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Leroy P. Steele Prize

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The Leroy P. Steele Prizes are awarded every year since 1970 by the American Mathematical Society for distinguished research work and writing in the field of mathematics. Since 1993, the awards have been split into three categories: lifetime achievement, mathematical exposition, and research.

The prizes were begun from a bequest of Leroy P. Steele and were set up in honor of George David Birkhoff, William Fogg Osgood and William Caspar Graustein. The way the prizes are awarded was changed in 1976 and 1993, but the initial aim of honoring expository writing as well as research has been retained. The prizes—$10,000 for lifetime achievement,[1] and $5,000 for mathematical exposition[2] and for research[3]—are not given on a strict national basis, but relate to writing in English (originally, or in translation) and mathematical activity in the United States.

Steele Prize for Lifetime Achievement

[edit]

Steele Prize for Mathematical Exposition

[edit]
Year Prizewinner Citation
2026 Michael E. Taylor for his fundamental treatise "Partial Differential Equations, Volumes I-III," published in 1996 as volumes 115-117 of Springer Verlag's Applied Mathematical Sciences series.[4]
2025 James S. Milne for his extensive corpus of excellent expository works provided on his website.[5]
2024 Benson Farb and Dan Margalit for their book A Primer on Mapping Class Groups.[6]
2023 Lawrence C. Evans for his book Partial Differential Equations.[7]
2022 Aise Johan de Jong for being the originator and maintainer of the Stacks Project.
2021 Noga Alon and Joel H. Spencer for their book The Probabilistic Method.[8]
2020 Martin R. Bridson and André Haefliger for their book Metric Spaces of Non-Positive Curvature.[9]
2019 Philippe Flajolet (posthumously) and Robert Sedgewick for their book Analytic Combinatorics,[10] an authoritative and highly accessible compendium of its subject, which demonstrates the deep interface between combinatorial mathematics and classical analysis.
2018 Martin Aigner and Günter M. Ziegler for their book Proofs from THE BOOK.[11]
2017 Dusa McDuff and Dietmar Salamon for their book J-holomorphic Curves and Symplectic Topology.[12]
2016 David A. Cox, John Little and Donal O'Shea for their book Ideals, Varieties, and Algorithms,[13] which has made algebraic geometry and computational commutative algebra accessible not just to mathematicians but to students and researchers in many fields.
2015 Robert Lazarsfeld for his books Positivity in Algebraic Geometry I and II,[14][15] published in 2004. These books were instant classics that have profoundly influenced and shaped research in algebraic geometry over the past decade.
2014 Yuri Burago, Dmitri Burago, Sergei Ivanov for their book A Course in Metric Geometry,[16] in recognition of excellence in exposition and promotion of fruitful ideas in geometry.
2013 John Guckenheimer, Philip Holmes in recognition of their book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields.[17]
2012 Michael Aschbacher, Richard Lyons, Stephen D. Smith, Ronald Solomon for their work The Classification of Finite Simple Groups: Groups of Characteristic 2 Type.[18]
2011 Henryk Iwaniec for his long record of excellent exposition, both in books and in classroom notes.
2010 David Eisenbud for his book Commutative Algebra with a View Toward Algebraic Geometry.[19]
2009 I. G. Macdonald for his book Symmetric Functions and Hall Polynomials.[20]
2008 Neil Trudinger for his book Elliptic Partial Differential Equations of Second Order,[21] written with the late David Gilbarg.
2007 David Mumford for his beautiful expository accounts of a host of aspects of algebraic geometry, including The Red Book of Varieties and Schemes.[22]
2006 Lars Hörmander for his book The Analysis of Linear Partial Differential Operators.[23][24][25][26]
2005 Branko Grünbaum for his book Convex Polytopes.[27]
2004 John Milnor in recognition of a lifetime of expository contributions ranging across a wide spectrum of disciplines including topology, symmetric bilinear forms, characteristic classes, Morse theory, game theory, algebraic K-theory, iterated rational maps... and the list goes on.
2003 John B. Garnett for his book Bounded Analytic Functions.[28]
2002 Yitzhak Katznelson for his book An Introduction to Harmonic Analysis.[29]
2001 Richard Stanley in recognition of the completion of his two-volume work Enumerative Combinatorics.
2000 John H. Conway in recognition of his many expository contributions in automata, the theory of games, lattices, coding theory, group theory, and quadratic forms.
1999 Serge Lang for his many mathematics books. Among Lang's most famous texts are Algebra[30] and Algebraic Number Theory.[31]
1998 Joseph H. Silverman for his books The Arithmetic of Elliptic Curves[32] and Advanced Topics in the Arithmetic of Elliptic Curves.[33]
1997 Anthony W. Knapp for his book Representation Theory of Semisimple Groups,[34] a beautifully written book which starts from scratch but takes the reader far into a highly developed subject.
1996 Bruce Berndt for the four volumes, Ramanujan's Notebooks, parts I, II, III, and IV.[35][36][37][38]
1996 William Fulton for his book Intersection Theory.[39]
1995 Jean-Pierre Serre for his 1970 book Cours d'Arithmétique,[40] with its English translation, published in 1973 by Springer Verlag, A Course in Arithmetic.[41]
1994 Ingrid Daubechies for her book Ten Lectures on Wavelets.[42]
1993 Walter Rudin for his books Principles of Mathematical Analysis[43] and Real and Complex Analysis.[44]

