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Encyclopedia > Michael Atiyah

Sir Michael Francis Atiyah, OM, FRS (b. April 22, 1929) is a Lebanese-British mathematician, widely considered one of the greatest geometers of the 20th century. His path-breaking work with Isadore Singer led to the proof of the Atiyah-Singer index theorem in the 1960s, a result that has helped to pave the way for the development of several branches of mathematics since that time. The Order of Merit is a British and Commonwealth Order bestowed by the Monarch. ... The Fellowship of the Royal Society was founded in 1660. ... is the 112th day of the year (113th in leap years) in the Gregorian calendar. ... Year 1929 (MCMXXIX) was a common year starting on Tuesday (link will display the full calendar) of the Gregorian calendar. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999... Isadore Singer (born 1924) is an Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology. ... In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. ... In the mathematics of manifolds and differential operators, the Atiyah-Singer index theorem is an important unifying result that connects topology and analysis. ... The 1960s decade refers to the years from 1960 to 1969, inclusive. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...


He had also founded, earlier and together with Friedrich Hirzebruch, the study of another major tool in algebraic topology: topological K-theory. It was inspired by Alexander Grothendieck's work on generalising the Riemann-Roch theorem, and has since generated algebraic K-theory and many applications to mathematical physics. Friedrich E.P. Hirzebruch (born 17 October 1927) is a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... In mathematics, topological K-theory is a branch of algebraic topology. ... Alexander Grothendieck (born March 28, 1928 in Berlin, Germany) is one of the most important mathematicians of the 20th century. ... In mathematics, specifically in complex analysis and algebraic geometry, the Riemann-Roch theorem is an important tool in the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. ... In mathematics, algebraic K-theory is an advanced part of homological algebra concerned with defining and applying a sequence Kn(R) of functors from rings to abelian groups, for n = 0,1,2, ... . Here for traditional reasons the cases of K0 and K1 are thought of in somewhat different terms... Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories. ...


In 1966, when he was thirty-seven years old, he was awarded the Fields Medal, for his work in developing K-theory, a generalized Lefschetz fixed-point theorem (jointly with Raoul Bott) and the Atiyah-Singer theorem, for which he also won, in 2004, the Abel Prize jointly with Isadore Singer. Year 1966 (MCMLXVI) was a common year starting on Saturday (link will display full calendar) of the 1966 Gregorian calendar. ... The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years. ... In mathematics, the Lefschetz fixed-point theorem counts the number of fixed points of a mapping from a topological space X to itself (subject to some mild conditions on X), by means of traces of the induced mappings on the homology groups of X. The counting is subject to some... Raoul Bott (Harvard University News Office) Raoul Bott, FRS (born September 24, 1923, died December 20, 2005) was a mathematician known for numerous basic contributions to geometry in its broad sense. ... Year 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... The Abel Prize is awarded annually by the King of Norway to outstanding mathematicians. ... Isadore Singer (born 1924) is an Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology. ...


Among the other prizes he has received are the Feltrinelli Prize from the Accademia Nazionale dei Lincei (1981) and the King Faisal International Prize for Science (1987). The Accademia dei Lincei, (literally the Academy of the Lynxes, but also known as the Lincean Academy), is located at the Palazzo Corsini on the Via della Lungara in Rome, Italy. ... Year 1981 (MCMLXXXI) was a common year starting on Thursday (link displays the 1981 Gregorian calendar). ... Year 1987 (MCMLXXXVII) was a common year starting on Thursday (link displays 1987 Gregorian calendar). ...


Atiyah was knighted in 1983 and made a member of the Order of Merit in 1992. Year 1983 (MCMLXXXIII) was a common year starting on Saturday (link displays the 1983 Gregorian calendar). ... The Order of Merit is a British and Commonwealth Order bestowed by the Monarch. ... Year 1992 (MCMXCII) was a leap year starting on Wednesday (link will display full 1992 Gregorian calendar). ...


He is listed as a Distinguished Supporter of the British Humanist Association. The British Humanist Association is an organisation of the United Kingdom which promotes Humanism. ...

Contents

Biography

Atiyah was born in London to a Scottish mother and Lebanese Arab writer Edward Atiyah. Patrick Atiyah, professor of law, is his brother.[1] He was brought up mostly in Cairo, Egypt and the Sudan. He later went to Manchester Grammar School and then Trinity College, Cambridge. He was a student of W. V. D. Hodge at Cambridge, where he was awarded a doctorate in 1955 for a thesis entitled Some Applications of Topological Methods in Algebraic Geometry. This article is about the capital of England and the United Kingdom. ... This article is about the country. ... Edward Atiyah (1903-64) was born in Lebanon. ... Patrick S. Atiyah QC FBA (born March 5, 1931) is an English lawyer and academic. ... For other uses, see Cairo (disambiguation). ... The Manchester Grammar School (MGS) is an independent boys school (ages 11-18) in Fallowfield, Manchester, England. ... Full name The College of the Holy and Undivided Trinity Motto Virtus vera nobilitas Virtue is true Nobility Named after The Holy Trinity Previous names King’s Hall and Michaelhouse (until merged in 1546) Established 1546 Sister College(s) Christ Church Master The Lord Rees of Ludlow Location Trinity Street... This article is about a mathematician. ... Year 1955 (MCMLV) was a common year starting on Saturday (link displays the 1955 Gregorian calendar). ...


