Fields medali
matematiklarga beriladigan mukofot
Fields medali (talaffuzi: Filds) (inglizcha: Fields Medal) — 40 yoshga toʻlmagan matematiklarga Xalqaro matematika ittifoqi tomonidan beriladigan mukofot. Medal toʻrt yilda bir marta Xalqaro matematiklar kongressida ikki, uch yoki toʻrt matematikka beriladi. Mukofot ittifoqning Xalqaro kongressida topshiriladi.
| Fields medali | |
 Fields mukofoti obversi (oldi) | |
| Mukofot sohasi | Matematika |
| Tashkilotchi | Xalqaro matematika ittifoqi |
| Mamlakat | Oʻzgarib turadi |
| Birinchi berilgan yili | 1936 |
| Oxirgi berilgan yili | 2018 |
| Rasmiy vebsayti | |
|---|---|
Fields medali matematiklarga beriladigan eng yuqori sharaflardan biri hisoblanadi va u „matematiklarning Nobel mukofoti“ deb taʼriflanadi. Ammo ikki mukofot oʻrtasida bir qancha muhim farqlar mavjud, shu jumladan, mukofotlarning berilish surati, mukofotlar soni va laureatlarga qoʻyiladigan cheklovlar. ARWU tomonidan har yili oʻtkaziladigan akademik mukammallik soʻroviga koʻra, Fields medali butun dunyo boʻylab matematika boʻyicha eng aʼlo mukofot sifatida koʻriladi. 2013-2014-yillarda IREG tomonidan oʻtkazilgan yana bir soʻrovda Fields Medali matematika boʻyicha Abel mukofotidan keyingi ikkinchi eng nufuzli xalqaro mukofot deb topildi.
Sovrin 2006-yildan beri 15,000 Kanada dollariga teng boʻlgan pul mukofoti bilan birga beriladi. Mukofot kanadalik matematik John Charles Fields sharafiga nomlangan. Fields mukofotga asos solishda muhim rol oʻynagan. U hatto Fields medali dizaynini ishlab chiqqan va mukofotni moliyalashtirishga muhim hissa qoʻshgan.
Medal birinchi marta 1936-yilda Finlandiya matematigi Lars Ahlfors va amerikalik matematik Jesse Douglasga berilgan. Sovrin 1950-yildan beri har toʻrt yilda bir marta berilib kelinmoqda. Uning maqsadi fanga katta hissa qoʻshgan yosh matematik tadqiqotchilarni eʼtirof etish va qoʻllab-quvvatlashdir. 2014-yilda eronlik matematik Maryam Mirzaxoniy Fields mukofoti bilan taqdirlangan birinchi ayol boʻldi. Bugunga qadar umumiy hisobda 60 kishiga Fields medali topshirildi.
Fields mukofoti sovrindorlari
| Yil | Xalqaro matematiklar kongressi boʻlib oʻtgan joy | Sovrindorlar[1] | Fuqaroligi (mukofot topshirilganda) | Ishlagan joyi (mukofot topshirilganda) | Ishlagan joyi (hozirgi/soʻnggi) | Sabablari |
|---|---|---|---|---|---|---|
| 1936 | Oslo, Norvegiya | Lars Ahlfors | Finlandiya | Helsinki universiteti, Finlandiya | Harvard universiteti, AQSh[2][3] | [4] |
| Jesse Douglas | AQSh | Massachusetts texnologiya instituti, AQSh | New York shahar kolleji, US[5][6] | „Muayyan chegarani bogʻlovchi va shunday chegara orqali belgilanuvchi minimal sathlarni aniqlashga bagʻishlangan Plateau masalasi boʻyicha muhim ishlarni bajargan“. (inglizcha: Did important work on the Plateau problem which is concerned with finding minimal surfaces connecting and determined by some fixed boundary.)[4] | ||
| 1950 | Cambridge, AQSh | Laurent Schwartz | Fransiya | Nancy universiteti, Fransiya | Paris 7 universiteti, Fransiya[7][8] | "Developed the theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics."[9] |
| Atle Selberg | Norvegiya | Perspektiv tadqiqotlar instituti, AQSh | Perspektiv tadqiqotlar instituti, AQSh[10] | "Developed generalizations of the sieve methods of Viggo Brun; achieved major results on zeros of the Riemann zeta function; gave an elementary proof of the prime number theorem (with P. Erdős), with a generalization to prime numbers in an arbitrary arithmetic progression."[9] | ||
| 1954 | Amsterdam, Niderlandiya | Kunihiko Kodayra | Yaponiya | Tokio universiteti, Yaponiya va Perspektiv tadqiqotlar instituti, AQSh[11] | Tokio universiteti, Yaponiya[12] | "Achieved major results in the theory of harmonic integrals and numerous applications to Kählerian and more specifically to algebraic varieties. He demonstrated, by sheaf cohomology, that such varieties are Hodge manifolds."[13] |
| Jean-Pierre Serre | Fransiya | Nancy universiteti, Fransiya | Collège de France, Fransiya[14][15] | "Achieved major results on the homotopy groups of spheres, especially in his use of the method of spectral sequences. Reformulated and extended some of the main results of complex variable theory in terms of sheaves."[13] | ||
