Fields medali

Fields medali  — 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 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 Fuqaroligi(mukofot topshirilganda) Ishlagan joyi(mukofot topshirilganda) Ishlagan joyi(hozirgi/soʻnggi) Sabablari 1936 Oslo, Norvegiya Lars Ahlfors Finlandiya Helsinki universiteti, Finlandiya Harvard universiteti, AQSh Jesse Douglas AQSh Massachusetts texnologiya instituti, AQSh New York shahar kolleji, US „Muayyan chegarani bogʻlovchi va shunday chegara orqali belgilanuvchi minimal sathlarni aniqlashga bagʻishlangan Plateau masalasi boʻyicha muhim ishlarni bajargan“. 1950 Cambridge, AQSh Laurent Schwartz Fransiya Nancy universiteti, Fransiya Paris 7 universiteti, Fransiya "Developed the theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics." Atle Selberg Norvegiya Perspektiv tadqiqotlar instituti, AQSh Perspektiv tadqiqotlar instituti, AQSh "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." 1954 Amsterdam, Niderlandiya Kunihiko Kodayra Yaponiya Tokio universiteti, Yaponiya va Perspektiv tadqiqotlar instituti, AQSh Tokio universiteti, Yaponiya "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." Jean-Pierre Serre Fransiya Nancy universiteti, Fransiya Collège de France, Fransiya "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." 1958 Edinburgh, Buyuk Britaniya Klaus Roth Buyuk Britaniya London universitet kolleji, Buyuk Britaniya London imperial kolleji, Buyuk Britaniya "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)." René Thom Fransiya Strasbourg universiteti, Fransiya Oliy ilmiy tadqiqotlar instituti, Fransiya "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." 1962 Stockholm, Shvetsiya Lars Hörmander Shvetsiya Stockholm unviersiteti, Shvetsiya Lund universiteti, Shvetsiya "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." John Milnor AQSh Princeton universiteti, AQSh Stony Brook universiteti, AQSh "Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology." 1966 Moskva, SSSR Michael Atiyah Buyuk Britaniya Oxford unviersiteti, Buyuk Britaniya Edinburgh universiteti, Buyuk Britaniya "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'." Paul Cohen AQSh Stanford universiteti, AQSh Stanford universiteti, AQSh "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." Alexander Grothendieck Hech qanday Oliy ilmiy tadqiqotlar instituti, Fransiya Ilmiy tadqiqotlar milliy instituti, Fransiya "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’." Stephen Smale AQSh California universiteti, Berkeley, AQSh Hong Kong shahar universiteti, Hong Kong "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." 1970 Nice, Fransiya Alan Baker Buyuk Britaniya Cambridge universiteti, Buyuk Britaniya Trinity kolleji, Cambridge, Buyuk Britaniya "Generalized the Gelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified." Heysuke Hironaka Yaponiya Harvard universiteti, AQSh Kyoto universiteti, Yaponiya "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." Sergey Novikov Sovet Ittifoqi Moskva davlat universiteti, SSSR Steklov matematika instituti, Rossiya
Moskva davlat universiteti, Rossiya
Maryland universiteti, AQSh "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." John Thompson AQSh Cambridge universiteti, Angliya Cambridge universiteti, Angliya
Florida universiteti, AQSh "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." 1974 Vancouver, Kanada Enrico Bombieri Italiya Pisa universiteti, Italiya Perspektiv tadqiqotlar instituti, AQSh "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." David Mumford AQSh Harvard universiteti, AQSh Brown universiteti, AQSh "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." 1978 Helsinki, Finlandiya Pierre Deligne Belgiya Oliy ilmiy tadqiqotlar instituti, Fransiya Perspektiv tadqiqotlar instituti, AQSh < "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." Charles Fefferman AQSh Princeton universiteti, AQSh Princeton universiteti, AQSh< "Contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results." Grigoriy Margulis Sovet Ittifoqi Moskva davlat universiteti, SSSR Yale universiteti, AQSh "Provided innovative analysis of the structure of Lie groups. His work belongs to combinatorics, differential geometry, ergodic theory, dynamical systems, and Lie groups." Daniel Quillen AQSh Massachusetts texnologiya instituti, AQSh Oxford universiteti, Angliya "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." 1982 Varshava, Polsha Alain Connes Fransiya Oliy ilmiy tadqiqotlar instituti, Fransiya Oliy ilmiy tadqiqotlar instituti, Fransiya
Collège de France, Fransiya
Ohio davlat universiteti, US "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." William Thurston AQSh Princeton universiteti, AQSh Cornell universiteti, AQSh "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." Shing-Tung Yau Hech qanday Perspektiv tadqiqotlar instituti, AQSh Harvard universiteti, AQSh "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." 1986 Berkeley, AQSh Simon Donaldson AQSh Oxford universiteti, Buyuk Britaniya London imperial kolleji, Buyuk Britaniya Stony Brook University, US "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." Gerd Faltings Germaniya Federativ Respublikasi Princeton universiteti, AQSh Max Planck matematika instituti, Germaniya "Using methods of arithmetic algebraic geometry, he received medal primarily for his proof of the Mordell Conjecture." Michael Freedman AQSh California universiteti, San Diego, AQSh Microsoft Research, AQSh "Developed new methods for topological analysis of four-manifolds. One of his results is a proof of the four-dimensional Poincaré Conjecture." 1990 Kyoto, Yaponiya Vladimir Drinfeld Sovet Ittifoqi B. I. Verkin nomidagi past harorat fizika-texnika instituti, Sovet Ittifoqi Chicago universiteti, AQSh "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, 
Vanderbilt universiteti, AQSh "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 "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 "Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems." 1994 Zurich, Shveysariya Jean Bourgain Belgiya Oliy ilmiy tadqiqotlar instituti, Fransiya Perspektiv tadiqoqotlar instituti, AQSh "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 "... 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 "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 "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 "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 "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 "Contributions to four problems of geometry." Curtis McMullen AQSh Harvard universiteti, AQSh Harvard universiteti, AQSh "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 "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 "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 "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 "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 "For his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory." Wendelin Werner Fransiya Paris-Sud universiteti, Fransiya ETH Zurich, Shveysariya "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 "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 "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
Sankt-Peterburg davlat universiteti, Rossiya "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 "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
Instituto Nacional de Matemática Pura e Aplicada, Braziliya 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." Manjul Bhargava Kanada, AQSh Princeton universiteti, AQSh Princeton universiteti, AQSh "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." Martin Hairer Avstriya Warwick universiteti, Buyuk Britaniya London imperial kolleji, Buyuk Britaniya Maryam Mirzaxoniy Eron Stanford universiteti, AQSh Stanford universiteti, AQSh 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." 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." 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." Akshay Venkatesh Avstraliya Stanford universiteti, AQSh Stanford universiteti, AQSh
Perspektiv tadqiqotlar instituti, AQSh"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." 2022 Helsinki, Finlandiya Hugo Duminil-Copin Institut des Hautes Études Scientifiques, Fransiya 
Geneva universiteti, Shveysariya Institut des Hautes Études Scientifiques, Fransiya 
Geneva universiteti, Shveysariya "For solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four." 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." 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." 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."

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