Topic on Project talk:Sandbox/Structured Discussions test

Test content copied from en:Monk

In the following reply I will include a sample work-case taken from recent editing work I was involved in.

THIS IS A SAMPLE TAKEN FROM RECENT WIKIPEDIA WORK I WAS INVOLVED IN.

RFC

Hello Everyone,I prepared a table for Fields Medal page which,in my opinion,would help us to reach a consensus about edits which have to be done to the page.Of course,I did my best to make it as complete as I could.I think it can be replaced with existing table in the article.(I must greatly thank dcljr for proposing a new and excellent table format): RfC started 14:12, 17 August 2014 (UTC)

Year	ICM Location	Medalists[1]	Affiliation (When Awarded)	Birthplace	Current/Last Affiliation	Citation
1936	Oslo, Norway	Lars Ahlfors	University of Helsinki, Finland	Finland	Harvard University, US[2][3]	"Awarded medal for research on covering surfaces related to Riemann surfaces of inverse functions of entire and meromorphic functions. Opened up a new fileds of analysis."
		Jesse Douglas	Massachusetts Institute of Technology, US	United States	City College of New York, US[4][5]	"Did important work of the Plateau problem which is concerned with finding minimal surfaces connecting and determined by some fixed boundary."
1950	Cambridge, US	Laurent Schwartz	University of Nancy, France	France	University of Paris VII, France[6][7]	"Developed the theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics."
		Atle Selberg	Institute for Advanced Study, US	Norway	Institute for Advanced Study, US[8]	"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. Erdös), with a generalization to prime numbers in an arbitrary arithmetic progression."
1954	Amsterdam, Netherland	Kunihiko Kodaira	Institute for Advanced Study, US Princeton University, US	Japan	University of Tokyo, Japan[9]	"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	University of Nancy, France	France	Collège de France, France[10][11]	"Achieved major results on the homotopy groups of spheres, especially in his use of the method of spectral sequences. Reformulated and exented some of the main results of complex variable theory in terms of sheaves."
1958	Edinburgh, UK	Klaus Roth	University College London, UK	Weimar Republic	Imperial College London, UK[12]	"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 Erdös and Turán of 1935)."
		René Thom	University of Strasbourg, France	France	Institut des Hautes Études Scientifiques, France[13]	"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, Sweden	Lars Hörmander	University of Stockholm, Sweden	Sweden	Lund University, Sweden[14]	"Worked in partial diffential 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	Princeton University, US	United States	Stony Brook University, US[15]	"Proved that a 7-dimensional sphere can have several differential structures; this led to the creation of the field of differential topology."
1966	Moscow, USSR	Michael Atiyah	University of Oxford, UK	United Kingdom	University of Edinburgh, UK[16]	"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 Joseph Cohen	Stanford University, US	United States	Stanford University, US[17]	"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	Institut des Hautes Études Scientifiques, France	Weimar Republic	Centre National de la Recherche Scientifique , France[18]	"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 "Tohoku paper""
		Stephen Smale	University of California, Berkeley, US	United States	City University of Hong Kong, Hong Kong[19]	"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, France	Alan Baker	University of Cambridge, UK	United Kingdom	Trinity College, Cambridge, UK[20]	"Generalized the Gelfond-Schneider theorem (the solution to Hilbert's seventh problem). From this work he generated transcendental numbers not previously identified."
		Heisuke Hironaka	Harvard University, US	Japan	Kyoto University, Japan[21][22]	"Generalized work of Zariski who had proved for dimension"
		John G. Thompson	University of Cambridge, UK	United States	University of Cambridge, UK [23]	"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."
		Sergei Novikov	Moscow State University, USSR	USSR	Steklov Mathematical Institute, Russia Moscow State University, Russia University of Maryland-College Park, US[24][25]	"Made important advances in topology, the most well-known being his proof of the topological invariance of the Pontrjagin classes of the differentiable manifold. His work included a study of the cohomology and homotopy of Thom spaces."
1974	Vancouver, Canada	Enrico Bombieri	University of Pisa, Italy	Italy	Institute for Advanced Study, US[26]	"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	Harvard University, US	United States	Brown University, US[27]	"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, Finland	Pierre Deligne	Institut des Hautes Études Scientifiques, France	Belgium	Institute for Advanced Study, US[28]	"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	Princeton University, US	United States	Princeton University, US[29]	"Contributed several innovations that revised the study of multidimensional complex analysis by finding correct generalizations of classical (low-dimensional) results."
		Daniel Quillen	Massachusetts Institute of Technology, US	United States	University of Oxford, UK[30]	"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."
		Grigori Margulis	Princeton University, US	USSR	Yale University, US[31]	"Provided innovative analysis of the structure of Lie groups. His work belongs to combinatorics, differential geometry, ergodic theory, dynamical systems, and Lie groups."
