The Many Faces of Nicolas Bourbaki
Stokes' theorem is a superb generalization of the
fundamental theorem of calculus.
Some Incarnations of Stokes' Theorem
| Gradient Conservativity |
òab
grad f . dM
=
f(b) - f(a)
|
| Kelvin-Stokes' Formula |
òòS rot U . dS
=
òC U . dM
|
| Ostrogradsky's Theorem |
òòòV
div U dV
=
òòS U . dS
|
Nicolas Bourbaki and this general result are partly due to each other...
Nicolas Bourbaki was
born
on January 14th 1935,
as the collective identity of a group of several highly talented young French mathematicians,
in part from the urge to elucidate the general validity of the above formula
(as reported by André Weil, then 28).
The Bourbaki collaboration has been extremely
influential in France and elsewhere.
Bourbaki brought about new riguor based on the
logical foundations of mathematics
(and also, along the way, some controversial reforms in mathematical teaching).
The active founding members of the Nicolas Bourbaki group
were:
The official list of founders also includes a few members who were less active,
namely: Jean Coulomb,
Charles
Ehresmann (1905-1979), René de Possel and Szolem Mandelbrojt
(uncle and early mentor of the young
Benoît
Mandelbrot, of future fractal fame).
Jean
Leray (1906-1998) and
Paul
Dubreil (1904-1994) were present at preliminary meetings before the
actual foundation of the Bourbaki group.
The rule was that all members of the collective would have to leave by the age
of 50 (Grothendieck and Lang left early, in anger).
Other bourbakists include:
The ambition of the founders was to put on a fresh solid foundation the
entire mathematical knowledge of their time.
This has taken the form of a collection of books entitled
Elements de Mathématique (note the militant use of the grammatically
incorrect singular form of Mathématiques).
The Association is alive and well,
although it's not nearly as active and/or influential as it once was
(the latest volumes in the collection were published in 1983 and 1998).
One of the first items on the original agenda was the above formula, which
unifies great results of vector calculus.
| 
Born: 5 March, 1915, in Paris (France)