He was one of the founders, with Hirzebruch, of topological K-theory, a branch of algebraic topology. He has collaborated with many other mathematicians, for example with Raoul Bott and Isadore Singer on the Atiyah–Bott fixed-point theorem and related developments leading to the Atiyah-Singer index theorem. This led to work in representation theory, and on the heat equation on manifolds. He later turned to an interest in gauge field theories, particularly Yang-Mills theory, paving the way for the work of others such as Witten. Friedrich E.P. Hirzebruch (born 17 October 1927) is a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. ... Raoul Bott (Harvard University News Office) Raoul Bott, FRS (born September 24, 1923, died December 20, 2005) was a mathematician known for numerous basic contributions to geometry in its broad sense. ... Isadore Singer (born 1924) is an Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology. ... In mathematics, the Atiyah–Bott fixed-point theorem is a general form of Lefschetz fixed-point theorem for smooth manifolds M , which uses an elliptic complex on M. This is a system of elliptic differential operators on vector bundles, which can replace the de Rham complex constructed from smooth differential... In the mathematics of manifolds and differential operators, the Atiyah-Singer index theorem is an important unifying result that connects topology and analysis. ... In mathematics Representation theory is the name given to the study of standard representations of abstract mathematical structures. ... The heat equation is an important partial differential equation which describes the variation of temperature in a given region over time. ... On a sphere, the sum of the angles of a triangle is not equal to 180° (see spherical trigonometry). ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Edward Witten (born August 26, 1951) is an American theoretical physicist and professor at the Institute for Advanced Study. ...


Atiyah's many students include such illustrious mathematicians as Simon Donaldson, Nigel Hitchin, Peter Kronheimer, Graeme Segal, Lisa Jeffrey, Frances Kirwan, who work in gauge theory and symplectic geometry, and Ruth Lawrence, an eighteen year old prodigy at the time of her completion of her PhD. Simon Kirwan Donaldson, born in Cambridge in 1957, is an English mathematician famous for his work on the topology of smooth (differentiable) four-dimensional manifolds. ... Nigel Hitchin (b. ... Peter Benedict Kronheimer is a British mathematician, known for his work on gauge theory and its applications to 3- and 4-dimensional topology. ... Graeme B. Segal is a mathematician at Oxford University. ... Professor Frances Clare Kirwan is a British mathematician, currently a Professor of Mathematics at the University of Oxford. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In mathematics, a symplectic manifold is a smooth manifold equipped with a closed, nondegenerate 2-form. ... Ruth Elke Lawrence (born August 2, 1971) is an Associate Professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology. ...


Career

Atiyah rejuvenated British mathematics during his years at Oxford and Cambridge. He was also the driving force behind the creation of the Isaac Newton Institute for Mathematical Sciences in Cambridge and became its first director. He received the Royal Medal of the Royal Society in 1968 and its Copley Medal in 1988. He served as president of the London Mathematical Society (1974 - 1976). In the 1990s, he has been president of the Royal Society, and master of Trinity College, Cambridge. The University of Oxford (usually abbreviated as Oxon. ... Opened in 1992, the Isaac Newton Institute for Mathematical Sciences is the United Kingdoms de facto national research institute for mathematics and theoretical physics. ... Year 1968 (MCMLXVIII) was a leap year starting on Monday (link will display full calendar) of the Gregorian calendar. ... The Copley Medal is a scientific award for work in any field of science, the highest award granted by the Royal Society of London. ... Year 1988 (MCMLXXXVIII) was a leap year starting on Friday (link displays 1988 Gregorian calendar). ... The London Mathematical Society (LMS) is the leading mathematical society in England. ... Year 1974 (MCMLXXIV) was a common year starting on Tuesday (link will display full calendar) of the 1974 Gregorian calendar. ... Year 1976 Pick up sticks(MCMLXXVI) was a leap year starting on Thursday (link will display full calendar) of the Gregorian calendar. ... For other uses, see Royal Society (disambiguation). ... Full name The College of the Holy and Undivided Trinity Motto Virtus vera nobilitas Virtue is true Nobility Named after The Holy Trinity Previous names King’s Hall and Michaelhouse (until merged in 1546) Established 1546 Sister College(s) Christ Church Master The Lord Rees of Ludlow Location Trinity Street...