Steele Prize for Seminal Contribution to Research

[edit]
Year Prizewinner Citation
2026[45] László Erdős, Benjamin Schlein, and Horng-Tzer Yau for their three papers "Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices",[46] "Local semicircle law and complete delocalization for Wigner random matrices",[47] and "Universality of random matrices and local relaxation flow".[48]
2025 Kenneth A. Ribet for his paper "A modular construction of unramified p-extensions of Q(μp)".[49]
2024 József Balogh, Robert Morris, and Wojciech Samotij for their paper "Independent sets in hypergraphs".[50]
David Saxton and Andrew Thomason for their paper "Hypergraph containers".[51]
2023 Peter B. Kronheimer and Tomasz S. Mrowka for their paper "Gauge theory for embedded surfaces, I".[52]
2022 Michel Goemans and David P. Williamson for their paper "Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming".[53]
2021 Murray Gerstenhaber for his two papers "The cohomology structure of an associative ring"[54] and "On the deformation of rings and algebras".[55]
2020 Craig Tracy and Harold Widom for their paper "Level-spacing distributions and the Airy kernel".[56]
2019 Haruzo Hida for his highly original paper "Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms".[57]
2018 Sergey Fomin, Andrei Zelevinsky for their paper "Cluster algebras I: Foundations".[58]
2017 Leon Simon for his fundamental contributions to geometric analysis and, in particular, for his paper "Asymptotics for a class of non-linear evolution equations, with applications to geometric problems".[59]
2016 Andrew Majda for his monographs "The existence of multidimensional shock fronts"[60] and "The stability of multidimensional shock fronts".[61]
2015 Rostislav Grigorchuk for his influential paper "Degrees of growth of finitely generated groups and the theory of invariant means",[62] which appeared in Russian in 1984[63] and in English translation a year later. The paper stands as a landmark in the development of the now-burgeoning area of geometric group theory.
2014 Luis Caffarelli, Robert Kohn and Louis Nirenberg for their paper "Partial regularity of suitable weak solutions of the Navier-Stokes equations".[64]
2013 Saharon Shelah for his book Classification Theory and the Number of Non-Isomorphic Models.[65]
2012 William Thurston for his contributions to low dimensional topology, and in particular for a series of highly original papers, starting with "Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds",[66] that revolutionized 3-manifold theory.
2011 Ingrid Daubechies for her paper, "Orthonormal bases of compactly supported wavelets".[67]
2010 Robert Griess for his construction of the "monster" sporadic finite simple group, which he first announced in "A construction of F1 as automorphisms of a 196,883-dimensional algebra"[68] with details published in "The friendly giant".[69]
2009 Richard S. Hamilton for his paper "Three-manifolds with positive Ricci curvature".[70]
2008 Endre Szemerédi for his paper "On sets of integers containing no k elements in arithmetic progression".[71]
