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Joel David Hamkins

Published podcast speaker

Claims
24
Episodes
1
Shows
1
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0

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What Joel said.

6 transcript-backed records

01 / evaluation

The motivation is misplaced. And so I worry that this is a very dangerous source of error because it often happens in mathematics that… I mean, if I think back to when I was an undergrad, here at Caltech, I was a math major eventually, and at that time, LaTeX was a pretty new thing and I was learning LaTeX, and so I was typing up my homeworks in LaTeX and they looked beautiful.

“The motivation is misplaced. And so I worry that this is a very dangerous source of error because it often happens in mathematics that… I mean, if I think back to when I was an undergrad, here at Caltech, I was a math major eventually, and at that time, LaTeX was a pretty new thing and I was learning LaTeX, and so I was typing up my homeworks in LaTeX and they looked beautiful.”
Publisher
Lex Fridman Podcast

02 / evaluation

For example, there’s this threefold repetition rule in ordinary chess, but we just, we just get rid of this for infinite chess because, of course, threefold repetition is just a proxy for infinite play.

“For example, there’s this threefold repetition rule in ordinary chess, but we just, we just get rid of this for infinite chess because, of course, threefold repetition is just a proxy for infinite play.”
Publisher
Lex Fridman Podcast

03 / evaluation

I mean, because it’s an asymptotic property, it’s really in the limit as the size of the inputs goes to infinity, that’s the only time that polynomial or NP becomes relevant. And so maybe it’s important to keep that in mind when… Sometimes you find kind of overblown remarks made about, you know, if P equals NP, then this will be incredibly important for human civilization because it means that we’ll have feasible algorithms for solving these incredibly important… …problems in NP.

“I mean, because it’s an asymptotic property, it’s really in the limit as the size of the inputs goes to infinity, that’s the only time that polynomial or NP becomes relevant. And so maybe it’s important to keep that in mind when… Sometimes you find kind of overblown remarks made about, you know, if P equals NP, then this will be incredibly important for human civilization because it means that we’ll have feasible algorithms for solving these incredibly important… …problems in NP.”
Publisher
Lex Fridman Podcast

05 / evaluation

It’s a kind of birth of the subject of mathematical logic. But to understand the theorems, you really have to start a little bit earlier with Hilbert’s program because at that time, you know, with the Russell Paradox and so on, there were these various contradictions popping up in various parts of set theory and the Burali-Forti paradox and so on.

“It’s a kind of birth of the subject of mathematical logic. But to understand the theorems, you really have to start a little bit earlier with Hilbert’s program because at that time, you know, with the Russell Paradox and so on, there were these various contradictions popping up in various parts of set theory and the Burali-Forti paradox and so on.”
Publisher
Lex Fridman Podcast

06 / evaluation

Because I think, for example, if you prove a new result with a bad argument or a complicated argument, that’s great because you proved something new.

“Because I think, for example, if you prove a new result with a bad argument or a complicated argument, that’s great because you proved something new.”
Publisher
Lex Fridman Podcast
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