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October 10, 2019

Foundations of Math and Physics One Century After Hilbert

Posted by John Baez

I wrote a review of this book with chapters by Penrose, Witten, Connes, Atiyah, Smolin and others:

It gave me a chance to say a bit—just a tiny bit—about the current state of fundamental physics and the foundations of mathematics.

Posted at October 10, 2019 8:16 AM UTC

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Re: Foundations of Math and Physics One Century After Hilbert

It might have been an interesting experiment to mix it up and have the contributors write about each other’s projects: Connes on twistors, Penrose on noncommutative geometry, etc.

I’m surprised the claim about the 6-sphere got through. That’s pretty far out of my wheelhouse, and even I’d heard that Atiyah’s proof has not been generally accepted.

Posted by: Blake Stacey on October 11, 2019 12:26 AM | Permalink | Reply to this

Re: Foundations of Math and Physics One Century After Hilbert

Blake wrote:

It might have been an interesting experiment to mix it up and have the contributors write about each other’s projects: Connes on twistors, Penrose on noncommutative geometry, etc.

That would be very enlightening. I’ve already read these people talking about their own stuff, over and over.

[…] even I’d heard that Atiyah’s proof has not been generally accepted.

Yes, and “not generally accepted” is the understatement of the day. He was beginning to lose it around this time, and the hole in this so-called proof is so big that it’s really just a gaping hole with a bit of proof around the edges. That’s why I said he was “falsely claiming to prove” the conjecture, instead of saying that the proof was wrong. It’s a pity this was ever published.

Posted by: John Baez on October 11, 2019 1:24 AM | Permalink | Reply to this

Re: Foundations of Math and Physics One Century After Hilbert

Yes, it’s unfortunate. I wonder if there was some “we need to have a chapter by Atiyah” thinking involved.

(Apparently there is a way to rule out at least one type of complex structure on the 6-sphere using twistors.)

Posted by: Blake Stacey on October 13, 2019 1:43 AM | Permalink | Reply to this

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