2007 Karen Uhlenbeck for her foundational contributions in analytic aspects of mathematical gauge theory. These results appeared in the two papers "Removable singularities in Yang-Mills fields"[72] and "Connections with Lp bounds on curvature".[73]
2006 Clifford S. Gardner, John M. Greene, Martin D. Kruskal, Robert M. Miura for their paper "Korteweg-deVries equation and generalizations. VI. Methods for exact solution".[74]
2005 Robert P. Langlands for his paper "Problems in the theory of automorphic forms".[75] This is the paper that introduced what are now known as the Langlands conjectures.
2004 Lawrence C. Evans and Nicolai V. Krylov for the "Evans-Krylov theorem" as established in the papers "Classical solutions of fully nonlinear convex, second order elliptic equations"[76] and "Boundedly inhomogeneous elliptic and parabolic equations", first published in Russian[77] then translated into English.[78]
2003 Ronald Jensen and Michael Morley to Ronald Jensen for his paper "The fine structure of the constructible hierarchy",[79] and to Michael Morley for his paper "Categoricity in power".[80]
2002 Mark Goresky and Robert MacPherson for their papers "Intersection homology theory"[81] and "Intersection homology II".[82]
2001 Leslie F. Greengard and Vladimir Rokhlin for their paper "A fast algorithm for particle simulations".[83]
2000 Barry Mazur for his paper "Modular curves and the Eisenstein ideal".[84]
1999 Michael G. Crandall for two seminal papers: "Viscosity solutions of Hamilton-Jacobi equations"[85] (joint with Pierre-Louis Lions) and "Generation of semi-groups of nonlinear transformations on general Banach spaces"[86] (joint with Thomas M. Liggett).
1999 John F. Nash for his remarkable paper "The imbedding problem for Riemannian manifolds".[87]
1998 Herbert Wilf and Doron Zeilberger for their paper "Rational functions certify combinatorial identities".[88]
1997 Mikhail Gromov for his paper "Pseudo holomorphic curves in symplectic manifolds",[89] which revolutionized the subject of symplectic geometry and topology and is central to much current research activity, including quantum cohomology and mirror symmetry.
1996 Daniel Stroock and S. R. Srinivasa Varadhan for their four papers "Diffusion processes with continuous coefficients I, II"[90][91], "On the support of diffusion processes with applications to the strong maximum principle",[92] "Diffusion processes with boundary conditions",[93] and their book Multidimensional Diffusion Processes.[94]
1995 Edward Nelson for the following two papers in mathematical physics characterized by leaders of the field as extremely innovative: "A quartic interaction in two dimensions"[95] and "Construction of quantum fields from Markoff fields".[96] In these papers he showed for the first time how to use the powerful tools of probability theory to attack the hard analytic questions of constructive quantum field theory, controlling renormalizations with estimates in the first paper, and in the second turning Euclidean quantum field theory into a subset of the theory of stochastic processes.
1994 Louis de Branges for his proof of the Bieberbach conjecture.[97]
1993 George Daniel Mostow for his book Strong Rigidity of Locally Symmetric Spaces.[98]

