the Abel Committee. He hopes that the International Mathematical Union can recommend a candidate to compete for the first Abel Prize.
Winners (3 pieces) recommend a candidate to compete for the first Abel Award.
2005: Peter D. Lax (New York University) (contribution to solving hyperbolic partial differential equations).
In 2006:Lennart Carleson (Royal Swedish Institute of Technology) (for his profound and significant contributions to harmonic analysis and smooth dynamic systems).
2007: American Indian mathematician, professor of New York UniversitySriniva Varadan(Commending him for his outstanding contributions to the study of probability theory).
2008: John Griggs Thompson, professor of University of Florida, USA, and professor of French AcademyJacques Tits (Jacques Tits) (for their achievements in the field of algebra, especially in the field of modern group theory).
2009: French Russian mathematicianMikhail Gromov(In recognition of his contribution to modern geometry).
2010: Algebraic Number Theory and Algebraic Geometry, University of Texas, USAJohn Tate（John Tate）。
2011: Professor Milnor, an American mathematician, in recognition of his pioneering discoveries in topology, geometry and algebra.
2012: Hungarian mathematicianAndre Semeretti(Endre Szemer é di) in recognition of his outstanding contributions to discrete mathematics and theoretical computer science, as well as his profound influence on the number theory and ergodic theory.
2013: Belgian mathematicianDeligne For his pioneering contribution to algebraic geometry and his revolutionary influence on "number theory", "representation theory" and related fields.
2014: Russian mathematicianYakov Sinai(Yakov G. Sinai) in recognition of his outstanding contributions in dynamic systems, ergodicity theory and mathematical physics, with a prize of $1 million.
Gauss Award
Carl Friedrich Gauss Award for Mathematical Applications(Carl Friedrich Gauss Prize) was awarded at the International Conference of Mathematicians, together with the Fields Prize and the Neverliner Prize, to praise mathematicians whose research work has had a profound impact on other fields of mathematics.Unlike the other two awards, the Gauss Award does not set age limits, because the impact of research may take many years to show.This award is based onJohann Carl Friedrich Gauss It is named to commemorate the extensive application of his research in science, engineering and statistics.Awards include medals and bonuses.The bonus amount for 2006 was 10000 euros.The bonus was funded from the surplus of the 1998 International Conference of Mathematicians in Berlin, Germany.
The obverse of the medal is the portrait of Gauss, and the back is a curve passing through the circle and square, representing Gaussleast square methodCalculateCeresTrack.
The first Gauss Award was held in Spain on August 22, 2006MadridAwarded by the International Congress of Mathematicians to Japanese mathematiciansItoqing。
Su Buqing AwardThe ad hoc international prize evaluation committee is responsible for the selection, which is awarded once every four years, one person at a time, and the prize is 1000 dollars.
The first award named after Chinese mathematicians——International Union of Industrial and Applied Mathematics(ICIAM) Su Buqing Award, announced the first list of winners, and Dr. Gilbert Straw of Massachusetts Institute of Technology was awarded this honor.
The International Congress of Industrial and Applied Mathematics, established in 1987, is held every four years and is the highest level of industrial and applied mathematicians' congress.The conference has Lagrange Award, Kurtz Award, Pioneer Award and Maxwell Award.In July 2003, the International Federation of Industrial and Applied Mathematics held the Fifth International Congress of Industrial and Applied Mathematics in Sydney, and established the "Su Buqing Prize" named after the late famous mathematician Su Buqing,It aims to reward individuals who have made outstanding contributions to the application of mathematics to economic take-off and human development - the first international mathematics award named after Chinese mathematicians.
