Re: [HoTT] Why did Voevodsky find existing proof assistants to be 'impractical'?

[Yuhao Huang <temp.use88@gmail.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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