Leroy P. Steele Prizes awarded prior to 1993

[edit]
Year Prizewinner Citation
1992 Jacques Dixmier for his books Algèbres de von Neumann (von Neumann Algebras),[99] Les C*-algèbres et leurs représentations (C*-Algebras and Their Representations),[100] and Algèbres enveloppantes (Enveloping Algebras).[101]
James Glimm for his paper "Solutions in the large for nonlinear hyperbolic systems of conservation laws".[102]
Peter Lax for his numerous and fundamental contributions to the theory and applications of linear and nonlinear partial differential equations and functional analysis, for his leadership in the development of computational and applied mathematics, and for his extraordinary impact as a teacher.
1991 Jean-François Trèves for Introduction to Pseudodifferential and Fourier Integral Operators, volumes I and II.[103][104]
Eugenio Calabi for his fundamental work on global differential geometry, especially complex differential geometry.
Armand Borel for his extensive contributions in geometry and topology, the theory of Lie groups, their lattices and representations and the theory of automorphic forms, the theory of algebraic groups and their representations and extensive organizational and educational efforts to develop and disseminate modern mathematics.
1990 R. D. Richtmyer for his book Difference Methods for Initial-Value Problems [105] (second edition with K. W. Morton).
Bertram Kostant for his paper "On the existence and irreducibility of certain series of representations".[106]
Raoul Bott for having been instrumental in changing the face of geometry and topology, with his incisive contributions to characteristic classes, K-theory, index theory, and many other tools of modern mathematics.
1989 Daniel Gorenstein for his book Finite Simple Groups, An Introduction to Their Classification[107] and his two survey articles "The classification of finite simple groups"[108] and "Classifying the finite simple groups".[109]
Alberto Calderón for his paper "Uniqueness in the Cauchy problem for partial differential equations".[110]
Irving Kaplansky for his lasting impact on mathematics, particularly mathematics in America. By his energetic example, his enthusiastic exposition, and his overall generosity, he has made striking changes in mathematics and has inspired generations of younger mathematicians.
1988 Sigurður Helgason for his books Differential Geometry and Symmetric Spaces,[111] Differential Geometry, Lie Groups, and Symmetric Spaces,[112] and Groups and Geometric Analysis.[113]
Gian-Carlo Rota for his paper "On the foundations of combinatorial theory I. Theory of Möbius Functions".[114]
Deane Montgomery for his lasting impact on mathematics, particularly mathematics in America. He is one of the founders of the modern theory of transformation groups and is particularly known for his contributions to the solution of Hilbert's fifth problem.
1987 Martin Gardner for his many books and articles on mathematics and particularly for his column "Mathematical Games" in Scientific American.
Herbert Federer and Wendell Fleming for their pioneering paper "Normal and integral currents".[115]
Samuel Eilenberg for his fundamental contributions to topology and algebra, in particular for his classic papers on singular homology and his work on axiomatic homology theory which had a profound influence on the development of algebraic topology.
1986 Donald E. Knuth for his expository work, The Art of Computer Programming, 3 Volumes (1st Edition 1968, 2nd Edition 1973).
Rudolf E. Kálmán for his two fundamental papers, "A new approach to linear filtering and prediction problems"[116] and "Mathematical description of linear dynamical systems",[117] and for his contribution to a third paper, "New results in linear filtering and prediction theory"[118] (with Richard S. Bucy).
Saunders Mac Lane for his many contributions to algebra and algebraic topology, and in particular for his pioneering work in homological and categorical algebra.
1985 Michael Spivak for his five-volume set, "A Comprehensive Introduction to Differential Geometry" (second edition, Publish or Perish, 1979).
Robert Steinberg for three papers on various aspects of the theory of algebraic groups: "Representations of algebraic groups",[119] "Regular elements of semisimple algebraic groups",[120] and Endomorphisms of Linear Algebraic Groups.[121]
Hassler Whitney for his fundamental work on geometric problems, particularly in the general theory of manifolds, in the study of differentiable functions on closed sets, in geometric integration theory, and in the geometry of the tangents to a singular analytic space.
1984 Elias M. Stein for his book Singular Integrals and the Differentiability Properties of Functions.[122]