Chern Medal
In 2009, the International Mathematical Union announced its establishment“Chern Medal ”In order to recognize mathematicians who have made outstanding achievements, the winners will receive a prize of 500000 dollars in addition to the medal.The winners of the "Chen Shengshen Award" must donate half of the 250000 yuan to social organizations to promote mathematical research, education and other related activities.Half of the prize belongs to the "organization prize", which is donated to the organization promoting the progress of mathematics according to the will of the winners[7]。
The award is selected every four years, with one winner each time.The first "Chen Shengshen Award" will be awarded at the International Conference of Mathematicians in India in August 2010.This is the first prize of the International Mathematical Union named after a Chinese mathematician.[8]
The International Conference of Mathematicians, founded in 1897 and sponsored by the International Mathematical Union, is the highest level global academic conference in mathematical science.Chen Shengshen was invited to give academic speeches at the International Conference of Mathematicians three times before his death, and helped to hold the conference in China for the first time.
Chen Xingshen studied at Nankai University, Tsinghua University, Hamburg University in Germany, University of Paris in France, and taught at Southwest Associated University, Princeton University in the United States, University of Chicago, and University of California Berkeley. He was the founding director of the former Institute of Mathematics of the Central Academy, the National Institute of Mathematics, and the Nankai Institute of MathematicsYang Zhenning、Liao Shantao、Wu Wenjun、Qiu ChengtongAnd a large number of world-class scientists.[9]
In 2010, the first Chen Shengshen Award was awarded to Louis Nirenberg, an outstanding Canadian mathematician.[1]
In 2014, Philip Griffiths won the second Chen Shengshen Award.[7]
Wolf Prize
On January 1, 1976, Ricardo Wolf and his family donated 10 million dollars to establishWolf FoundationIts purpose is to promote the development of science and art all over the world. The Wolf Prize is a lifelong achievement.
The Wolff Prize is mainly awarded to those who have made outstanding contributions to the promotion of human science and art civilization. It is selected once a year to award those who have made outstanding achievements in the fields of agriculture, chemistry, mathematics, medicine and physics, or in one of the four major projects of architecture, music, painting and sculpture in the field of art.Among themWolf Prize The impact is greatest.
List of Wolf Mathematics Awards
In 1978,Gail Fante(Moscow University), Carl Siegel (Gottingen University).
In 1979,Jean Leray (French Society),Andre Vey(Princeton Institute for Advanced Studies).
In 1980, Henri Gardang (French Society), Kolmogorov (Moscow University).
In 1981,Alfos, Ocsar Zariski (Harvard University).
In 1982,Hassler Whitney (Princeton Institute of Advanced Studies), Mark Krein (Ukrainian Academy of Sciences).
In 1983,Chen Xingshen(University of California, Berkeley), Eldesh (Hungarian Academy of Sciences).
In 2008,Pierre Deligne (Princeton Institute for Advanced Studies),Philip GriffithPhillip Griffiths (Princeton Institute for Advanced Studies), David Mumford (Brown University).
In 2010,Qiu Chengtong(Harvard University, the Chinese University of Hong Kong, Zhejiang University),Dennis Sullivan Dennis Sullivan (Stony Brook University).
