The
first thing you notice is that he is a very graceful writer when he so
chooses. You do not see this in his mathematical writings, which are
straightforward and businesslike, when not (very occasionally)
interrupted by some dyspeptic outburst (we quoted one of them here).
And as he stresses the importance of hewing to original languages
whenever possible (he himself was an admirable polyglot), we shall so
hew here.
~
Weil prefaces his book with a tribute to his late wife:
Notre mariage a été de ceux qui font mentir La Rochefoucauld. Fulsere vere candidi mihi soles…
For an elucidation of that Latin tag, I naturally turned to that fons sapientiae, Dr. Massey, who replied by return of post:
"Bright suns truly shone for me"
It's from Catullus Carmina 8, in which the poet is depressed after being dumped by his lover Lesbia.
~
Since
Weil was born in 1906 (and ripened early), and the memoirs were not
published until 1991, we sometimes get the benefit of the long view.
Alluding to the current Lake-Wobegone system of American puericulture,
he remarks:
N’est-il
pas étrange que l’émulation se trouve honnie à présent comme ressort
pédagogique, alors que l’esprit de compétition, dans presque tout les
domaines, n’a peut-être jamais été si âpre qu’il l’est aujourd’hui ?
He also speaks somewhat dismissively of “the New Math” fad in schools, counterposing the value of a traditional grammatical education for training the mind:
Est-ce
pure coïncidence que l’Inde, avec Pânini, ait inventé la grammaire
avant d’inventer la numération décimale et les nombres négatifs, et
que par la suite grammaire et algèbre aient pris toutes deux dans la
civilisation médiévale de langue arabe l’essor que l’on sait ?
Naguère on a cru préparer les petits enfants à l’étude des
mathématiques en les forçant à parler d’ensembles, de bijections, de
nombres cardinaux et de l’ensemble vide. Peut-être n’y étais-je pas
moins bien préparé par l’étude de l’analyse grammatical …
Later
in the volume (p. 120) we read of another glancing yet important brush
between linguistics and pure mathematics : the ushering of structure, rather than number, to center stage:
Quant au choix du mot de structure,
mes souvenirs sont en défaut; mais à cette époque il était déjà entré
… dans le vocabulaire des linguistes, et je conservais des contacts
avec ce milieu, et tout particulièrement avec Emile Benveniste …
*
Si cela vous parle,
savourez la série
noire
en argot authentique
d’Amérique :
*
~
André
Weil was the brother of the better-known Simone Weil. In the preface,
he excuses himself for alluding to her but little, pleading that he has
already said what he has to say, to her biographer. But, recounting a
stroll with some monks at Santo Domingo de Silos, he writes:
De
leur conversation, au cours de la promenade rituelle dans le cloître,
il m’est resté une phrase. Comme il était question d’un saint au
comportement quelque peu excentrique, l’un d’eux fit observer doucement,
«Mais le christianisme est une folie» («el cristianismo es una
locura»); ce propos, parfaitement orthodoxe, m’est souvent revenu à
l’esprit au sujet de la vie de ma sœur.
~
Weil’s 1938 cri de cœur, “Science française”, which begins "J'en ai assez!", and which was refused publication at the time, is reprinted in the Œuvres scientifiques,
as was its eventual post-war airing. But since neither version names
names, nor does Wikipedia mention the incidents in question s.v. Jean Perrin, here is a tidbit (p. 126):
L’une
des cliques en question, et sans doute la plus puissante, avait à sa
tête le physicien Jean Perrin, prix Nobel, … inventeur du C.N.R.S. Non
content des moyens importants dont il disposait déjà, il imagina de
créer toute une hiérarchie de médailles assorties de récompenses
pécuniaires, depuis la grande médaille d’or jusqu’aux médaillettes …
Il n’était pas difficile de soupçonner que la devise en serait:
«Nul n’aura de l’esprit que nous et nos amis.»
«Nul n’aura de l’esprit que nous et nos amis.»
*
Pour d’autres
friandises
de la confiserie
du docteur Justice,
consultez:
*
I
am reminded of a comment one writer made on the much-ballyhoo’d
creation of some new honor or other (it may have been the MacArthur):
“another lap in the meritocratic rat-race”.
~
All
told, the book is mathematically disappointing. I don’t mean that it
should have been stuffed with equations. But we do hope for some
insight into mathematical ideation, such as is furnished by the memoirs
of Hardy or of Hadamard. For one thing, the field he helped to found,
algebraic geometry, has the reputation of being one of the most
ferociously abstract of all human endeavors. It must be very different
working in that field, or in topos theory, from solving the four-color
problem or classifying finite simple groups. But of this we get not an
inkling.