1982	Warsaw, Poland	Alain Connes	Institut des Hautes Études Scientifiques, France	France	Institut des Hautes Études Scientifiques, France Collège de France, France Ohio State University, US[32]	"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	Princeton University, US	United States	Cornell University, US[33]	"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	Institute for Advanced Study, US	China	Harvard University, US[34]	"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, US	Simon Donaldson	University of Oxford, UK	United Kingdom	Imperial College London, UK[35]	"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	Princeton University, US	West Germany	Max Planck Institute for Mathematics, Germany[36]	"Using methods of arithmetic algebraic geometry, he received medal primarily for his proof of the Mordell Conjecture."
		Michael Freedman	University of California, San Diego, US	United States	Template:FlagiconMicrosoft Station Q[37]	"Developed new methods for topological analysis of four-manifolds. One of his results is a proof of the four-dimensional Poincaré Conjecture."
1990	Kyoto, Japan	Vladimir Drinfeld	University of Kharkiv, USSR	USSR	University of Chicago, US[38]	"For his work on quantum groups and for his work in number theory."
		Vaughan F. R. Jones	University of California, Berkeley, US	New Zealand	University of California, Berkeley, US[39], Vanderbilt University, US[40]	"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	Kyoto University, Japan	Japan	Kyoto University, Japan[41]	"for the proof of Hartshorne’s conjecture and his work on the classification of three-dimensional algebraic varieties."
		Edward Witten	Institute for Advanced Study, US	United States	Institute for Advanced Study, US[42]	"... his ability to interpret physical ideas in mathematical form is quite unique."[43]
1994	Zurich, Switzerland	Jean Bourgain	Institut des Hautes Études Scientifiques, France	Belgium	Institute for Advanced Study, France[44]	"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	Paris Dauphine University, France	France	Collège de France, France École polytechnique, France[45]	"... 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	Paris-Sud 11 University, France	France	Collège de France, France[46]	"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."
		Efim Zelmanov	University of California, San Diego, US	USSR	Steklov Mathematical Institute, Russia, University of California, San Diego, US[47]	"For his solution to the restricted Burnside problem."
1998	Berlin, Germany	Richard Borcherds	University of California, Berkeley, US University of Cambridge, UK	South Africa	University of California, Berkeley, US[48]	"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	University of Cambridge, UK	United Kingdom	University of Cambridge, UK[49]	"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."
		Maxim Kontsevich	Institut des Hautes Études Scientifiques, France Rutgers University, US	USSR	Institut des Hautes Études Scientifiques, France Rutgers University, US[50]	"contributions to four problems of geometry"
		Curtis T. McMullen	Harvard University, US	United States	Harvard University, US[51]	"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	Beijing, China	Laurent Lafforgue	Institut des Hautes Études Scientifiques, France	France	Institut des Hautes Études Scientifiques, France[52]	"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 Voevodsky	Institute for Advanced Study, US	USSR	Institute for Advanced Study, US[53]	" 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, Spain	Andrei Okounkov	Princeton University, US	USSR	Columbia University, US[54]	"for his contributions bridging probability, representation theory and algebraic geometry"
		Grigori Perelman	None	USSR	Steklov Mathematical Institute, Russia[55]	"for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow"
		Terence Tao	University of California, Los Angeles, US	Australia	University of California, Los Angeles, US[56]	"for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory "
		Wendelin Werner	Paris-Sud 11 University, France	West Germany	ETH Zurich, Switzerland[57]	"for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory"
2010	Hyderabad, India	Elon Lindenstrauss	Hebrew University of Jerusalem, Israel Princeton University, US	Israel	Hebrew University of Jerusalem, Israel[58]	"For his results on measure rigidity in ergodic theory, and their applications to number theory."
		Ngô Bảo Châu	Paris-Sud 11 University, France Institute for Advanced Study, US	North Vietnam	Paris-Sud 11 University, France University of Chicago, US Vietnam Institute for Advanced Study, Vietnam[59]	"For his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods"
		Stanislav Smirnov	University of Geneva, Switzerland	USSR	University of Geneva, Switzerland[60]	"For the proof of conformal invariance of percolation and the planar Ising model in statistical physics"
		Cédric Villani	École Normale Supérieure de Lyon, France Institut Henri Poincaré, France	France	Lyon University, France Institut Henri Poincaré, France[61]	"For his proofs of nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation."
2014	Seoul, South Korea	Artur Avila	Paris Diderot University, France CNRS, France Instituto Nacional de Matemática Pura e Aplicada, Brazil	Brazil	Paris Diderot University, France CNRS, France Instituto Nacional de Matemática Pura e Aplicada, Brazil[62]	"is awarded a Fields Medal 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	Princeton University, US	Canada	Princeton University, US[63][64]	"is awarded a Fields Medal 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	University of Warwick, UK	Austria	University of Warwick, UK[65][66][67]	"is awarded a Fields Medal for his outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations."
		Maryam Mirzakhani	Stanford University, US	Iran	Stanford University, US[68][69]	"is awarded the Fields Medal for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces."
2018	Rio de Janeiro, Brazil[70]	n/a	n/a	n/a	n/a	n/a