Fields Medal
Fields Medal It was first issued by the International Mathematical Union in 1936.[2]
Fields' requirements for winners include a provision that all winners should be no older than 40 years old.French mathematician, winner of the Fields Prize in 1954SearleKeep the record of the minimum age at the time of winning the prize: young mathematicians who are 27 years old and whose winners must be under 40 years old before the New Year's Day of that year.The Fields Prize is a gold medal and a $1500 prize.Award winning mathematician:[2]
Annual location
full name
Native place
Award winning achievements
1936
Oslo
Alfos
Finland, American
Deng Ruowa's conjecture, coverage theory, Riemann surface, complex analysis
Douglas
U.S.A
Solving the problem of Prato minimal surface
1950
Cambridge
Schwarz
France
Generalized function theory
Selberg
Norway, American
Sieve theory, prime number theorem, Riemann hypothesis, harmonic analysis of weakly symmetric Riemann spaces, discontinuous groups and their applications to Dirichlet series, ion groups of continuous groups
The concept of fiber congruence, the homology of fiber, bottom space and whole space, homotopy theory
1958
Edinburgh
Ross
Germany, British
Thue Siegel Ross theorem
Tom
France
Catastrophe theory, topological edge matching theory, singularity theory
1962
Stockholm
Hermander
Sweden
Linear partial differential operator theory, existence of solutions of linear partial differential equations with variable coefficients, pseudo differential operator theory
Milno
U.S.A
Differential Structure on Seven dimensional Sphere in Differential Topology and Negation of Poincare's Main Conjecture
1966
Moscow
atiyah
britain
Atia Singer index theorem, K-theory, fixed point principle
Cohen
U.S.A
Continuity Hypothesis and Independence of ZF System
Grotondick
France
Theoretical system of algebraic geometry, functional analysis, homology algebra
Smail
U.S.A
Generalized Poincare conjecture, modern abstract differential dynamic system theory
1970
Nice
Baker
britain
More than a dozen long-standing problems and quadratic fields in number theory
Hiroshima Pingyou
Japan
Singularity elimination of algebraic varieties of any dimension, general singularity theory
Novikov
Soviet Union
Topological invariance of differential topological edge matching theory, foliation theory, soliton theory, differential manifold rational Pontryagin class
Thompson
U.S.A
Bernside conjecture, Freudian conjecture, finite group theory
1974
Vancouver
Mumford
British, American
Algebraic geometry parametric module theory, geometric invariance theory
Bombieri
Italy
The big screen method of mathematics, 1+3 in Goldbach's conjecture, and the Bernstein conjecture of the minimal surface problem
1978
Helsinki
Feverman
U.S.A
Linear partial differential equations, the dual relationship between Hardy space and bounded mean oscillation function space BMO, and the biholomorphic mapping from strictly pseudoconvex domain with smooth boundary to another can be smoothly extended to the boundary
Deligne
Belgium
weil conjecture
Quillen
U.S.A
Adams conjecture
Magulis
Soviet Union
Selberg conjecture
1983
Warsaw
Connes
France
Operator Algebra and Algebra Classification
Thurston
U.S.A
Topological Classification of Leaf Structure and Three Dimensional Closed Manifold on Three Dimensional Manifold
Qiu Chengtong
Chinese, American
Karabi conjecture in differential geometry, positive mass conjecture in general relativity, high-dimensional Minkowski problem, topology of three-dimensional manifold, minimal surface
1986
Berkeley
Donaldson
britain
Four-dimensional manifold topology
Fartings
Germany
Mordell conjecture in number theory, parameter module space of Abbe family, Riemann Roch theorem of arithmetic surface, p-adic Hodge theory
Friedman
U.S.A
Poincare conjecture of 4-dimensional manifold topology, classification theorem of general 4-dimensional manifold
1990
Tokyo
Derefeld
Soviet Union
Module theory, Hopf theory related to quantum groups
Jones
New Zealand
knot theory
mori
Japan
Classification of 3-dimensional algebraic varieties
The relationship between magic groups and modular functions: moonlight conjecture
Gals
britain
Hyperplane conjecture
Koncevich
Russia
Number of rational curves of algebraic varieties, guess of kink classification
McMullan
U.S.A
Hyperbolic geometry and chaos theory
2002
Beijing
Lafforgue
France
Langlands Program
Vladimir Woowski
Russian, American
Homology Theory of Algebraic Varieties, Milnor Conjecture
2006
Madrid
Andrei Okounkov
Russian, American
Probability Theory, Algebraic Representation Theory and Algebraic Geometry
Perelman
Russia
Geometry and revolutionary insight into the analysis and geometric structure of Ricky flow
Tao Zhexuan
Chinese, American
Partial Differential Equations, Combinatorial Mathematics, Harmonic Analysis and Stacking Number Theory
Wendelin Werner
German, French
Random conformal mapping, geometry of two-dimensional Brownian motion space and conformal field theory
2010
Hyderabad, India
Elon Lindenstrauss
Israel, American
Ergodicity theory
Wu Baozhu
Vietnamese, French
The basic lemma in automorphism theory, the basic lemma of the Langlands Program
Smirnov
Russia
Seepage theory, statistical physics
Villani
France
Boltzmann equation
[1]
Nevanlinna Prize
The Nevanlinna Prize is awarded to those who have made major contributions to mathematics in computer science.