| 1958 | Edinburgh, Buyuk Britaniya | Klaus Roth | Buyuk Britaniya | London universitet kolleji, Buyuk Britaniya | London imperial kolleji, Buyuk Britaniya[16] | "Solved in 1955 the famous Thue-Siegel problem concerning the approximation to algebraic numbers by rational numbers and proved in 1952 that a sequence with no three numbers in arithmetic progression has zero density (a conjecture of Erdős and Turán of 1935)."[17] |
| René Thom | Fransiya | Strasbourg universiteti, Fransiya | Oliy ilmiy tadqiqotlar instituti, Fransiya[18] | "In 1954 invented and developed the theory of cobordism in algebraic topology. This classification of manifolds used homotopy theory in a fundamental way and became a prime example of a general cohomology theory."[17] | ||
| 1962 | Stockholm, Shvetsiya | Lars Hörmander | Shvetsiya | Stockholm unviersiteti, Shvetsiya | Lund universiteti, Shvetsiya[19] | "Worked in partial differential equations. Specifically, contributed to the general theory of linear differential operators. The questions go back to one of Hilbert's problems at the 1900 congress."[20] |
| John Milnor | AQSh | Princeton universiteti, AQSh | Stony Brook universiteti, AQSh[21] | "Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology."[20] | ||
| 1966 | Moskva, SSSR | Michael Atiyah | Buyuk Britaniya | Oxford unviersiteti, Buyuk Britaniya | Edinburgh universiteti, Buyuk Britaniya[22] | "Did joint work with Hirzebruch in K-theory; proved jointly with Singer the index theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the 'Lefschetz formula'."[23] |
| Paul Cohen | AQSh | Stanford universiteti, AQSh | Stanford universiteti, AQSh[24] | "Used technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. The latter problem was the first of Hilbert's problems of the 1900 Congress."[23] | ||
| Alexander Grothendieck | Hech qanday | Oliy ilmiy tadqiqotlar instituti, Fransiya | Ilmiy tadqiqotlar milliy instituti, Fransiya[25] | "Built on work of Weil and Zariski and effected fundamental advances in algebraic geometry. He introduced the idea of K-theory (the Grothendieck groups and rings). Revolutionized homological algebra in his celebrated ʻTôhoku paper’."[23] | ||
| Stephen Smale | AQSh | California universiteti, Berkeley, AQSh | Hong Kong shahar universiteti, Hong Kong[26] | "Worked in differential topology where he proved the generalized Poincaré conjecture in dimension n≥5: Every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. Introduced the method of handle-bodies to solve this and related problems."[23] | ||
| 1970 | Nice, Fransiya | Alan Baker | Buyuk Britaniya | Cambridge universiteti, Buyuk Britaniya | Trinity kolleji, Cambridge, Buyuk Britaniya[27] | "Generalized the Gelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified."[28] |
| Heysuke Hironaka | Yaponiya | Harvard universiteti, AQSh | Kyoto universiteti, Yaponiya[29][30] | "Generalized work of Zariski who had proved for dimension ≤ 3 the theorem concerning the resolution of singularities on an algebraic variety. Hironaka proved the results in any dimension."[28] | ||
| Sergey Novikov | Sovet Ittifoqi | Moskva davlat universiteti, SSSR | Steklov matematika instituti, Rossiya Moskva davlat universiteti, RossiyaMaryland universiteti, AQSh [31][32] | "Made important advances in topology, the most well-known being his proof of the topological invariance of the Pontryagin classes of the differentiable manifold. His work included a study of the cohomology and homotopy of Thom spaces."[28] | ||
| John Thompson | AQSh | Cambridge universiteti, Angliya | Cambridge universiteti, Angliya | "Proved jointly with W. Feit that all non-cyclic finite simple groups have even order. The extension of this work by Thompson determined the minimal simple finite groups, that is, the simple finite groups whose proper subgroups are solvable."[28] | ||
| 1974 | Vancouver, Kanada | Enrico Bombieri | Italiya | Pisa universiteti, Italiya | Perspektiv tadqiqotlar instituti, AQSh[34] | "Major contributions in the primes, in univalent functions and the local Bieberbach conjecture, in theory of functions of several complex variables, and in theory of partial differential equations and minimal surfaces – in particular, to the solution of Bernstein's problem in higher dimensions."[35] |
