Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Mathematics Without Mathematicians

borretti.me

Post reply on HN
Print view View original

31–40 of 57 posts

Re: Mathematics Without Mathematicians

#31

Post by fidotron »

Grimblewald wrote: post #4
serious_angel wrote: post #2

> The AIs will exceed humans in taste and intuition... > The AIs will be better teachers than the humans. In any case, there won’t be a human audience for expository work of frontier math. > No human needs to understand any of it... Absolute nonsense. I am sorry, but... is it appropriate to not consider the author sick or having some mental disorder? It seems like the person has no idea what they are talking about, o…

While I agree the claims may be strong, they're not inconceivable. I still think current AI architectures are fundamentally incapable of replacing us in any of the ways discussed, however it is now something I consider plausible as seeing happen in my lifetime.

Furthermore, any attempt to pretend otherwise is an appeal to the idea we are in literal fact haunted by our own internal demons that are inexplicable to science or mathematics.

One of the effects of this entire debate is it's exposed how many people claiming to be pure mechanistic rationalists actually never were. At least those of an openly religious inclination have been sticking to their position consistently.

Re: Mathematics Without Mathematicians

#32

Post by breezybottom »

pfdietz wrote: post #11
Twey wrote: post #6

> The result is that we will live in a demon-haunted world, full of marvelous devices whose operation we will not understand, based on engineering principles we will not understand, discovered using formalisms we will not understand. Well, that's just where we started — and then we developed science and mathematics to understand it. Why would it be any different if the demons live in our technological progeny instead…

This already describes the world for the vast majority of people. These changes are just the same thing coming to a thin intellectual elite who thought they were immune. ["First time?" meme]

So what? You can't see the difference between "the average person doesn't understand it" and "no one understands it"?

Re: Mathematics Without Mathematicians

#33

Post by 4bpp »

pfdietz wrote: post #11
Twey wrote: post #6

> The result is that we will live in a demon-haunted world, full of marvelous devices whose operation we will not understand, based on engineering principles we will not understand, discovered using formalisms we will not understand. Well, that's just where we started — and then we developed science and mathematics to understand it. Why would it be any different if the demons live in our technological progeny instead…

This already describes the world for the vast majority of people. These changes are just the same thing coming to a thin intellectual elite who thought they were immune. ["First time?" meme]

I can see humanity walking to its collective doom with a sense of satisfaction, like "at least/last it is happening to those other guys too".

Re: Mathematics Without Mathematicians

#34

Post by breezybottom »

Nevermark wrote: post #10
Twey wrote: post #6

> The result is that we will live in a demon-haunted world, full of marvelous devices whose operation we will not understand, based on engineering principles we will not understand, discovered using formalisms we will not understand. Well, that's just where we started — and then we developed science and mathematics to understand it. Why would it be any different if the demons live in our technological progeny instead…

Those "demons" didn't eat our lunch? (I know that can be interpreted as flippant, but it is intended as a serious answer. Because each impact like this, is not an end to some transition, but just one more point on an accelerating line.) My personal view - which gets a lot of flak here, is the advent of AI is on par with the Big Bang and the first replication-independent cells. Cognition is in the process of taking th…

Colonizing the solar system for resources is something that's said by people who don't understand astronomy or space technology (like Elon Musk).

Re: Mathematics Without Mathematicians

#35

Post by gradschool »

I don't move in these circles but the way I picture it is that higher mathematics in its purest form has no applications but is rather a medium of creative expression among a select few. How is AI generating voluminous opaque proofs of esoteric results so different from generating millions of hours of music nobody likes or has time to hear that we think the former is world-changing while the latter is just slop?

Re: Mathematics Without Mathematicians

#36

Post by pfdietz »

breezybottom wrote: post #32
pfdietz wrote: post #11

Earlier quoted context omitted.

This already describes the world for the vast majority of people. These changes are just the same thing coming to a thin intellectual elite who thought they were immune. ["First time?" meme]

So what? You can't see the difference between "the average person doesn't understand it" and "no one understands it"?

I can see the difference. But is that a difference that matters? Why is the thin elite layer you are referring to a group anyone else should care about, any more than any other occupational minority that's been rudely displaced over the past centuries?

Re: Mathematics Without Mathematicians

#38

Post by heaney-555 »

gradschool wrote: post #35

I don't move in these circles but the way I picture it is that higher mathematics in its purest form has no applications but is rather a medium of creative expression among a select few. How is AI generating voluminous opaque proofs of esoteric results so different from generating millions of hours of music nobody likes or has time to hear that we think the former is world-changing while the latter is just slop?

Do you seriously not see the difference, or are you being intentionally obtuse?

Plus, no, multiple of the problems Astra solved do have real-world applications in computer science, and perhaps even chip design.

Re: Mathematics Without Mathematicians

#39

Post by heaney-555 »

c2c2c wrote: post #21

I am growing tired of seeing the terms "cope" and "moving the goalposts" in response to discussions around AI. Is there not value in trying to understand what the strengths and weaknesses of the technology are? How can we do that without examining the limitations of the models' current abilities? If we simply dismiss those arguments out of hand as feeble attempts to deny the inevitable rise of superintelligence, then…

>Is there not value in trying to understand what the strengths and weaknesses of the technology are?

There is, but having that discussion without a discussion and understanding of the velocity with which those strengths are improving and those weaknesses are disappearing is pointless.

Worse, much of the discussion is already outdated by where the latest models (with proper agentic harnesses) are.

Re: Mathematics Without Mathematicians

#40

Post by latexr »

The word “cope” shows up nine times in this short post. It was frankly annoying to the point it’s hard to take the arguments seriously, because it’s starting from an obvious base of “people who disagree are all wrong and their arguments aren’t worth taking seriously”.

It’s akin to the subset of cryptocurrency proponents who fervently argue that people who are against cryptocurrencies have that opinion because they’re jealous they didn’t become rich. It shows a profound lack of understanding—and, more importantly, an unwillingness to understand—the other side of the argument.

This is made evident by the very first “argument” of moving the goal posts. It’s dismissed off-hand, without even explaining what those entail. That’s the same as saying “if a person makes a fallacious argument, they’re wrong and you can ignore them”¹. But crucially, sometimes what we ourselves think is a fallacious argument, isn’t. “Moving the goal posts” is probably the most misused accusation I see in LLM discussions. It’s basically a talking point by now.

¹ Which is itself a fallacy: https://en.wikipedia.org/wiki/Argument_from_fallacy

Post reply on HN