The award was awarded in 1981 byInternational Congress of MathematiciansThe Executive Committee was established.In April 1982, he received a gift from the University of Helsinki, named in memory of the Finnish mathematician Rolf Nevanlinna who died the previous year.The prize is a gold medal and a cash prize, which are awarded every four years at the International Congress of Mathematicians.Winners must be no more than 40 years old in the year of award.
Euler(Leonhard Euler, A.D. 1707-1783), born in Basel, Switzerland, in 1707, entered at the age of 13University of BaselRead and get the most famous mathematician at that timeJohann Bernoulli (Johann Bernoulli, 1667-1748).[10][14]
Euler, an outstanding mathematician
Euler is one of the most prolific outstanding mathematicians in the history of science. He has written 886 books and papers, of which analysis, algebra and number theory account for 40%, geometry 18%, physics and mechanics 28%, astronomy 11%, ballistics, navigation, architecture 3%,Petersburg Academy of SciencesIn order to sort out his works, he has been busy for 47 years.Gauss, a mathematician, once said: "Studying Euler's works is always the best way to understand mathematics".Due to overwork, Euler suffered from eye disease at the age of 28 and eventually lost her sight.After Euler was completely blind, he still studied with memory and mental arithmetic until his death, which lasted for 17 years.Euler's memory and mental calculation ability are rare. He can retell the contents of his notes in his youth. Mental calculation is not limited to simple operations. Advanced mathematics can also be completed by mental calculation.From the age of 19, Lagrange communicated with Euler to discuss the general solution of isoperimetric problems, which led to the birth of variational methods.The isoperimetric problem has been considered by Euler for many years. Lagrange's solution has won Euler's warm praise.On the afternoon of September 18, 1783, Euler invited his friends to dinner to celebrate his success in calculating the law of the rise of the balloon. Shortly after Uranus was discovered, Euler wrote the gist of calculating the orbit of Uranus, and laughed with his grandson. After drinking tea, he suddenly suffered from a disease, his pipe fell from his hand, and murmured, "I am dead." Euler finally "stopped life and calculation."。
Zu Chongzhi
Image of Zu Chong
Zu ChongzhiIt has been calculated that the moon will circle the earth for 27.21223 days, which is almost no error with the modern recognized 27.21222 days.One of the many craters on the moon is named "Zu Chongzhi".Zu Chongzhi also calculated that the pi should be between 3.1415926 and 3.1415927.The "Palace of Discovery" science museum in Paris, France also hasZu ChongzhiHis name and what he foundPiValue juxtaposition.On the gallery wall of the auditorium of Moscow State University, the portraits of famous scientists from all over the world inlaid with colored marble also include the Chinese Zu Chongzhi andLi ShiJane.[10]
Tao ZhexuanHe is an Australian Chinese mathematician and currently teaches atUniversity of CaliforniaDepartment of Mathematics, University of Los Angeles (UCLA).He is engaged in analysis andnumber theoryHe and Ben Green proved in 2004 that there exists a prime arithmetic sequence of arbitrary finite length.He won theFields Medal , is followingQiu ChengtongThe second Chinese who won the award later.
