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He was a founder of fields like metamathematics and modern logic.

(Ptolemy's model predicted phases, but timed quite differently fromGalileo's observations.)Since the planets move without friction, their motions offer a pureview of the Laws of Motion; this is one reason that the heliocentricbreakthroughs of Copernicus, Kepler and Newton triggered the advancesin mathematical physics which led to the Scientific Revolution.

Eventually he turned to mathematical biology and made notablecontributions to that field, e.g.

We don't bother with thatbaby stuff around here."

Birkhoff is one of the greatest native-born American mathematiciansever, and did important work in many fields.

Several other important results are named after him, e.g.

Birkhoff's intellectual interests went beyond mathematics; he once wrote"The transcendent importance of love and goodwill in all human relationsis shown by their mighty beneficent effect upon the individual and society."

Weyl studied under Hilbert and became one of the premiermathematicians of the 20th century.

It remains an unsolved problem (likely tobe defeated soon with high-speed computers) whether 78557is the smallest such "Sierpinski number."

Lefschetz was born in Russia, educated as an engineerin France, moved to U.S.A., was severely handicapped in an accident,and then switched to pure mathematics.

Minkowski saidthat his "views of space and time ...

Sierpinski won a gold medal as an undergraduate bymaking a major improvement to a famous theorem by Gaussabout lattice points inside a circle.

This didn't worry Brouwer who once wrote:"The construction itself is an art, its application to the worldan evil parasite."

Noether was an innovative researcherwho was considered the greatest master of abstract algebra ever;her advances included a new theory of ideals, the inverse Galois problem,and the general theory of commutative rings.

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Last Modified: Summer 2013 | | | Powered by

Brouwer is most famous as the founder of Intuitionism,a philosophy of mathematics in sharp contrastto Hilbert's Formalism, but Brouwer's philosophy alsoinvolved ethics and aesthetics and has been compared withthose of Schopenhauer and Nietzsche.

He also worked in analysis, solving the Hausdorff moment problem.

Brouwer is most famous as the founder of Intuitionism,a philosophy of mathematics in sharp contrastto Hilbert's Formalism, but Brouwer's philosophy alsoinvolved ethics and aesthetics and has been compared withthose of Schopenhauer and Nietzsche.

He proved several important theorems, e.g.

He is an honorary member of the Institute of Computational and Applied Mathematics, Greece, as well as an honorary Member of the Philological Society Parnassos, Greece. He is an honorary citizen of Oinousses and of Delphoi.

He is the President of the Governing Body of the National Library of Greece, a member of the Advisory Board of the Goulandris Natural History Museum, a member of the International Advisory Board of the Institute of Mathematical Sciences, Imperial College, UK, and a member of the Advisory Board of the Centre for Nonlinear Mathematics and Applications, Loughborough University, UK. He is or has been a member of the Editorial Board of more than twenty scientific journals, including Proceedings of the Royal Society (Series A), Journal of Mathematical Physics, Selecta Mathematica, Studies in Applied Mathematics and Nonlinearity. He is also Co-Editor in chief of the Journal of Nonlinear Science and Associate Editor of the following three series: Progress in Physics and Mathematical Physics (Birkhauser), Modern Mechanics and Mathematics (CRC) and Publishing Program in Mathematics (de Gruyter).

He has delivered more than 250 invited talks and colloquia at international conferences and major universities including Harvard, Stanford, Princeton, Yale, Berkeley, MIT, Caltech, Columbia, Oxford and Tokyo. Among his recent presentations are the opening address of the 45th Mathematical Olympiad, Greece, 2004, an invited address at the celebration of the Royal Irish Academy for the Bicentennial of W.R. Hamilton, Ireland, 2005, the SIAM Invited Address at the Annual meeting of AMS and MAA, USA, 2006, the opening plenary address of the international conference “Nonlinear Waves - Theory and Applications”, China, 2008, and the opening plenary address at the 2nd World Congress of Controversies in Neurology, 2008. He has also given several presentations addressing relations between mathematics, philosophy and neuroscience, including talks at Oxford, Beijing and the Athens Concert Hall.

He is the author or co-author of three monographs and of more than 250 papers, as well as the co-editor of seven books. He has published in different areas of science ranging from abstract areas such as differential geometry and bi-Hamiltonian structures, to applied areas such as models of chronic myelogenous leukaemia (with J.B. Keller) and protein folding (with I.M. Gel’fand). In particular, he has made seminal contributions in the field of integrability and has played a significant role in the solution of important mathematical problems arising in medical imaging. In the Special Millenium Issue: Mathematical Physics - Past and Future of the Journal of Mathematical Physics, June 2000, which summarised the “most important developments in mathematical physics in the 20th century”, A.S. Fokas was asked to contribute an article on integrability.

Prerequisite(s): Corequisite: MATH 104

Brouwer is often considered the "Father of Topology;"among his important theorems were the Fixed Point Theorem,the "Hairy Ball" Theorem,the Jordan-Brouwer Separation Theorem,and the Invariance of Dimension.

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