| David Mumford | AQSh | Harvard universiteti, AQSh | Brown universiteti, AQSh[36] | "Contributed to problems of the existence and structure of varieties of moduli, varieties whose points parametrize isomorphism classes of some type of geometric object. Also made several important contributions to the theory of algebraic surfaces."[35] | ||
| 1978 | Helsinki, Finlandiya | Pierre Deligne | Belgiya | Oliy ilmiy tadqiqotlar instituti, Fransiya | Perspektiv tadqiqotlar instituti, AQSh[37] | "Gave solution of the three Weil conjectures concerning generalizations of the Riemann hypothesis to finite fields. His work did much to unify algebraic geometry and algebraic number theory."[38] |
| Charles Fefferman | AQSh | Princeton universiteti, AQSh | Princeton universiteti, AQSh[39] | "Contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results."[38] | ||
| Grigoriy Margulis | Sovet Ittifoqi | Moskva davlat universiteti, SSSR | Yale universiteti, AQSh[40] | "Provided innovative analysis of the structure of Lie groups. His work belongs to combinatorics, differential geometry, ergodic theory, dynamical systems, and Lie groups."[38] | ||
| Daniel Quillen | AQSh | Massachusetts texnologiya instituti, AQSh | Oxford universiteti, Angliya[41] | "The prime architect of the higher algebraic K-theory, a new tool that successfully employed geometric and topological methods and ideas to formulate and solve major problems in algebra, particularly ring theory and module theory."[38] | ||
| 1982 | Varshava, Polsha | Alain Connes | Fransiya | Oliy ilmiy tadqiqotlar instituti, Fransiya | Oliy ilmiy tadqiqotlar instituti, Fransiya Collège de France, FransiyaOhio davlat universiteti, US[42] | "Contributed to the theory of operator algebras, particularly the general classification and structure theorem of factors of type III, classification of automorphisms of the hyperfinite factor, classification of injective factors, and applications of the theory of C*-algebras to foliations and differential geometry in general."[43] |
| William Thurston | AQSh | Princeton universiteti, AQSh | Cornell universiteti, AQSh[44] | "Revolutionized study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry. Contributed idea that a very large class of closed 3-manifolds carry a hyperbolic structure."[43] | ||
| Shing-Tung Yau | Hech qanday | Perspektiv tadqiqotlar instituti, AQSh | Harvard universiteti, AQSh[45] | "Made contributions in differential equations, also to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge–Ampère equations."[43] | ||
| 1986 | Berkeley, AQSh | Simon Donaldson | AQSh | Oxford universiteti, Buyuk Britaniya | London imperial kolleji, Buyuk Britaniya[46] Stony Brook University, US[47] | "Received medal primarily for his work on topology of four-manifolds, especially for showing that there is a differential structure on euclidian four-space which is different from the usual structure."[48] |
| Gerd Faltings | Germaniya Federativ Respublikasi | Princeton universiteti, AQSh | Max Planck matematika instituti, Germaniya[49] | "Using methods of arithmetic algebraic geometry, he received medal primarily for his proof of the Mordell Conjecture."[48] | ||
| Michael Freedman | AQSh | California universiteti, San Diego, AQSh | Microsoft Research, AQSh[50] | "Developed new methods for topological analysis of four-manifolds. One of his results is a proof of the four-dimensional Poincaré Conjecture."[48] | ||
| 1990 | Kyoto, Yaponiya | Vladimir Drinfeld | Sovet Ittifoqi | B. I. Verkin nomidagi past harorat fizika-texnika instituti, Sovet Ittifoqi[51] | Chicago universiteti, AQSh[52] | "For his work on quantum groups and for his work in number theory." |
| Vaughan Jones | Yangi Zelandiya | California universiteti, Berkeley, AQSh | California universiteti, Berkeley, AQSh,[53] | "For his discovery of an unexpected link between the mathematical study of knots – a field that dates back to the 19th century – and statistical mechanics, a form of mathematics used to study complex systems with large numbers of components." | ||
| Shigefumi Mori | Yaponiya | Kyoto universiteti, Yaponiya | Kyoto universiteti, Yaponiya[55] | "For the proof of Hartshorne’s conjecture and his work on the classification of three-dimensional algebraic varieties." | ||
| Edward Witten | AQSh | Perspektiv tadqiqotlar instituti, AQSh | Perspektiv tadqiqotlar instituti, AQSh[56] | "Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems."[57] | ||