Atiyah was also active on the international scene. He has served as president of the Pugwash Conferences on Science and World Affairs. He was responsible for the founding of the InterAcademy Panel on International Issues, a global network of the world's scientific academies which aims to help its member academies to shape public policy in areas related to science. He also instigated the formation of the Association of European Academies (ALLEA), and has played an important role in the shaping of today’s European Mathematical Society (EMS). Pugwash encounter and tour held at the National Accelerator Laboratory, now Fermilab, September 12, 1970. ... The European Mathematical Society (EMS) is an european organization dedicated to the development of mathematics in Europe. ...


Atiyah is now retired and an honorary professor at the University of Edinburgh. He served as Chancellor of the University of Leicester between 1995 and 2005, from where he received a Distinguished Honorary Fellowship in 2007. He has also been professor of mathematics at the Institute for Advanced Study in Princeton, New Jersey. Atiyah has been the president of the Royal Society of Edinburgh since 2005. The University of Edinburgh (Scottish Gaelic: ), founded in 1582,[4] is a renowned centre for teaching and research in Edinburgh, Scotland. ... A Chancellor is the head of a university. ... University of Leicester seen from Victoria Park - Left to right: the Department of Engineering, the Attenborough tower, the Charles Wilson building. ... Year 1995 (MCMXCV) was a common year starting on Sunday (link will display full 1995 Gregorian calendar). ... Year 2005 (MMV) was a common year starting on Saturday (link displays full calendar) of the Gregorian calendar. ... The meaning of the word professor (Latin: one who claims publicly to be an expert) varies. ... Fuld Hall The Institute for Advanced Study is a private institution in Princeton Township, New Jersey, U.S.A., designed to foster pure cutting-edge research by scientists and scholars in a variety of fields without the complications of teaching or funding, or the agendas of sponsorship. ... Nassau Street, Princetons main street. ... The Royal Society of Edinburghs Building on the corner of George St. ... Year 2005 (MMV) was a common year starting on Saturday (link displays full calendar) of the Gregorian calendar. ...


In 2004 he was awarded The Abel Prize for mathematics together with Isadore M. Singer from MIT. Isadore Singer (born 1924) is an Institute Professor in the Department of Mathematics at the Massachusetts Institute of Technology. ... Mapúa Institute of Technology (MIT, MapúaTech or simply Mapúa) is a private, non-sectarian, Filipino tertiary institute located in Intramuros, Manila. ...


His Erdős number is 3, via a chain of collaborations involving Laurel A. Smith and Persi Diaconis. He is a foreign member of the Russian Academy of Sciences. The ErdÅ‘s number, honouring the late Hungarian mathematician Paul ErdÅ‘s, one of the most prolific writers of mathematical papers, is a way of describing the collaborative distance, in regard to mathematical papers, between an author and ErdÅ‘s. ... Persi Diaconis at Stanford (Summer 2004). ... Russian Academy of Sciences: main building Russian Academy of Sciences (Росси́йская Акаде́мия Нау́к) is the national academy of Russia. ...


Professor Atiyah is a Distinguished Supporter of the British Humanist Association. The British Humanist Association is an organisation of the United Kingdom which promotes Humanism. ...


Books

  • Siamo tutti matematici, Di Renzo Editore, Roma, 2007

References

Honorary titles
Preceded by
Sir George Porter
President of the Royal Society
1990–1995
Succeeded by
Sir Aaron Klug
Preceded by
Sir Andrew Huxley
Master of Trinity College, Cambridge
1990–1997
Succeeded by
Amartya Sen
Preceded by
The Lord Porter of Luddenham
Chancellor of the University of Leicester
1995–2005
Succeeded by
Sir Peter Williams

  Results from FactBites:
 
Michael Atiyah - Wikipedia, the free encyclopedia (419 words)
Atiyah is now retired and an honorary professor at the University of Edinburgh and Chancellor of the University of Leicester.
Atiyah was responsible for the founding of the InterAcademy Panel on International Issues, a global network of the world's scientific academies which aims to help its member academies to shape public policy in areas related to science.
Michael Francis Atiyah was knighted in 1983 and made a member of the Order of Merit in 1992.
Atiyah–Singer index theorem - Wikipedia, the free encyclopedia (902 words)
When Michael Atiyah and Isadore Singer were awarded the Abel Prize by the Norwegian Academy of Science and Letters in 2004, the prize announcement explained the Atiyah–Singer index theorem in these words:
In papers written or published in the period around 1962-1965 the theorem was stated and proved by Michael Atiyah, Raoul Bott and Isadore Singer.
Atiyah promoted for a while a notion of elliptic topology for which the index theorem was the central notion.
  More results at FactBites »

 
 

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