What does the end of mathematics look like?
awanderingmind.blog
What does the end of mathematics look like?
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Re: What does the end of mathematics look like?
#2We'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 capitalist machinery of proprietary machine learning models churning out proof after proof, and theory after theory, conjured from the aether of all possible true statements?
I don't think that this is possible even in theory, as computational resources are limited and "the aether of all possible true statements" is incomprehensively vast. (There's a massive orders-of-magnitude difference in size between true-seeming-yet-false statements and the number of elementary particles in the visible universe. More statements than particles.) You can't brute force it.
Re: What does the end of mathematics look like?
#3We'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?
Re: What does the end of mathematics look like?
#4We'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?
That will change quickly if capitalists see that as an obstacle. Right now, they don't really care about that, as for example software (much of which is just math) is already patentable in the US.
Re: What does the end of mathematics look like?
#5Considering 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 theorems on top of theorems with increasing complexity, until a point is reached that it becomes just too tedious (but not impossible) for a human being to work through the proof.
Re: What does the end of mathematics look like?
#6We'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…
> We'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.
I agree, but... Spend time formalising a large part of existing mathematics and proofs, train a bunch of sufficiently powerful and generative models with that, and with cooperative problem solving and proof strategies, and give them access to proof assistants and adequate compute resources, and something interesting could happen.
I suspect the barrier is finding a business model that would pay for this. Turning mathematics into an industrial, extruded-on-demand product might work, but I dont know who (except maybe the NSA) would stump-up the money.
Re: What does the end of mathematics look like?
#7This 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.
Re: What does the end of mathematics look like?
#8When does math become recreational for people?
Re: What does the end of mathematics look like?
#9This 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.
Agreed if I had saw that first I wouldn't have clicked
Re: What does the end of mathematics look like?
#10[deleted]