| 1994 | Zurich, Shveysariya | Jean Bourgain | Belgiya | Oliy ilmiy tadqiqotlar instituti, Fransiya | Perspektiv tadiqoqotlar instituti, AQSh[58] | "Bourgain's work touches on several central topics of mathematical analysis: the geometry of Banach spaces, convexity in high dimensions, harmonic analysis, ergodic theory, and finally, nonlinear partial differential equations from mathematical physics." |
| Pierre-Louis Lions | Fransiya | Paris-Dauphine universiteti, Fransiya | Collège de France, Fransiya Politexnika maktabi, Fransiya[59] | "... Such nonlinear partial differential equation simply do not have smooth or even C1 solutions existing after short times. ... The only option is therefore to search for some kind of "weak" solution. This undertaking is in effect to figure out how to allow for certain kinds of "physically correct" singularities and how to forbid others. ... Lions and Crandall at last broke open the problem by focusing attention on viscosity solutions, which are defined in terms of certain inequalities holding wherever the graph of the solution is touched on one side or the other by a smooth test function." | ||
| Jean-Christophe Yoccoz | Fransiya | Paris-Sud universiteti, Fransiya | Collège de France, Fransiya[60] | "Proving stability properties - dynamic stability, such as that sought for the solar system, or structural stability, meaning persistence under parameter changes of the global properties of the system." | ||
| Yefim Zelmanov | Rossiya | California universiteti, San Diego, AQSh | Steklov matematik instituti, Rossiya, California universiteti, San Diego, AQSh[61] | "For his solution to the restricted Burnside problem." | ||
| 1998 | Berlin, Germany | Richard Borcherds | Buyuk Britaniya | California universiteti, Berkeley, AQSh Cambridge universiteti, Buyuk Britaniya | California universiteti, Berkeley, AQSh[62] | "For his work on the introduction of vertex algebras, the proof of the Moonshine conjecture and for his discovery of a new class of automorphic infinite products." |
| Timothy Gowers | United Kingdom | University of Cambridge, UK | University of Cambridge, UK[63] | "William Timothy Gowers has provided important contributions to functional analysis, making extensive use of methods from combination theory. These two fields apparently have little to do with each other, and a significant achievement of Gowers has been to combine these fruitfully." | ||
| Maksim Konsevich | Rossiya | Oliy ilmiy tadqiqotlar instituti, Fransiya Rutgers universiteti, AQSh | Oliy ilmiy tadqiqotlar instituti, Fransiya Rutgers uiversiteti, AQSh[64] | "Contributions to four problems of geometry." | ||
| Curtis McMullen | AQSh | Harvard universiteti, AQSh | Harvard universiteti, AQSh[65] | "He has made important contributions to various branches of the theory of dynamical systems, such as the algorithmic study of polynomial equations, the study of the distribution of the points of a lattice of a Lie group, hyperbolic geometry, holomorphic dynamics and the renormalization of maps of the interval." | ||
| 2002 | Pekin, Xitoy | Laurent Lafforgue | Fransiya | Ilmiy tadqiqotlar milliy markazi, Fransiya | Ilmiy tadqiqotlar milliy markazi, Fransiya[66] | "Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups GLr (r≥1) over function fields." |
| Vladimir Voyevodskiy | Rossiya | Perspektiv tadqiqotlar instituti, AQSh | Perspektiv tadqiqotlar instituti, AQSh[67] | "He defined and developed motivic cohomology and the A1-homotopy theory of algebraic varieties; he proved the Milnor conjectures on the K-theory of fields." | ||
| 2006 | Madrid, Ispaniya | Andrey Okunkov | Rossiya | Princeton universiteti, AQSh | Columbia universiteti, AQSh[68] | "For his contributions bridging probability, representation theory and algebraic geometry." |
| Grigoriy Perelman (mukofotni rad etgan) | Rossiya | Hech qanday | Rossiya Fanlar akademiyasining V. A. Steklov nomidagi matematika institutining Sankt-Peterburg boʻlimi, Rossiya[69] | "For his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow." | ||
| Terence Tao | Avstraliya | California universiteti, Los Angeles, AQSh | California universiteti, Los Angeles, AQSh[70] | "For his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory." | ||