Lennart Carleson for his papers "An interpolation problem for bounded analytic functions",[123] "Interpolation by bounded analytic functions and the Corona problem",[124] and "On convergence and growth of partial sums of Fourier series".[125]
Joseph L. Doob for his fundamental work in establishing probability as a branch of mathematics and for his continuing profound influence on its development.
1983 Paul R. Halmos for his many graduate texts in mathematics and for his articles on how to write, talk and publish mathematics.
Stephen Cole Kleene for three important papers which formed the basis for later developments in generalized recursion theory and descriptive set theory: "Arithmetical predicates and function quantifiers"[126], "On the forms of the predicates in the theory of constructive ordinals (second paper)",[127] and "Hierarchies of number-theoretic predicates".[128]
Shiing-Shen Chern for the cumulative influence of his total mathematical work, high level of research over a period of time, particular influence on the development of the field of differential geometry, and influence on mathematics through Ph.D. students.
1982 Lars Ahlfors for his expository work in Complex Analysis,[129] and in Lectures on Quasiconformal Mappings[130] and Conformal Invariants.[131]
Tsit Yuen Lam for his expository work in his book Algebraic Theory of Quadratic Forms,[132] and four of his papers: "K0 and K1 — an introduction to algebraic K-theory",[133] Ten lectures on quadratic forms over fields (1977), Serre's Conjecture,[134] and "The theory of ordered fields".[135]
John W. Milnor for a paper of fundamental and lasting importance, "On manifolds homeomorphic to the 7-sphere".[136]
Fritz John for the cumulative influence of his total mathematical work, high level of research over a period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students.
1981 Oscar Zariski for his work in algebraic geometry, especially his fundamental contributions to the algebraic foundations of this subject.
Eberhard Hopf for three papers of fundamental and lasting importance: "Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differential systems",[137][138] "A mathematical example displaying features of turbulence"[139] and "The partial differential equation ut + uux = μxx".[140]
Nelson Dunford and Jacob T. Schwartz for their three-volume expository book, Linear Operators.[141][142][143]
1980 André Weil for the total effect of his work on the general course of twentieth century mathematics, especially in the many areas in which he has made fundamental contributions.
Harold M. Edwards for mathematical exposition in his books Riemann's Zeta Function[144] and Fermat's Last Theorem.[145]
Gerhard Hochschild for his significant work in homological algebra and its applications.
1979 Antoni Zygmund for his cumulative influence on the theory of Fourier series, real variables, and related areas of analysis.
Robin Hartshorne[146] for his expository research article "Equivalence relations on algebraic cycles and subvarieties of small codimension"[147] and his book Algebraic Geometry.[148]
Joseph J. Kohn for his fundamental papers "Harmonic integrals on strongly pseudo-convex manifolds I, II".[149][150]
Salomon Bochner for his cumulative influence on the fields of probability theory, Fourier analysis, several complex variables, and differential geometry.
Hans Lewy for three fundamental papers: "On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables",[151] "An example of a smooth linear partial differential equation without solution",[152] and "On hulls of holomorphy".[153]
1975 George W. Mackey for his paper "Ergodic theory and its significance for statistical mechanics and probability theory".[154]
H. Blaine Lawson for his paper "Foliations".[155]
Lipman Bers for his paper "Uniformization, moduli, and Kleinian groups".[156]
Martin Davis for his paper "Hilbert's tenth problem is unsolvable".[157]
Joseph L. Taylor for his paper Measure Algebras.[158]
1972 Edward B. Curtis for his paper "Simplicial homotopy theory".[159]
William J. Ellison for his paper "Waring's problem".[160]
Lawrence E. Payne[161] for his paper "Isoperimetric inequalities and their applications".[162]
Dana S. Scott for his paper "A proof of the independence of the continuum hypothesis".[163]
1971 James B. Carrell for his paper, written jointly with Jean Dieudonné, "Invariant theory, old and new".[164]
Jean Dieudonné for his paper "Algebraic geometry"[165] and for his paper, written jointly with James B. Carrell, "Invariant theory, old and new".[164]
Phillip A. Griffiths for his paper "Periods of integrals on algebraic manifolds".[166]
1970 Solomon Lefschetz for his paper "A page of mathematical autobiography".[167]

