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PRESS RELEASE
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25 January 2001


Crafoord Prize to one of the world's foremost mathematicians
The Royal Swedish Academy of
Sciences decided at its meeting on 24 January 2001 to award the 2001 Crafoord
Prize in mathematics to
Alain Connes,
Professor at IHES and Collège
de France, Paris,
"for his penetrating work on the theory of operator algebras and for having
been a founder of the noncommutative geometry".
The French mathematician Alain Connes is counted among the world's foremost mathematicians.
He has made pioneering and unique contributions to the theory of operator algebras
and noncommutative geometry. The latter is a new field of mathematics, in
the creation of which Alain Connes has played a decisive part.
Operator algebras
At the beginning of the 1930s the HungarianAmerican mathematician John von Neumann
started developing a theory for the algebras of operators in what is termed Hilbert
space. He was inspired by developments in quantum mechanics where these algebras
played a central part. von Neumann delimited a particular type of such algebras,
which mathematicians now term "von Neumann algebras", together with
a special type of buildingblock of which such algebras are formed, termed factors.
Together with F. J. Murray, von Neumann roughly classified these algebras into
three types, I, II and III. von Neumann later turned to other interests and it
was not until the period between 1966 and 1971 that the development was resumed
and many different typeIII factors were constructed. It was here that Alain Connes
entered the picture, in 1972. While a good deal of preparatory work had been done,
during the next ten years Connes totally revolutionised this picture by solving
most of the unsolved problems in the area. For this he was awarded the Fields
Prize in 1983.
By further developing this theory, Alain Connes soon entered new, untrodden territory.
An entirely new area of mathematics began to take shape, the noncommutative
geometry.
Noncommutative geometry
Geometry as it has developed from Descartes onwards is based on the notion of
points in systems of coordinates. Geometric properties are reflected in algebraic
properties of functions where points in space represent variables. The algebras
that can be constructed in this way are usually commutative, meaning that the
result of an operation is independent of the order in which it is performed. An
example is ordinary multiplication: a · b = b · a.
But in the study of the algebras of operators one often encounters noncommutative
properties. Matrix multiplication is an example of something that is not normally
commutative: A · B does not equal B · A. Alain Connes' idea is,
using such a noncommutative algebra as a base, to consider it as an expression
of a fictitious "noncommutative" space. Such a space requires a different
and more abstract conceptual apparatus than what we are used to from classical
geometry. The concept of point, for example, is meaningless in noncommutative
geometry.
Alain Connes' work has also provided powerful new methods useable in theoretical
physics for treating e.g. renormalization theory and the standard model of quantum
and particle physics. He has also demonstrated that these new mathematical tools
can be used for understanding and proving the Riemann hypothesis of the zeta function,
considered the most famous open problem in mathematics.
***
Alain Connes
Alain Connes, 53, was born in Draguignan (Var), France on 1 April 1947. He attended
the Ecole Normale Supérieure (ENS) in Paris 196670. Since 1979 he has
held the Léon Motchane Professorship at the Institut des Hautes Études
Scientifiques (IHES) at BuressurYvette outside Paris, and since 1984 also a
professorship in analysis and geometry at the Collège de France in Paris.
He received the Fields Medal in 1983 (the most highly regarded mathematical prize
in the world) and is a member of many scientific academies including Académie
des Sciences, Paris, and National Academy of Sciences, USA.
The 2001 Crafoord Prize will be presented by H.M. the King of Sweden on
26 September 2001 at a ceremony at the Royal Swedish Academy of Sciences in Stockholm.
The prize consists of a gold medal and 500,000 USD.
The AnnaGreta and Holger Crafoord Foundation was established in 1980 for
promoting basic research in mathematics, astronomy, the biosciences (particularly
ecology), the geosciences and polyarthritis (joint rheumatism). The prize was
awarded for the first time in 1982 in mathematics and has since been awarded by
subject area in the order given above. The Crafoord Prize consists of an international
prize and research grants to Swedish scientists.
Earlier laureates in mathematics are Vladimir I. Arnold, Russia and Louis
Nirenberg, USA (1982), Pierre Deligne, Belgium and USA and Alexandre Grothendieck*,
France (1988), and Simon Donaldson, England and ShingTung Yau, USA (1994).
* Grothendieck declined the prize
Information on the web:
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2001 Crafoord Prize


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