Jacques Salomon Hadamard
(December 8, 1865 –
October 17, 1963) was
a French mathematician who made major contributions in
number theory, complex function theory, differential geometry and partial differential
equations.
Biography
The son of
a teacher, Amédée Hadamard, of Jewish
descent, and Claire Marie Jeanne Picard, Hadamard attended the
Lycée
Charlemagne and Lycée Louis-le-Grand, where his father taught. In 1884 Hadamard
entered the École Normale Supérieure, having been placed first in the entrance
examinations both there and at the École
Polytechnique. His teachers included
Tannery,
Hermite,
Darboux,
Appell,
Goursat and
Picard. He obtained his doctorate
in 1892 and in the same year was awarded the
Grand Prix des
Sciences Mathématiques for his prize essay on the
Riemann zeta function.
In 1892 Hadamard married Louise-Anna Trénel, also of Jewish
descent, with whom he had three sons and two daughters. The
following year he took up a lectureship in the
University of Bordeaux, where he
proved his
celebrated
inequality on determinants, which led to the discovery of
Hadamard matrices when equality
holds. In 1896 he made two important contributions: he proved the
prime number theorem, using
complex function theory
(also proved independently by
de la Vallée Poussin); and he was
awarded the Bordin Prize of the
French Academy of Sciences for
his work on
geodesics in the
differential geometry of
surfaces and
dynamical
systems. In the same year he was appointed Professor of
Astronomy and Rational Mechanics in Bordeaux. His foundational work
on geometry and
symbolic dynamics
continued in 1898 with the study of geodesics on surfaces of
negative curvature. For his
cumulative work, he was awarded the
Prix
Poncelet in 1898.
After the
Dreyfus affair, which
involved him personally because his wife was related to Dreyfus,
Hadamard became politically active and a staunch supporter of
Jewish causes though he professed to be an
atheist in his religion.
In 1897 he
moved back to Paris, holding positions in the Sorbonne and the
Collège de
France, where he was appointed Professor of Mechanics in
1909. In addition to this post, he was appointed to
chairs of analysis at the École Polytechnique in 1912 and at the École Centrale in 1920, succeeding
Jordan and Appell. In Paris
Hadamard concentrated his interests on the problems of mathematical
physics, in particular
partial differential
equations, the
calculus of
variations and the foundations of
functional analysis.
He introduced the idea
of well-posed problem
and the method of descent
in the theory of partial
differential equations, culminating in his seminal book on the
subject, based on lectures given at Yale University in 1922. He was elected to the
French Academy of Sciences in
1916, in succession to
Poincaré, whose
complete works he helped edit. Later in his life he wrote on
probability theory and
mathematical education. He was
awarded the
CNRS Gold medal for his
lifetime achievements in 1956.
Hadamard's students included
Maurice Fréchet,
Paul Lévy,
Szolem Mandelbrojt and
André Weil.
On creativity
In his book
Psychology of Invention in the Mathematical
Field, Hadamard uses
introspection to describe mathematical thought
processes. In sharp contrast to authors who identify
language and
cognition, he
describes his own mathematical thinking as largely wordless, often
accompanied by
mental images that
represent the entire solution to a problem. He surveyed 100 of the
leading physicists of the day (approximately 1900), asking them how
they did their work. Many of the responses mirrored his; some
reported seeing mathematical concepts as colors.
Hadamard described the experiences of the
mathematicians/theoretical physicists
Carl Friedrich Gauss,
Hermann von Helmholtz,
Henri Poincaré and others as viewing
entire solutions with “sudden spontaneousness.” The same has been
reported in literature by many others, such as Denis Brian,
G. H.
Hardy,,
B. L.
van der Waerden,, Harold Ruegg.,
Friedrich Kekulé
(dreamed of benzene ring) and
Tesla.
Hadamard described the process as having four steps of the
five-step
Graham Wallas creative process model, with the first three also
having been put forth by Helmholtz:
- Preparation
- Incubation
- Illumination
- Verification
Writings
- ( Princeton University Press, 1945)
See also
Notes
References
- Denis Brian Einstein: A Life (John Wiley and Sons,
1996) ISBN 0-471-11459-6
- Jacques Hadamard The Psychology of Invention in the
Mathematical Field (Dover, 1954) ISBN 0-486-20107-4
- C. G. Jung The Collected Works of C. G.
Jung. Volume 8. The Structure and Dynamics of
the Psyche. (Princeton, 1981) ISBN 0-691-09774-7
- Robert Kanigel The Man Who Knew Infinity: A Life of the
Genius Ramanujan (Washington Square Press, 1992) ISBN
0-671-75061-5
- Marie-Louise von Franz, Psyche and Matter (Shambhala,
1992) ISBN 0-87773-902-1
Further reading
External links