

A 1940 Letter of André Weil on Analogy in Mathematics [pdf] - asciilifeform
http://www.ams.org/notices/200503/fea-weil.pdf

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gruseom
This looks great and I'm looking forward to reading it properly. But it gave
me a jolt to read the following:

 _Weil wrote this fourteen-page letter to Simone Weil, his sister [...] Keep
in mind that the letter was not written for a mathematician, even though
Simone could not understand most of it._

Could not understand it? Why'd he write it to her then? (Edit: he commented on
this; see below.)

Simone Weil was brilliant. She had remarkable mathematical gifts, though she
decided early on that she wasn't good at math by comparing herself to her
brother. (André was not only a mathematical genius, he was 3 years older. Talk
about an unfortunate data point.) She ended up, in her brief life, doing
remarkable philosophical, political, and spiritual work. Her intellect was as
deep and as original as they come. At the time this letter was written, she
would have been at the height of her powers (working for the French resistance
in London, as I recall, writing a book about how to rebuild France after the
war - a book which de Gaulle supposedly threw in the garbage without reading).

Simone and André Weil used to act scenes from Greek tragedy _in Greek_ when
she was 4 and he was 7. As George Grant once said, that family had
intellectual culture in a way we in modern North America can't even imagine.

To make patronizing comments about what Simone Weil couldn't understand is
pretty ignorant. Based on what we know about her, though, she wouldn't have
minded.

(Sorry this comment has nothing to do with the actual content of the post.)

~~~
smanek
The letter itself says: "So, I decided to write them down, even if for the
most part they are incomprehensible to you" and "you may be able to understand
the beginning; you will understand nothing of what follows that."

That shows that Andre thought Simone wouldn't understand it.

~~~
gruseom
Oh, that's interesting. I probably shouldn't have commented without reading
the whole thing, especially since what I said was a bit off-topic. (It's often
easier to comment on tangential things, which makes a lot of discussions go
awry.) I recommend upvoting mgreenbe, who actually has something on-topic to
say!

Come to think of it, I vaguely remember reading this, or excerpts from it,
years ago.

------
mgreenbe
This notion of "analogy" is formalized in category theory. At times this is
done to great effect --- the generalizing power of category theory can help a
mathematician see the forest for the trees. This has been done to great
effect, e.g., in programming language theory. Then again, at times category
theory is shallow, nothing more than abstract nonsense. (N.B. this is a
technical term.)

The strict formalist in me likes category theory because it has so many names
for things, many of which are in Greek. The intuitionist in me thinks the
field is pointless but likes drawings with arrows in them. All in all, it's a
win-win. :)

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dedalus
Its very succint but for those interested in number theory its a great precis