Wu Wenjun
Wu Wenjun, 2000National Highest Science and Technology AwardWinners.Academician Wu Wenjun is a famous mathematician whose research work involves many fields of mathematics.In many years of research, we have achieved fruitful results.Its main achievements are in two fields: topology and mathematical mechanization.He laid the groundwork for topology.His research on demonstrative category and demonstrative category has been called "Wu Formula", "Wu demonstrative category" and "Wu demonstrative category" by the international mathematical community, and has been widely cited by international peers, with far-reaching influence and world-renowned reputation.[15]
Born in Xiushui County, Jiaxing, Zhejiang Province on October 28, 1911, Chinese American, a world-class geometer in the 20th century, he pioneered and led global differential geometry, fiber bundle differential geometry“Declarative class”Research in such fields as the "father of differential geometry" in the world, won the National Science Award of the United States“Wolf Prize ”And the "Run Run Shaw Award" and many other extremely high scientific awards.[7][10]
Quotations of mathematicians
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"Those who do not understand geometry are not allowed to enter"."If anyone does not know that the same side of the diagonal of a square is incommensurable, he is not worthy of the title"Plato
"In the world of mathematics, what matters is not what we know, but how we know it"."All things are numbered"Pythagoras
"Although we are not allowed to see through the secrets of nature's essence so as to know the real causes of phenomena, it may still happen that certain fictional assumptions are enough to explain many phenomena"."Because the structure of the universe is the most perfect and is the creation of the wisest God, if there is no certain maximum or minimum law in the universe, nothing will happen at all"Euler
The essence of mathematics lies in its freedom."In the field of mathematics, the art of asking questions is more important than the art of answering questions." "In the field of mathematics, the art of asking questions is more important than the art of answering questions." --cantor
"No problem can touch people's feelings as deeply as infinity, and few other concepts can stimulate reason to produce fruitful ideas as infinity does. However, no other concept can be expounded as infinity.""As long as a branch of science can raise a large number of questions, it is full of vitality, and the lack of questions indicates the termination or decline of independent development"."Unlimited! No other problem has ever touched the human mind so deeply." "We must know, and we will know." --Hilbert
"Problems are the heart of mathematics"P. R. Halmos
"Mathematics is the key to science"Bacon
"Mathematics is the word God uses to write the universe"Galileo
"Mathematics is accurate and concise in expression, abstract and universal in logic, and flexible in form. It is an ideal tool for communication in the universe"Zhou Haizhong
"Only when a science successfully uses mathematics can it reach the level of real perfection"Marx
"The scientific level of a country can be measured by the mathematics it consumes"Rao
"Some beautiful theorems in mathematics have such characteristics: they are very easy to be summarized from facts, but the proof is extremely deep." "Mathematics is the queen of science; number theory is the queen of mathematics.".This is the motivation for us to continue our research, and it can make us find something. ""If others think about the truth of mathematics as deeply and persistently as I do, they will also find my discovery"Gaussian
"God created integers, and all other numbers are man-made." --Clonek
"The God who rules on Olympus is an eternal number"."God is an arithmetician".
"Mr. Fourier believes that the main purpose of mathematics is to serve mankind and explain natural phenomena; but philosophers like him should know that the only purpose of science is to honor the human mind, so a question about numbers has the same meaning as a question about the universe system." - Jacobi
"A mathematician without a certain popularity of poetry will never become a complete mathematician"."I will never regard my work as a personal matter, nor pursue fame and praise. I just do my best for the progress of the truth. It doesn't matter to me whether it is me or someone else, but the important thing is that it is closer to the truth"Weierstrass
"Pure mathematics is the most original creation of human spirit in its modern development stage." "This is a reliable rule. When the author of mathematical or philosophical works writes in vague and profound words, he is talking nonsense." -Whitehead
"Give me five coefficients, and I will draw an elephant; give me six coefficients, and the elephant will wag its tail." "It would be a serious mistake to think that there is necessity only in geometric proof or in sensory evidence. Give me five coefficients, and I will draw an elephant; give me the sixth coefficient, and the elephant will wag its tail.One must be sure that if he is adding many new terms to science and letting readers continue to study the wonderful and inexhaustible things in front of them, science has made great progress "."A man dies, but his career lasts forever"Cauchy
"Use all the power of the mind to choose the path we should follow.""Mathematics is the most powerful knowledge tool left by human knowledge activities and the root of some phenomena. Mathematics is unchangeable and objective, and God will build the universe with mathematical rules"Descartes