| Wendelin Werner | Fransiya | Paris-Sud universiteti, Fransiya | ETH Zurich, Shveysariya[71] | "For his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory." | ||
| 2010 | Haydarobod, Hindiston | Elon Lindenstrauss | Isroil | Quddus yahudiy universiteti, Isroil Princeton universiteti, AQSh | Quddus yahudiy universiteti, Isroil[72] | "For his results on measure rigidity in ergodic theory, and their applications to number theory." |
| Ngo Bao Tyau | Vyetnam, Fransiya | Paris-Sud universiteti, Fransiya Perspektiv tadqiqotlar instituti, AQSh | Chicago universiteti, AQSh Vietnam Institute for Advanced Study, Vietnam[73] | "For his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods." | ||
| Stanislav Smirnov | Rossiya | Geneva universiteti, Shveysariya | Geneva universiteti, Shveysariya | "For the proof of conformal invariance of percolation and the planar Ising model in statistical physics." | ||
| Cédric Villani | Fransiya | Oliy normal maktab, Fransiya Henri Poincaré instituti, Fransiya | Lyon universiteti, Fransiya Henri Poincaré instituti, Fransiya[75] | "For his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation." | ||
| 2014 | Seoul, Janubiy Koreya | Artur Avila | Braziliya, Fransiya | Paris Diderot universiteti, Fransiya Ilmiy tadqiqotlar milliy markazi, Fransiya | Zurich universiteti, Shveysariya Instituto Nacional de Matemática Pura e Aplicada, Braziliya | "For his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle."[76] |
| Manjul Bhargava | Kanada, AQSh | Princeton universiteti, AQSh | Princeton universiteti, AQSh[77][78][79] | "For developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves."[76] | ||
| Martin Hairer | Avstriya | Warwick universiteti, Buyuk Britaniya | London imperial kolleji, Buyuk Britaniya | [76] | ||
| Maryam Mirzaxoniy | Eron | Stanford universiteti, AQSh | Stanford universiteti, AQSh[80][81] | [76] | ||
| 2018 | Rio de Janeiro, Braziliya | Caucher Birkar | Eron, Britaniya | Cambridge universiteti, Britaniya | Cambridge universiteti, Britaniya | "For the proof of the boundedness of Fano varieties and for contributions to the minimal model program."[82] |
| Alessio Figalli | Italiya | Swiss Federal Institute of Technology Zurich, Shveysariya | Swiss Federal Institute of Technology Zurich, Shveysariya | "For contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability."[82] | ||
| Peter Scholze | Germaniya | Bonn universiteti, Germaniya | Bonn universiteti, Germaniya | "For transforming arithmetic algebraic geometry over p-adic fields through his introduction of perfectoid spaces, with application to Galois representations, and for the development of new cohomology theories."[82] | ||
| Akshay Venkatesh | Avstraliya | Stanford universiteti, AQSh | Stanford universiteti, AQSh Perspektiv tadqiqotlar instituti, AQSh[83] | "For his synthesis of analytic number theory, homogeneous dynamics, topology, and representation theory, which has resolved long-standing problems in areas such as the equidistribution of arithmetic objects."[82] | ||
| 2022 | Helsinki, Finlandiya[izoh 1] | Hugo Duminil-Copin | Institut des Hautes Études Scientifiques, Fransiya Geneva universiteti, Shveysariya [86] | Institut des Hautes Études Scientifiques, Fransiya Geneva universiteti, Shveysariya [86] | "For solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four."[87] | |
| June Huh | Princeton universiteti, AQSh | Princeton universiteti, AQSh | "For bringing the ideas of Hodge theory to combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture."[87] | |||
| James Maynard | Oxford universiteti, Buyuk Britaniya | Oxford universiteti, Buyuk Britaniya | "For contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation."[87] | |||
| Marina Vyazovskaya | École Polytechnique Fédérale de Lausanne, Shveysariya | École Polytechnique Fédérale de Lausanne, Shveysariya | "For the proof that the  lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related extremal problems and interpolation problems in Fourier analysis."[87] |
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 | Vikiomborda Fields medali haqida turkum mavjud |
- Rasmiy sahifa (Xalqaro matematika ittifoqi saytida) (Wayback Machine saytida 2018-12-26 sanasida arxivlangan) (ingl.)
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