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长城
长城是中国北方的军事防御工程。秦始皇下令连接并修筑北方长城。
秦始皇
秦始皇，嬴政，秦朝开国皇帝。统一六国后，在北方连接并修筑长城。
Alexander Grothendieck
Alexander Grothendieck, later Alexandre Grothendieck in French (; German: [ˌalɛˈksandɐ ˈɡʁoːtn̩ˌdiːk] ; French: [ɡʁɔtɛndik]; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century. Grothendieck began his productive and public career as a mathematician in 1949. In 1958, he was appointed a research professor at the Institut des hautes études scientifiques (IHÉS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding. He received the Fields Medal in 1966 for advances in algebraic geometry, homological algebra, and K-theory. He later became professor at the University of Montpellier and, while still producing relevant mathematical work, he withdrew from the mathematical community and devoted himself to political and religious pursuits (first Buddhism and later, a more Catholic Christian vision). In 1991, he moved to the French village of Lasserre in the Pyrenees, where he lived in seclusion, still working on mathematics and his philosophical and religious thoughts until his death in 2014.
Peter Gustav Lejeune Dirichlet
Johann Peter Gustav Lejeune Dirichlet (; German: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician. In number theory, he proved special cases of Fermat's Last Theorem and created analytic number theory. In analysis, he advanced the theory of Fourier series and was one of the first to give the modern formal definition of a function. In mathematical physics, he studied potential theory, boundary-value problems, heat diffusion, and hydrodynamics. Although his surname is Lejeune Dirichlet, he is commonly referred to by his mononym Dirichlet, in particular for results named after him.
Hertha Ayrton
Phoebe Sarah Hertha Ayrton (born Phoebe Sarah Marks; 28 April 1854 – 26 August 1923), known in her adult life as Hertha Ayrton, was an English electrical engineer, mathematician, physicist and inventor, and suffragette. She was awarded the Hughes Medal by the Royal Society for her work on electric arcs and ripple marks in sand and water.
Adolphe Quetelet
Lambert Adolphe Jacques Quetelet (French: [kətlɛ] ; 22 February 1796 – 17 February 1874) was a Belgian astronomer, mathematician, statistician, and sociologist who founded and directed the Brussels Observatory and was influential in introducing statistical methods to the social sciences. His name is sometimes spelled with an accent as Quételet. He also founded the science of anthropometry and developed the body mass index (BMI) scale, originally called the Quetelet Index. His work on measuring human characteristic to determine the ideal l'homme moyen ("the average man") played a key role in the origins of eugenics.
Hermann Grassmann
Hermann Günther Grassmann (German: Graßmann, pronounced [ˈhɛʁman ˈɡʏntɐ ˈɡʁasman]; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was little noted until he was in his sixties. His work preceded and exceeded the concept which is now known as a vector space. He introduced the Grassmannian, the space which parameterizes all k-dimensional linear subspaces of an n-dimensional vector space V. In linguistics he helped free language history and structure from each other.
Hermann Minkowski
Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, ETH Zürich, and the University of Göttingen, described variously as German, Polish, Lithuanian-German, or Russian. He created and developed the geometry of numbers and elements of convex geometry, and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity. Minkowski is perhaps best known for his foundational work describing space and time as a four-dimensional space, now known as "Minkowski spacetime", which facilitated geometric interpretations of Albert Einstein's special theory of relativity (1905).
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor ( KAN-tor; German: [ˈɡeːɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfɪlɪp ˈkantoːɐ̯]; 3 March [O.S. 19 February] 1845 – 6 January 1918) was a mathematician who played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware. Originally, Cantor's theory of transfinite numbers was regarded as counter-intuitive – even shocking. This caused it to encounter resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections; see Controversy over Cantor's theory. Cantor, a devout Lutheran Christian, believed the theory had been communicated to him by God. Some Christian theologians (particularly neo-Scholastics) saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God – on one occasion equating the theory of transfinite numbers with pantheism – a proposition that Cantor vigorously rejected. Not all theologians were against Cantor's theory; prominent neo-scholastic philosopher Konstantin Gutberlet was in favor of it, and Cardinal Johann Baptist Franzelin accepted it as a valid theory (after Cantor made some important clarifications). The objections to Cantor's work were occasionally fierce: Leopold Kronecker's public opposition and personal attacks included describing Cantor as a "scientific charlatan", a "renegade" and a "corrupter of youth". Kronecker objected to Cantor's proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable, results now included in a standard mathematics curriculum. Writing decades after Cantor's death, Wittgenstein lamented that mathematics is "ridden through and through with the pernicious idioms of set theory", which he dismissed as "utter nonsense" that is "laughable" and "wrong". Cantor's recurring bouts of depression from 1884 to the end of his life have been blamed on the hostile attitude of many of his contemporaries, though some have explained these episodes as probable manifestations of a bipolar disorder. The harsh criticism has been matched by later accolades. In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer for work in mathematics. David Hilbert defended Cantor's work from its critics by declaring, "No one shall expel us from the paradise that Cantor has created."