"I don't know what people in the world will think of me; however, I feel that I am just like a child playing on the beach, picking up a relatively smooth pebble and finding a beautiful shell; in front of me, the sea of truth has not been found at all." "The reason why I see farther than Descartes is that I stand on the shoulders of giants.""No great discovery can be made without a bold guess"Newton
"The imaginary number is a wonderful human deity. It seems to be an amphibian between existence and nonexistence." "Things that do not work cannot exist." "After considering a few things, the whole thing comes down to pure geometry, which is a goal of physics and mechanics." --Leibniz
"Read Euler, read Euler, he is our teacher." "The greatest advantage of astronomical science is to eliminate the mistakes caused by ignoring our real relationship with nature. Because social order must be based on this relationship, such mistakes are even more disastrous. Truth and justice are the eternal foundation of social order.I hope we can get rid of this dangerous maxim and say that deception and slavery are sometimes more useful than guaranteeing their happiness!The historical experience of all ages has proved that whoever breaks these sacred laws will be punished "Laplace
"If I inherit considerable wealth, I may not have much value in mathematics."."A man's contribution is strictly inversely proportional to his conceit, which seems to be an axiom of moral conduct"Lagrange
"My success only depends on two things. One is to unswervingly stick to the end; the other is to use your hands to create the figures that come up in your mind." --Mengri
"Sophisticated argumentation is often not achieved overnight, but is the result of people's long-term learning. I also learned slowly, and I will continue to learn." "Learn directly from the masters rather than their students." --Abel
"After all, it is the work of a master, which is extraordinary"Galois
"Choose a certain research object and persevere. You may never reach the end, but you will find something interesting along the way."Klein
"The movement form of thinking is usually like this: conscious research - subconscious activity - conscious research." "Life is a continuous struggle. If we occasionally enjoy peace, it is our ancestors who fought tenaciously. If our spirit and our vigilance relax for a moment, we will lose the achievements our ancestors have won for us.""If we want to foresee the future of mathematics, the appropriate way is to study the history and current situation of the subject"Poincare
"If a person has done excellent mathematical work and wants to attract the attention of the mathematical community, it is really easy. No matter how humble and unknown the person is, he only needs to do one thing: send his statement on the results to the authority in a leading position." --Model
"Mathematicians usually find a theorem by intuition; the result is first likely to him, and then he starts to make a proof." --Hardy
"Science needs experiments. But experiments cannot be absolutely accurate. If there is a mathematical theory, it is completely correct to rely on inference. This is the reason why science cannot leave mathematics. Many basic scientific concepts often need mathematical concepts to express themselves. So mathematicians have a meal, but it is natural that they cannot win Nobel Prizes.""The Nobel Prize is so eye-catching that mathematicians cannot concentrate on their own research." "We appreciate mathematics, and we need mathematics." "The goal of a mathematician is to understand mathematics. The development of mathematics in history has gone two ways: increasing the understanding of known materials, and promoting the scope." --Chen Xingshen
"The simple composition of integers has been the source of mathematical rebirth for centuries." --Berkhov
"Things are related to each other, and each has its own way. So although the branches are divided into different parts, they can share the same knowledge with each other, but only one end of them can be distributed. The reason is explained in words, and when the pictures are broken up, the common people can also be contracted to be comprehensive, and the people who look at them can think too much." --Liu Hui
"Geometry sometimes seems to be ahead of analysis, but in fact, geometry is ahead of analysis, just like a servant walking in front of the master, it is for the master to open the way." "Maybe I can not inappropriately ask for the title of Adam in mathematics, because I believe that mathematical rational creation is named by me (already popular)More than other mathematicians of the same era combined. "--Sylvester
"The numbers in the late order are not supernatural. They are tangible and can be checked, and the numbers can be deduced"Zu Chongzhi
"Travelers who do not cross the bridge without personally checking the soundness of each part of the bridge cannot go far. Even in mathematics, some things have to take risks." --Horace Lamb
Mathematical achievements
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Many research achievements in ancient Chinese arithmetic contain some ideas and methods of later western mathematics, and some modern mathematical research achievements are named after Chinese mathematicians.Here are some important contributions of modern Chinese mathematicians.
