When does math become recreational for people?
In my case, when you aren't paid to do it, and don't have (much) time to study it formally anymore.
What does the end of mathematics look like?
21–30 of 94 posts
Re: What does the end of mathematics look like?
#22This article is written in an unnecessarily extravagant style, IMO. Also, I appreciate anonymity, but, to my point > I live by myself in a remote mountain cave beyond the ken of civilised persons, and can only be contacted during a full moon, using certain arcane rites that are too horrible to speak of. Okay.
As always, HN has no sense of humour...
Some people do!
Re: What does the end of mathematics look like?
#23We'll know that the time draws nearer when an AI confirms or refutes Mochizuki's proof of the abc conjecture. As of right now, I don't think they're capable of doing that. And, as they can't even check a very (very!) complex proof, they won't be able to conjure any inhumanly complex proofs de novo . Also: > To expand: what if the practice of mathematics becomes completely determined by the diktats of a vast capitalis…
I am not suggesting models will be capable of generating 'all' proofs - that is clearly impossible. Merely that they will get better at doing so, and there is no clear reason at the moment to believe they will never reach a human level of competence. If you have one model functioning at such a level, it is presumably trivial to have a million of them, none of which will need to be paid, housed, or sleep etc.
Re: What does the end of mathematics look like?
#24Considering that mathematics is, at its core, a language for defining relationships between quantities, and then relationships between those relationships, so on and so forth, I think it's fair to assume that the possible number of such relationships are infinite. Some of these relationships will obviously be useful in the real world, but they don't always have to be. I too, suspect that we can keep on building theor…
> a language for defining relationships between quantities
Could you expand on this? I don't see maths as a language for quantities specifically (i.e. what does symmetry have to do with quantities).
> just too tedious (but not impossible) for a human being to work through the proof.
Already happened with the four colour theorem arguably.
Re: What does the end of mathematics look like?
#25We'll know that the time draws nearer when an AI confirms or refutes Mochizuki's proof of the abc conjecture. As of right now, I don't think they're capable of doing that. And, as they can't even check a very (very!) complex proof, they won't be able to conjure any inhumanly complex proofs de novo . Also: > To expand: what if the practice of mathematics becomes completely determined by the diktats of a vast capitalis…
also why would capitalists expand resources on churning out proof after proof when mathematical proofs are not patentable?
A reasonable question - another way of looking at it is that theorems are just a side effect of mathematical research. Much of the world economy depends on things like cryptography, which involves a bunch of theorems. The question is then 'what as yet undiscovered mathematical realms might models think up that could make people money'? It is hard to imagine what doesn't exist yet, but much harder to imagine that all potentially profitable mathematics has already been discovered. This could 'just' look like algorithmic improvements.
Re: What does the end of mathematics look like?
#26When does math become recreational for people?
How is that any different than people programming for fun?
Re: What does the end of mathematics look like?
#27Earlier quoted context omitted.
>>I live by myself in a remote mountain cave = I live in California, and the nearest Starbucks is more than 20 miles away. >>can only be contacted during a full moon = As a night person, I am awake when the streetlight outside my house turns on. >>certain arcane rites that are too horrible to speak of = In order to contact me, you must install Microsoft Teams. Overall, it's not that bad, except for the MS team thing.…
The man is south african, we are geologically blessed and have a lot of pleasant remote mountain caves =)
True!
I don't literally live in a cave, but fortunately not everyone is so allergic to whimsical language :D.
Re: What does the end of mathematics look like?
#28We'll know that the time draws nearer when an AI confirms or refutes Mochizuki's proof of the abc conjecture. As of right now, I don't think they're capable of doing that. And, as they can't even check a very (very!) complex proof, they won't be able to conjure any inhumanly complex proofs de novo . Also: > To expand: what if the practice of mathematics becomes completely determined by the diktats of a vast capitalis…
Why would an AI confirmation or rejection be more convincing than the proof itself?
Presumably an AI would formalise the proof in a system such as Lean, then you only need to trust the kernel of that proof system.
Rejecting a proof would be more complicated, because while for confirming a proof you only need to check that the main statement in the formalisation matches that of the conjecture, showing that a proof has been rejected requires knowledge of the proof itself (in general).
Re: What does the end of mathematics look like?
#29Earlier quoted context omitted.
As always, HN has no sense of humour...
Writing like a wanker isn't funny.
Why not just say to yourself, - "I don't think that's funny" - instead of generalizing on behalf of others with a word that is in essence, meaningless or rather, it means what you personally want it to mean for any particular occasion?
Re: What does the end of mathematics look like?
#30Considering that mathematics is, at its core, a language for defining relationships between quantities, and then relationships between those relationships, so on and so forth, I think it's fair to assume that the possible number of such relationships are infinite. Some of these relationships will obviously be useful in the real world, but they don't always have to be. I too, suspect that we can keep on building theor…
just the zfc axioms alone are already infinite. It's an axiom schema ranging over an infinite number of actual statements. That's just statements, without even considering symbols as you're saying.