See also

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References

[edit]
  1. ^ "AMS :: Leroy P. Steele Prize for Lifetime Achievement (1993 - present)". www.ams.org. Retrieved 2026-04-23.
  2. ^ "AMS :: Leroy P. Steele Prize for Mathematical Exposition (1993 - present)". www.ams.org. Retrieved 2026-04-23.
  3. ^ "AMS :: Leroy P. Steele Prize for Seminal Contribution to Research (1993 - present)". www.ams.org. Retrieved 2026-04-23.
  4. ^ Steele Prize for Mathematical Exposition 2026
  5. ^ Milne, James (2025-08-13). "Mathematics -- J.S. Milne". James Milne -- Home Page. Retrieved 2025-11-20.
  6. ^ Farb, Benson; Margalit, Dan (2011). A Primer on Mapping Class Groups. Princeton Mathematical Series. Princeton University Press. ISBN 978-0-69114794-9.
  7. ^ Evans, Lawrence C. (2010) [1998]. Partial Differential Equations. Graduate Studies in Mathematics. Vol. 19 (2nd ed.). Providence: American Mathematical Society. ISBN 978-1-4704-6942-9.
  8. ^ Alon, Noga; Spencer, Joel H. (2016) [1991]. The Probabilistic Method. Wiley Series in Discrete Mathematics and Optimization (4th ed.). Hoboken: John Wiley & Sons. ISBN 978-1-119-06195-3.
  9. ^ Bridson, Martin R.; Haefliger, André (1999). Metric Spaces of Non-Positive Curvature. A Series of Comprehensive Studies in Mathematics. Vol. 319. Springer Berlin, Heidelberg. ISBN 978-3-540-64324-1.
  10. ^ Flajolet, Philippe; Sedgewick, Robert (2009). Analytic Combinatorics. Cambridge University Press. ISBN 978-0-521-89806-5.
  11. ^ Aigner, Martin; Ziegler, Günter M. (2018) [1998]. Proofs from THE BOOK (6th ed.). Springer Berlin, Heidelberg. ISBN 978-3-662-57264-1.
  12. ^ McDuff, Dusa; Salamon, Dietmar (2012) [2004]. J-holomorphic Curves and Symplectic Topology. Colloquium Publications. Vol. 52 (2nd ed.). Providence: American Mathematical Society. ISBN 9781470479831.
  13. ^ Cox, David A.; Little, John; O'Shea, Donald (2016) [1992]. Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics (4th ed.). Springer Cham. ISBN 978-3-319-37427-7.
  14. ^ Lazarsfeld, Robert (2004). Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series. A Series of Modern Surveys in Mathematics. Vol. 48. Springer Berlin, Heidelberg. ISBN 978-3-540-22533-1.
  15. ^ Lazarsfeld, Robert (2004). Positivity in Algebraic Geometry II: Positivity for Vector Bundles, and Multiplier Ideals. A Series of Modern Surveys in Mathematics. Vol. 49. Springer Berlin, Heidelberg. ISBN 978-3-540-22534-8.
  16. ^ Burago, Dmitri; Burago, Yuri; Ivanov, Sergei (2001). A Course in Metric Geometry. Graduate Studies in Mathematics. Vol. 33. Providence: American Mathematical Society. ISBN 978-1-4704-6853-8.
  17. ^ Guckenheimer, John; Holmes, Philip (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Vol. 42. Springer New York. ISBN 978-0-387-90819-9.
  18. ^ Aschbacher, Michael; Lyons, Richard; Smith, Stephen D.; Solomon, Ronald (2011). The Classification of Finite Simple Groups: Groups of Characteristic 2 Type. Mathematical Surveys and Monographs. Vol. 172. Providence: American Mathematical Society. ISBN 9780821853368.
  19. ^ Eisenbud, David (1995). Commutative Algebra with a View Toward Algebraic Geometry. Graduate Texts in Mathematics. Vol. 150. Springer New York. ISBN 978-0-387-94268-1.
  20. ^ Macdonald, I. G. (1995) [1979]. Symmetric Functions and Hall Polynomials. Oxford Mathematical Monographs (2nd ed.). Oxford University Press. ISBN 9780198534891.
  21. ^ Gilbarg, David; Trudinger, Neil S. (2001) [1985]. Elliptic Partial Differential Equations of Second Order. Classics in Mathematics. Vol. 224 (2nd ed.). Springer Berlin, Heidelberg. ISBN 978-3-540-41160-4.
  22. ^ Mumford, David (1999) [1988]. The Red Book of Varieties and Schemes. Lecture Notes in Mathematics. Vol. 1358 (2nd ed.). Springer Berlin, Heidelberg. ISBN 978-3-540-63293-1.
  23. ^ Hörmander, Lars (2003) [1963]. The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis. Classics in Mathematics (2nd ed.). Springer Berlin, Heidelberg. ISBN 978-3-540-00662-6.
  24. ^ Hörmander, Lars (2005) [1963]. The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients. Classics in Mathematics (2nd ed.). Springer Berlin, Heidelberg. ISBN 978-3-540-22516-4.