Li ShanlanThe research results in the summation of series are named "Li Shanlan Identity"[10]。Hua Luogengbest-known Chinese mathematicianThe research results on complete trigonometric sums are called "Fahrenheit theorem";In addition, he andWang YuanThe method of approximate calculation of multiple integrals is called "Hua Wang method".Su BuqingThe research achievements in affine differential geometry are named "Sugh cone".Xiong QinglaiThe research results of meromorphic functions of whole functions and infinite orders are called "Xiong's infinite order".[10]Chen XingshenThe research results on demonstrative category are called "demonstrative category".Zhou WeiliangThe research achievements in algebraic geometry are called "Zhou's coordinates"; in addition, there are "Zhou's theorem" and "Zhou's ring" named after him.Wu WenjunThe important achievement in topology is named "Wu's Formula", and its method of machine proving geometric theorem is called "Wu's Method".Wang Hao's proposition about mathematical logic is called "Wang's paradox".Ke ZhaoThe research results on Cartland problem are called "Kirschner's theorem";In addition, his research results with mathematician Sun Qi in number theory are called "Ke Sun conjecture".Chen JingrunThe proposition put forward in the study of Goldbach's conjecture is called "Chen's theorem".Yang LeandZhang GuanghouThe research achievements in function theory are called "Yang Zhang Theorem".Lu QikengThe research on constant curvature manifolds is called "Lu's conjecture".Summer WalkThe research achievements in functional integral and invariant measure theory are called "Xia's inequality".Jiang BojuThe research results on the calculation of Nielsen number are called "Jiang's space";In addition, there is "Jiang's subgroup" named after him.Wang XutangThe research results of point set topology are called "Wang's theorem".Hou ZhentingThe research results on Markov processes are internationally named "Hou's theorem".Zhou HaizhongThe research results on the distribution of Mason prime numbers are internationally named "Zhou's conjecture".Yuan YaxiangThe research achievements in nonlinear programming have been internationally named "Yuan's Lemma".[13]
Mathematician story
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Descartes
Descartes (Rene Descartes), a famous French philosopher in the 17th century, once put forward the philosophy of "I think, therefore I am", and has the title of "father of modern philosophy".Descartes' contribution to mathematics is also indispensable. The plane rectangular coordinate system we learned in middle school is called "Cartesian coordinate system".We know that the concept of "variable" was first put forward by the famous mathematician Descartes in the 17th century. We know that the introduction of variable has brought about the emergence and development of a series of major mathematical disciplines such as function theory, equation theory, calculus, etc;It can be seen how significant the value of the proposed variable is.
hearsay,Descartes He once wandered to Sweden and met the beautiful Swedish princess CHRISTINA.Descartes found that Princess Christina was smart and became the princess's math teacher, so they were totally immersed in the world of mathematics.After knowing this, the king thought that Descartes was not worthy of his daughter. He not only forced them apart, but also confiscated all the letters Descartes wrote to the princess later.Later, Descartes caught the Black Death and sent the princess the last letter before he died. There was only one line in the letter: R=A (1-SIN 0).
Naturally, the king and ministers could not understand what this meant, so they had to return it to the princess.The princess set up a polar coordinate system on the paper, traced the points of the equation with a pen, and finally solved the secret of this line of words - this is the beautiful heart-shaped line.It seems that mathematicians also have their own romantic ways.
in fact,Descartes I did know Christina well.However, Descartes came to Sweden on October 4, 1649 at the invitation of Christina, who had become the Queen of Sweden at that time.Moreover, Descartes and Christina mainly talked about philosophical issues.It is recorded that, due to the tight schedule of Queen Christina, Descartes could only discuss philosophy with her at five o'clock in the morning.The cold weather and overwork made Descartes suffer from pneumonia, which is the real cause of death of Descartes.