Above
all, Weil was long a core member of one of the most sociologically
remarkable mathematical activities of all time: the Bourbaki group,
which labored collectively and published anonymously. What was that like ?
So, frustrated at the reticence of one of its founding members, I have no recourse but to quote the following satirical evaluation:
Named
after a French general of widely admired stupidity, the Bourbaki was
founded in the 1930’s .. A committee was formed and pedagogical
improvements discussed.
This
is the myth. In all of French history, no mathematician of standing
has ever concerned himself with the welfare of his students. The
Bourbaki was founded to amused the members of the Bourbaki.
To
a man, these mathematicians believed that their first order of business
was to correct, and, if possible, eliminate, the work of other
mathematicians.
-- David Berlinski, Infinite Ascent (2005)
~
En fin de compte
… Our attempt to experience mathematics more richly by reading the
memoirs of its practitioners, is like that of the gum-snapping
beautician devouring the latest tabloids for the off-screen escapades of
her favorite stars. In both cases, we court a simulacrum of what is
ultimately inaccessible. Indeed, the beautician is if anything
launched upon a more reasonable quest. If you think that Lindsay Lohan
is an interesting person, then her antics in the National Equirer
should be satisfying, since that shallow cipher is little more than the
sum of her antics. Whereas the well-written, travelogue-y accounts of
André Weil gave no sense of what it is like to have his sort of
towering mathematical mind -- they might have been written by anyone.
(Quine’s memoir, The Time of my Life, was disappointing in the same way.)
~
For another not-so-close encounter with algebraic geometry, via the man and not the math, click here:
~
André
Weil’s teacher Jaques Hadamard, a major figure of number theory and
cryptography, is best known to the lay public for his booklet Psychology of Invention in the Mathematical Field; my father, no mathematician, but a typical subscriber to Eisenhower-era Scientific American,
had it on his shelves, where I made its acquaintance in high school.
Spurred yet disappointed by Weil’s memoir, I ordered what I presumed to
be the French original of this book, via InterLibrary Loan; and in due
course it arrived at our local library.
Mais encore -- quelle déception
! For much the same reasons as Weil, Hadamard had fled (in 1940) to
the United States, and indeed specifically to Princeton. And it was
there that he wrote that memoir, in English, which Princeton University Press brought out in 1945.
France
just doesn’t know how to hold onto its mathematicians -- as Weil was
already complaining in 1938. And it was at Princeton that I made the
acquaintance of the likewise-exiled French mathematician who earned a
Fields medal for proving the Weil Conjectures, Pierre Deligne (we were
fellow parents at the Princeton Friends School, and met to plan-out Math
Day). A distinguished intellectual genealogy, all very baronial --
but abroad.
~
For more from this pen, including a soon-to-be-released new title:
~ Afterword ~
I have from time to time -- fitfully, fretfully -- pecked
away at some of the works of that French collectivity Bourbaki, without profit
or enjoyment. There is,
then, a certain wry comfort in this assessment by their celebrated countryman
René Thom:
No new theorem of any importance
came out of the immese effort at systematization of Nicolas Bourbaki -- which
in itself is not a true formalization, because Bourbaki uses a nonformalized
metalanguage.
-- René Thom, “’Modern’ Mathematics
(1971), repr. in Thomas Tymoczko, ed., New Directions in the Philosophy of Mathematics
(1986, rev. 1998), p. 73
[Update] The
slim pickings of mathematical morsels in Weil’s memoir are slightly supplemented by an
anecdote in a book I just finished reading, the highly entertaining Genius
in my Basement (2011), by Alex Masters. (The genius alluded to is not Weil but group-theorist Simon
Norton; more elsewhere anon.) The anthropologist Lévi-Srauss, he
relates, baffled at what structure underlay Australian marriage taboos
… went around New York … banging on
the doors of mathematicians. The
first was dismissive: “Mathematics
has four operations, and marriage is not one of them.” But the second was the young and
brilliant André Weil… “When in doubt,” cried Mr. Weil, “look for the group!”
and he bustled Lévi-Strauss off the street into his study.
Within a few days, Weil had solved the problem.
(“Group” in the sense of Group Theory, of course; though indeed sibs and clans can be
relevant.)
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