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Joel David Hamkins

Published podcast speaker

Claims
24
Episodes
1
Shows
1
Named items
0

Claim ledger

What Joel said.

10 transcript-backed records

02 / belief

I was an undergrad and LaTeX was sort of unheard of, and so I was producing these beautifully typeset, you know— …problem sets, solutions, and so on. And I would print it up and submit it and so on, and the grades would come back, terrible grades, and I realized what was happening— The copy was so beautiful, mathematically typeset in this way, it looked like the kind of mathematics you find in a book.

“I was an undergrad and LaTeX was sort of unheard of, and so I was producing these beautifully typeset, you know— …problem sets, solutions, and so on. And I would print it up and submit it and so on, and the grades would come back, terrible grades, and I realized what was happening— The copy was so beautiful, mathematically typeset in this way, it looked like the kind of mathematics you find in a book.”
Publisher
Lex Fridman Podcast

03 / belief

Although set theory continues to, in my view, have an extremely successful metamathematical analysis as a foundation, I think is much more successful than set theory for any of those other foundations, but it’s much less amenable to things like computer proof and so on, which is part of the motivation to find these alternative foundations.

“Although set theory continues to, in my view, have an extremely successful metamathematical analysis as a foundation, I think is much more successful than set theory for any of those other foundations, but it’s much less amenable to things like computer proof and so on, which is part of the motivation to find these alternative foundations.”
Publisher
Lex Fridman Podcast

04 / belief

Maybe they have a good math idea, and so I want to talk to them and interact with them. And so I think the Perelman case is maybe an instance where, you know, he’s such a brilliant mind and he solved this extremely famous and difficult problem, and that is a huge achievement.

“Maybe they have a good math idea, and so I want to talk to them and interact with them. And so I think the Perelman case is maybe an instance where, you know, he’s such a brilliant mind and he solved this extremely famous and difficult problem, and that is a huge achievement.”
Publisher
Lex Fridman Podcast

05 / belief

If I have the idea that my mathematical ontology is rich with objects, then I think that there are all kinds of functions and ways of choosing.

“If I have the idea that my mathematical ontology is rich with objects, then I think that there are all kinds of functions and ways of choosing.”
Publisher
Lex Fridman Podcast

06 / belief

There’s this concept of the set-theoretic mantle that I had introduced in a way that is extremely interesting. And so it’s historically quite funny, I think, because this research program that grew entirely out of the pluralist point of view ended up being picked up by the universe point of view research program in a way that is quite important.

“There’s this concept of the set-theoretic mantle that I had introduced in a way that is extremely interesting. And so it’s historically quite funny, I think, because this research program that grew entirely out of the pluralist point of view ended up being picked up by the universe point of view research program in a way that is quite important.”
Publisher
Lex Fridman Podcast

07 / belief

Whereas I think that we do have something a little better of an understanding of the nature of mathematical existence and abstract existence.

“Whereas I think that we do have something a little better of an understanding of the nature of mathematical existence and abstract existence.”
Publisher
Lex Fridman Podcast

08 / belief

I mean, my view is that, yeah, this isn’t traumatic at all. This is rather completely eye-opening in terms of our understanding of the nature of mathematical reality.

“I mean, my view is that, yeah, this isn’t traumatic at all. This is rather completely eye-opening in terms of our understanding of the nature of mathematical reality.”
Publisher
Lex Fridman Podcast

09 / belief

Yeah, I think so, because I guess part of the point of structuralism is that it doesn’t make sense to consider mathematical objects or individuals in isolation.

“Yeah, I think so, because I guess part of the point of structuralism is that it doesn’t make sense to consider mathematical objects or individuals in isolation.”
Publisher
Lex Fridman Podcast

10 / belief

I mean, the way I think about the Hilbert program seems extremely attractive in the historical context of being worried about the antinomies, the inconsistencies, and so how can we kind of block them. And so- It seems natural, first of all, to have a strong theory that’s going to answer all the questions, because the idea of logical independence and pervasiveness that we now know exists just wasn’t, you know, there was no known… They didn’t know anything like that happening ever.

“I mean, the way I think about the Hilbert program seems extremely attractive in the historical context of being worried about the antinomies, the inconsistencies, and so how can we kind of block them. And so- It seems natural, first of all, to have a strong theory that’s going to answer all the questions, because the idea of logical independence and pervasiveness that we now know exists just wasn’t, you know, there was no known… They didn’t know anything like that happening ever.”
Publisher
Lex Fridman Podcast
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