to one of the world's foremost mathematicians
Swedish Academy of Sciences decided at its meeting on 24 January
2001 to award the 2001 Crafoord Prize in mathematics to
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 non-commutative 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 non-commutative geometry.
The latter is a new field of mathematics, in the creation
of which Alain Connes has played a decisive part.
At the beginning of the 1930s the Hungarian-American 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 building-block 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 type-III 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 non-commutative 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
non-commutative 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 non-commutative algebra as a base, to consider it as an expression
of a fictitious "non-commutative" 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 non-commutative 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, 53, was born in Draguignan (Var), France on 1 April
1947. He attended the Ecole Normale Supérieure (ENS) in
Paris 1966-70. Since 1979 he has held the Léon Motchane
Professorship at the Institut des Hautes Études Scientifiques
(IHES) at Bures-sur-Yvette 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 Anna-Greta 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 Shing-Tung Yau, USA (1994).
* Grothendieck declined the prize