Edmund Husserl
Edmund Gustav Albrecht Husserl (Austrian German: [ˈɛdmʊnd ˈhʊsɐl]; 8 April 1859 – 27 April 1938) was an Austrian and German philosopher and mathematician who established the school of phenomenology. In his early work, he elaborated critiques of historicism and of psychologism in logic based on analyses of intentionality. In his mature work, he sought to develop a systematic foundational science based on the so-called phenomenological reduction. Arguing that transcendental consciousness sets the limits of all possible knowledge, Husserl redefined phenomenology as a transcendental idealist philosophy. Husserl's thought profoundly influenced 20th-century philosophy, and he remains a notable figure in contemporary philosophy and beyond. Husserl studied mathematics, taught by Karl Weierstrass and Leo Königsberger, and philosophy taught by Franz Brentano and Carl Stumpf. He taught philosophy as a Privatdozent at Halle from 1887, then as professor, first at Göttingen from 1901, then at Freiburg from 1916 until he retired in 1928, after which he remained highly productive. In 1933, under racial laws of the Nazi Party, Husserl was banned from using the library of the University of Freiburg due to his Jewish family background and months later resigned from the Deutsche Akademie. Following an illness, he died in Freiburg in 1938.
Alexis Clairaut
Alexis Claude Clairaut (; French: [alɛksi klod klɛʁo]; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and physicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Sir Isaac Newton had outlined in the Principia of 1687. Clairaut was one of the key figures in the expedition to the Lapland that helped to confirm Newton's deduction of the figure of the Earth. In that context, Clairaut deduced what is now known as Clairaut's theorem. He also tackled the gravitational three-body problem, being the first to obtain a satisfactory result for the apsidal precession of the Moon's orbit. In mathematics he is also credited with Clairaut's theorem on mixed partial derivatives, Clairaut's equation, and Clairaut's relation in differential geometry.
Hermann Weyl
Hermann Klaus Hugo Weyl ( VILE; German: [vaɪl]; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is associated with the University of Göttingen tradition of mathematics, represented by Carl Friedrich Gauss, David Hilbert and Hermann Minkowski. His research has had major significance for theoretical physics as well as purely mathematical disciplines such as number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years. Weyl contributed to an exceptionally wide range of fields, including works on space, time, matter, philosophy, logic, symmetry and the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. Freeman Dyson wrote that Weyl alone bore comparison with the "last great universal mathematicians of the nineteenth century", Henri Poincaré and David Hilbert. Michael Atiyah commented that whenever he examined a mathematical topic, he found that Weyl had preceded him.
Gerd Faltings
Gerd Faltings (German: [ɡɛʁt ˈfaltɪŋs] ; born 28 July 1954) is a German mathematician known for his work in arithmetic geometry. He was awarded the Fields Medal in 1986 for his proofs of the Mordell conjecture and several related conjectures. He won the Abel Prize in 2026 for these achievements.
John von Neumann
John von Neumann ( von NOY-mən; Hungarian: Neumann János Lajos; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, integrating pure and applied sciences and making major contributions to many fields, including mathematics, physics, economics, computing, and statistics. He was a pioneer in building the mathematical framework of quantum physics, in the development of functional analysis, and in game theory, introducing or codifying concepts including cellular automata, the universal constructor and the digital computer. His analysis of the structure of self-replication preceded the discovery of the structure of DNA. During World War II, von Neumann worked on the Manhattan Project. He developed the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon. Before and after the war, he consulted for many organizations including the Office of Scientific Research and Development, the United States Army's Ballistic Research Laboratory, the Armed Forces Special Weapons Project and the Oak Ridge National Laboratory. At the peak of his influence in the 1950s, he chaired a number of Defense Department committees including the Strategic Missile Evaluation Committee and the ICBM Scientific Advisory Committee. He was also a member of the influential Atomic Energy Commission in charge of all atomic energy development in the country. He played a key role alongside Bernard Schriever and Trevor Gardner in the design and development of the United States' first intercontinental ballistic missile (ICBM) programs. At that time he was considered the nation's foremost expert on nuclear weaponry and the leading defense scientist at the U.S. Department of Defense. Von Neumann's contributions and intellectual ability drew praise from colleagues in physics, mathematics, and beyond. His accolades include a Medal of Freedom and a crater on the Moon named in his honor.
Jean-Baptiste Biot
Jean-Baptiste Biot (; French: [ʒɑ̃ batist bjo]; 21 April 1774 – 3 February 1862) was a French physicist, astronomer, and mathematician who co-discovered the Biot–Savart law of magnetostatics with Félix Savart, established the reality of meteorites, made an early balloon flight, and studied the polarization of light. The biot (a CGS unit of electrical current), the mineral biotite, and Cape Biot in eastern Greenland were named in his honour.
Josef Stefan
Josef Stefan (Slovene: Jožef Štefan; 24 March 1835 – 7 January 1893) was a Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire.
Pierre de Fermat
Pierre de Fermat (; French: [pjɛʁ də fɛʁma]; 17 August 1601 – 12 January 1665) was a French magistrate, polymath, and mathematician credited for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' Arithmetica. He was also a lawyer at the parlement of Toulouse, France, a poet, a skilled Latinist, and a Hellenist.
Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann (12 April 1852 – 6 March 1939) was a German mathematician who proved in 1882 that π (pi) is a transcendental number, meaning it is not a root of any nonzero polynomial with rational coefficients.
János Bolyai
János Bolyai (; Hungarian: [ˈjaːnoʃ ˈboːjɒi]; 15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world.
Leopold Kronecker
Leopold Kronecker (German: [ˈkʁoːnɛkɐ]; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, abstract algebra and logic, and criticized Georg Cantor's work on set theory. Heinrich Weber quoted Kronecker as having said, "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" ("God made the integers, all else is the work of man"). Kronecker was a student and life-long friend of Ernst Kummer.