Friday, May 19, 2017

Yan Pradeau: "Algèbre"

"Maths is fun!", often exclaims over-eager (usually young) teacher, and
people tend to shrug at her/him and turn to their infinitely more interesting
gossip or politics or trade-exchange pages.

But in France, mathematics is serious business since centuries, and French
school, by its personalities, certainly IS fun, indeed.

Recently I had pleasure to read Yan Pradeau's "Algèbre", a short booklet
about one of most controversial French mathematicians of the XX
century-Alexander Grothendieck. As it often goes, he was also one of the
best mathematical minds of XX ct.

About him even to say "French" is over-statement, as he
was barely French, acquiring the nationality only at older age (in 1980-ies,
and he was born in 1928, in then Prussia). Most of his life he was
stateless, as his documents were destroyed in 1945, and he was reluctant to
obtain the other nationality, because of conscription obligation.

Following his parents, he was of an anarchist and pacifist political
orientation. His father, A. Schapiro was of a Hassidic Jewish origin, from
the borders of Ukraina, Belarus and Russia, and mather was of a German
protestant origin (his surname is by her). Both were from a rather bourgeois
background, but were declared, and fighting, anarchists of the leftist colors.

Alexander was a mathematical autodidact, and he brought novel generalizations
in geometry and algebra after the WWII. One thing which is well exposed in
the book, and which I was not aware of before, is that in the world wars
expired whole generations of mathematicians, and there remained a profound
vacuum in moderinzation of the discipline in the XX ct. Works of people like
A.G., alone and through group Bourbaki which was organized to promote the
program of novelization of mathematics, were instrumental in this. A.G. was
a kind of celebrity in French mathematical world in 1960-ies and 1970-ies.

Genius had it's price here, A.G. became more and more controversial in
1970-ies, fighting against militarization of the society in the Cold War.
In 1980-ies he completely abandoned the society, secluding
himself in a mountain village of few ten inhabitants. But he was not idle,
he was productive in "philosophical" writing of dubious value.

There is lots in the story about Groethedieck which is new to me, and I will
try to learn more about group Bourbaki. I was not aware of the program they
pursued, and their achievements. And today in Physics we often use results
of their work.

It is a kind of irony that I was recently living in the place where was important
centre of this movement-in Orsay, near Paris, and nearby Burres-sur Yvette,
and I did not know anything about this part of the history of the place.
The very paths I was walking, running or biking, were taken by those people,
not so long time ago. It certainly added an additional spice to my reading, as
also the fact that it was my 2nd book read in French.

Definitely a good read, I warmly recommend it.

No comments: