Discussion of Homotopy Type Theory and Univalent Foundations
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From: Yuhao Huang <temp.use88@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 12:29:56 -0800 (PST)
Message-ID: <0ef61665-eafd-40a0-8592-11bdd277d10b@googlegroups.com> (raw)
In-Reply-To: <cda95637-0ab0-4897-8e38-b5ebb288a658@googlegroups.com>

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>
> 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!)
>

Oh this is interesting... do you remember when this conversation was 
happening? Because in these slides (
https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/2014_09_Bernays_3%20presentation.pdf) 
he said "Next year I am starting a project of univalent formalization of my 
proof of Milnor’s Conjecture using this formalization of set theory as the 
starting point." (Page 11)

在 2019年11月5日星期二 UTC-8上午7:43:06,Daniel R. Grayson写道:
>
> 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.
>

在 2019年11月5日星期二 UTC-8上午7:43:06,Daniel R. Grayson写道:
>
> 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.
>

在 2019年11月5日星期二 UTC-8上午7:43:06,Daniel R. Grayson写道:
>
> 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.
>

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<div dir="ltr"><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">He once told me that he wasn&#39;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></blockquote><div><br></div><div>Oh this is interesting... do you remember when this conversation was happening? Because in these slides (<a href="https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/2014_09_Bernays_3%20presentation.pdf">https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/2014_09_Bernays_3%20presentation.pdf</a>) he said &quot;Next year I am starting a project of univalent formalization of my proof of Milnor’s Conjecture using this formalization of set theory as the starting point.&quot; (Page 11)<br></div><div> <br></div>在 2019年11月5日星期二 UTC-8上午7:43:06,Daniel R. Grayson写道:<blockquote class="gmail_quote" style="margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir="ltr">Re: &quot;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.&quot;<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&#39;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: &quot;The clearest evidence, in my mind, is that there is no definition of a scheme in UniMath.&quot;<br><br>That&#39;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></blockquote><br>在 2019年11月5日星期二 UTC-8上午7:43:06,Daniel R. Grayson写道:<blockquote class="gmail_quote" style="margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir="ltr">Re: &quot;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.&quot;<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&#39;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: &quot;The clearest evidence, in my mind, is that there is no definition of a scheme in UniMath.&quot;<br><br>That&#39;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></blockquote><br>在 2019年11月5日星期二 UTC-8上午7:43:06,Daniel R. Grayson写道:<blockquote class="gmail_quote" style="margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir="ltr">Re: &quot;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.&quot;<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&#39;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: &quot;The clearest evidence, in my mind, is that there is no definition of a scheme in UniMath.&quot;<br><br>That&#39;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></blockquote></div>

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  reply index

Thread 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 Roberts
2019-11-05 15:43           ` Daniel R. Grayson
2019-11-05 20:29             ` Yuhao Huang [this message]
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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