A 1940 Letter of André Weil on Analogy in Mathematics [pdf]
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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.)
That shows that Andre thought Simone wouldn't understand it.
Come to think of it, I vaguely remember reading this, or excerpts from it, years ago.
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. :)