From: "Daniel R. Grayson" <danielrichardgrayson@gmail.com> To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com> Subject: Re: [HoTT] Why did Voevodsky find existing proof assistants to be 'impractical'? Date: Tue, 5 Nov 2019 07:43:06 -0800 (PST) Message-ID: <cda95637-0ab0-4897-8e38-b5ebb288a658@googlegroups.com> (raw) In-Reply-To: <CAH52Xb3s0+vweUaSQBMBNLa5mRc9F1jrsg2sSoFmcE_4=dAt1w@mail.gmail.com> [-- Attachment #1.1: Type: text/plain, Size: 1554 bytes --] Re: "To get back to the original question, my understanding was that Voevodsky had done a bunch of scheme theory and it had got him a Fields medal and it was this mathematics which he was interested in at the time. He wanted to formalise his big theorem, just like Hales did." I think he was more interested in formalizing things like his early work with Kapranov on higher categories, which turned out to have a mistake in it. He once told me that he wasn't interested in formalizing his proof of Bloch-Kato, because he was sure it was right. (I should have asked him at the time how he could be so sure!) Re: "The clearest evidence, in my mind, is that there is no definition of a scheme in UniMath." That's sort of accidental. In early 2014, expecting to speak at an algebraic geometry in the summer, he mentioned that one idea he had for his talk would be to formalize the definition of scheme in UniMath and speak about it. I think he was distracted from that by thinking about C-systems. The UniMath project aims at formalizing all of mathematics, so the definition of scheme is one of the next things that (still) needs to be done. -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/cda95637-0ab0-4897-8e38-b5ebb288a658%40googlegroups.com. [-- Attachment #1.2: Type: text/html, Size: 1913 bytes --] <div dir="ltr">Re: "To get back to the original question, my understanding was that Voevodsky had done a bunch of scheme theory and it had got him a Fields medal and it was this mathematics which he was interested in at the time. He wanted to formalise his big theorem, just like Hales did."<br><div><br></div><div>I think he was more interested in formalizing things like his early work with Kapranov on higher categories, which turned out to have a mistake in it. He once told me that he wasn't interested in formalizing his proof of Bloch-Kato, because he was sure it was right. (I should have asked him at the time how he could be so sure!)<br><br>Re: "The clearest evidence, in my mind, is that there is no definition of a scheme in UniMath."<br><br>That's sort of accidental. In early 2014, expecting to speak at an algebraic geometry in the summer, he mentioned that one idea he had for his talk would be to formalize the definition of scheme in UniMath and speak about it. I think he was distracted from that by thinking about C-systems. The UniMath project aims at formalizing all of mathematics, so the definition of scheme is one of the next things that (still) needs to be done.</div></div> <p></p> -- <br /> You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group.<br /> To unsubscribe from this group and stop receiving emails from it, send an email to <a href="mailto:HomotopyTypeTheory+unsubscribe@googlegroups.com">HomotopyTypeTheory+unsubscribe@googlegroups.com</a>.<br /> To view this discussion on the web visit <a href="https://groups.google.com/d/msgid/HomotopyTypeTheory/cda95637-0ab0-4897-8e38-b5ebb288a658%40googlegroups.com?utm_medium=email&utm_source=footer">https://groups.google.com/d/msgid/HomotopyTypeTheory/cda95637-0ab0-4897-8e38-b5ebb288a658%40googlegroups.com</a>.<br />

next prev parent reply indexThread overview:18+ messages / expand[flat|nested] mbox.gz Atom feed top 2019-10-27 14:41 Nicolas Alexander Schmidt 2019-10-27 17:22 ` Bas Spitters 2019-11-03 11:38 ` Bas Spitters 2019-11-03 11:52 ` David Roberts 2019-11-03 19:13 ` Michael Shulman 2019-11-03 19:45 ` Valery Isaev 2019-11-03 22:23 ` Martín Hötzel Escardó 2019-11-04 23:20 ` Nicolas Alexander Schmidt 2019-11-04 18:42 ` Kevin Buzzard 2019-11-04 21:10 ` Michael Shulman 2019-11-04 23:26 ` David Roberts2019-11-05 15:43 ` Daniel R. Grayson [this message]2019-11-05 20:29 ` Yuhao Huang 2019-11-06 23:59 ` Daniel R. Grayson 2019-11-05 23:14 ` Martín Hötzel Escardó 2019-11-06 0:06 ` Stefan Monnier 2019-11-11 18:26 ` Licata, Dan 2019-11-03 7:29 ` Michael Shulman

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