  25. ^ Hörmander, Lars (2007) [1987]. The Analysis of Linear Partial Differential Operators III: Pseudo-Differential Operators. Classics in Mathematics (2nd ed.). Springer Berlin, Heidelberg. ISBN 978-3-540-49937-4.
  26. ^ Hörmander, Lars (2009) [1987]. The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators. Classics in Mathematics (2nd ed.). Springer Berlin, Heidelberg. ISBN 978-3-642-00117-8.
  27. ^ Grünbaum, Branko (2003) [1967]. Convex Polytopes. Graduate Texts in Mathematics. Vol. 221 (2nd ed.). Springer New York. ISBN 978-0-387-00424-2.
  28. ^ Garnett, John B. (2006) [1981]. Bounded Analytic Functions. Graduate Texts in Mathematics. Vol. 236 (2nd ed.). Springer New York. ISBN 978-0-387-33621-3.
  29. ^ Katznelson, Yitzhak (1976) [1968]. An Introduction to Harmonic Analysis (2nd ed.). New York: Dover Publications. ISBN 9780486633312.
  30. ^ Lang, Serge (2002) [1965]. Algebra. Graduate Texts in Mathematics. Vol. 211 (3rd ed.). Springer New York. ISBN 978-0-387-95385-4.
  31. ^ Lang, Serge (1994). Algebraic Number Theory. Graduate Texts in Mathematics. Vol. 110 (2nd ed.). Springer New York. ISBN 978-0-387-94225-4.
  32. ^ Silverman, Joseph H. (2009) [1986]. The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics. Vol. 106 (2nd ed.). Springer New York. ISBN 978-0-387-09493-9.
  33. ^ Silverman, Joseph H. (1994). Advanced Topics in the Arithmetic of Elliptic Curves. Graduate Texts in Mathematics. Vol. 151. Springer New York. ISBN 978-0-387-94325-1.
  34. ^ Knapp, Anthony W. (2001) [1986]. Representation Theory of Semisimple Groups. Princeton Landmarks in Mathematics (2nd ed.). Princeton University Press. ISBN 9780691090894.
  35. ^ Berndt, Bruce (1985). Ramanujan’s Notebooks, Part I. Springer New York. ISBN 9780387961101.
  36. ^ Berndt, Bruce (1988). Ramanujan’s Notebooks, Part II. Springer New York. ISBN 9780387967943.
  37. ^ Berndt, Bruce (1991). Ramanujan’s Notebooks, Part III. Springer New York. ISBN 9780387975030.
  38. ^ Berndt, Bruce (1993). Ramanujan’s Notebooks, Part IV. Springer New York. ISBN 9780387941097.
  39. ^ Fulton, William (1998) [1984]. Intersection Theory (2nd ed.). Springer New York. ISBN 978-0-387-98549-7.
  40. ^ Serre, Jean-Pierre (1994) [1970]. Cours d'Arithmétique. Collection le Mathématicien (in French) (4th ed.). Paris: Presses Universitaires de France. ISBN 9782130418351.
  41. ^ Serre, Jean-Pierre (1973). A Course in Arithmetic. Graduate Texts in Mathematics. Vol. 7. Springer New York. ISBN 978-0-387-90041-4.
  42. ^ Daubechies, Ingrid (1992). Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics. Vol. 61. Philadelphia: Society for Industrial and Applied Mathematics. ISBN 978-0-89871-274-2.
  43. ^ Rudin, Walter (1976) [1953]. Principles of Mathematical Analysis. International Series in Pure and Applied Mathematics (3rd ed.). New York: McGraw-Hill. ISBN 9780070542358.
  44. ^ Rudin, Walter (1987) [1966]. Real and Complex Analysis. McGraw-Hill Series in Higher Mathematics (3rd ed.). New York: McGraw-Hill. ISBN 9780070542341.
  45. ^ Erdős, Schlein, and Yau to Receive 2026 Steele Prize for Seminal Contribution to Research
  46. ^ Erdős, László; Schlein, Benjamin; Yau, Horng-Tzer (2009). "Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices". Annals of Probability. 37 (3): 815–852. arXiv:0711.1730. doi:10.1214/08-AOP421. JSTOR 30244304. MR 2537522. Zbl 1175.15028.
  47. ^ Erdős, László; Schlein, Benjamin; Yau, Horng-Tzer (2009). "Local semicircle law and complete delocalization for Wigner random matrices". Communications in Mathematical Physics. 287: 641–655. arXiv:0803.0542. doi:10.1007/s00220-008-0636-9.
  48. ^ Erdős, László; Schlein, Benjamin; Yau, Horng-Tzer (2011). "Universality of random matrices and local relaxation flow". Inventiones Mathematicae. 185 (1): 75–119. doi:10.1007/s00222-010-0302-7.
  49. ^ Ribet, Kenneth A. (1976). "A modular construction of unramified p-extensions of Q(μp)". Inventiones Mathematicae. 34 (3): 151–162. doi:10.1007/BF01403065. ISSN 0020-9910.
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