Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Yeah, so... So what's more real, physics or the mathematical platonic space?
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Somehow it feels like we're approaching some deep truth from different directions.
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
And we just haven't traveled as far in the physics world as we have in the mathematical world.
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Yeah, I wonder, like a thousand years from now, as physics progresses, what this same conversation would look like.
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Do you think there's breakthroughs a thousand years from now on the mathematics side?
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Because we've just discussed, and we'll return to...
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
a lot of turmoil a century ago.
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Do you think there's more turmoil to be had?
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
To take a tangent on a tangent, since you mentioned philosophy, maybe potentially more about the questions and maybe mathematics is about the answers, I have to say you are a legend, right?
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
on Math Overflow, which is like Stack Overflow, but for math.
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
You're ranked number one all time on there with currently over 246,000 reputation points.
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
How do you approach answering difficult questions on there?
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
How do you find the questions that grab you and how do you go about answering them?
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
To give some examples of questions you've answered, what are some reasonable sounding statements that are independent of ZFC?
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
What are the most misleading alternate definitions in taught mathematics?
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Is the analysis as taught in universities, in fact, the analysis of definable numbers, solutions to the continuum hypothesis?
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Most unintuitive application of the axiom of choice.
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Non-trivial theorems with trivial proofs.
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
Reductio ad absurdum or the contrapositive.
Lex Fridman Podcast
#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins
What is a chess piece mathematically?