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This is a massive loss for mathematics and the world :(

Although I've never met him, I've been strongly influenced by his writings and contributions to math, especially his down to earth blog posts.

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That's two Fields Medalists taken entirely too early in the past 3 months (the other being Maryam Mirzakhani). Very sad.

It is. I wonder what this will mean for Homotopy Type Theory.

I think that people will still develop the theory. It still needs a bunch of work but it seems popular enough to stay around.

Working in the field I rather have the feeling that it is slowly but surely falling asleep.

One of Voevodsky's views was that all the foundation for a dependently typed formalization of maths is already there, and that it mainly needs to be organized in a better way (cf his unimath project).

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