Galois
GaloisGalois, one of the greatest French mathematicians in the 19th century.When he was 16 years old, he took the entrance examination of Paris Polytechnic Institute. As a result, the examiners did not know what to say because of the big jump in solving the questions during the interview, and finally failed to pass the exam.
In the history of mathematics, Galois is undoubtedly the most legendary and romantic mathematician.At the age of 18, Galois brilliantly solved the top problem in the mathematical world at that time: why there is no general solution for polynomial equations of five or more degrees.He submitted this research result to the French Academy of Sciences, and Augustin Louis Cauchy was responsible for reviewing the manuscript;However, Cauchy suggested that he go back and polish it carefully (he had always thought that Cauchy had lost or hidden the paper, but the recent archives research of the French Academy of Sciences made Cauchy clear).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.In 1831, Galois submitted his paper for the third time. The reviewer at that time was Poisson. He thought Galois's paper was difficult to understand, so he refused to publish it.
Galois was arrested and imprisoned for some extreme political actions.Even in prison, he kept developing his 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 relationship soon broke down.The second month after he was released from prison, Galois decided to fight a political enemy for his beloved girl. Unfortunately, he was shot and died in the hospital the next day.Galois's last words before his death were to his brother Alfred: "Don't cry, I need enough courage to die at the age of 20."
As if feeling his own death, on the night before the duel, Galois wrote all his mathematical thoughts and handed them to his friend Chevalier together with three manuscript papers.At the end of the letter, Galois left a will, hoping that Chevalier would give the manuscript of the paper to Carl Gustav Jacob Jacobi and Carl Friedrich Gauss, two German mathematicians at that time, to let them express their opinions on these mathematical theorems publicly, so that more people would realize the importance of this mathematical theory.
According to Galois's will, Chevalier sent the manuscript to Jacobi and Gauss, but no reply was received.Until 1843, mathematiciansLiouville (Joseph Liouville) just confirmed Galois's research achievements and published them in the Journal de mat é matiques pures et appli - qu é es, which he sponsored.People summarized Galois' whole set of mathematical thoughts as "Galois theory".Galois used the method of group theory to make a unique analysis of the structure of the solution of algebraic equations. A series of algebraic equation solving problems, such as the root of polynomial equation, the impossibility of drawing with ruler and gauge, can be solved with Galois theory to get a simple and perfect solution.Galois theory has played a decisive role in the development of algebra in the future.
Mr. and Mrs. Sekkaresh
Hungarian mathematician in 1933George Szekeres (George Szekeres) is only 22 years old.At that time, he often discussed mathematics with his friends in Budapest, the capital of Hungary.Among these people, there is also a math geek born in Hungary, the great god PAUL ERD Ő S.At that time, however, Eldesh was only 20 years old.
At a math party, a beautiful classmate named Esther Klein put forward the conclusion that if you draw five points (any three points are not collinear) on a plane, there must be four points, which form a convex quadrilateral.Sekkaresh, Eldash and others thought for a long time, but they didn't know how to prove it.So, the beautiful student proudly announced her proof that the convex hull of these five points (the smallest convex polygon covering the entire point set) can only be pentagon, quadrilateral and triangle.The first two cases need not be discussed again. For the third case, if two points in a triangle are connected into a straight line, two of the three vertices of the triangle must be on the same side of the line, and the four points form a convex quadrilateral.Everyone shouted that it was wonderful.After that, Eldesh and Sekalish were still obsessed with this problem, so they tried to promote it.Finally, they published a paper in 1935 and successfully proved a stronger conclusion: for any positive integer N ≥ 3, there is always a positive integer M, so that as long as there are M points on the plane (and any three points are not collinear), then a convex N-polygon can be found from it.Eldash named this question "happy ending problem".
