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.