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Mathematics Without Mathematicians

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Re: Mathematics Without Mathematicians

#41

Post by aureate »

Claimed refutation of one of OpenAI's 10 claimed advances (their disproof of Connes' rigidity conjecture): https://philpapers.org/archive/NIEWTC.pdf

I am hopelessly ill qualified to judge.

Edit: Looking around at context, this has major crank warning signs (claims to also prove the conjecture, author has claimed solutions to both the Riemann Hypothesis and the Navier-Stokes problem and is involved in "alternative propulsion" research). I doubt OpenAI would have published without thorough verification.

Re: Mathematics Without Mathematicians

#42

Post by Nevermark »

breezybottom wrote: post #34
Nevermark wrote: post #10

Earlier quoted context omitted.

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).

Said with no rational given.

The solar system readily provides both the motivation, and the means, for technological colonization. It quickly pays and provides for its own utilization.

I do agree Musk's projections for biological/human colonization appear to be unrealistic. Just one challenge: it isn't clear humans can reproduce in non-Earth gravity. That is an extreme impediment.

Re: Mathematics Without Mathematicians

#43

Post by gradschool »

heaney-555 wrote: post #38
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.

Being obtuse comes effortlessly to me, I'm afraid. My comment pertains specifically to the kind mathematics that has no applications as a rebuttal to what I read as the author's main claim it will inevitably decline as a human endeavor. Saying that, I believe that AI has great potential to advance engineering.

Re: Mathematics Without Mathematicians

#44

Post by placebo »

fidotron wrote: post #31
Grimblewald wrote: post #4

Earlier quoted context omitted.

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.

Agreed. Unfortunately some religious inclinations can be just as tedious as pure mechanistic rational inclinations, even if they are consistent. Fortunately, these are not the only two options available. The future that the article points to is not necessarily only bad news - it might be the uncomfortable truth required to transcend our limiting beliefs.

Re: Mathematics Without Mathematicians

#45

Post by TimorousBestie »

bananaflag wrote: post #3
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…

I work in math and also believe in this stuff and have done so for years. You may call me sick if you wish so. My only cope among those was, using the author's words, "We will teach the mathematics AI discovers." This was back in 2018, before GPT-2. I abandoned it when I realized AIs will become better at explaining math before they become better at doing math. I still have some hope in the last one "mathematicians a…

> I still have some hope in the last one "mathematicians and the mathematically-inclined will still do math on their own". Maybe some limited communities of this sort will form.

I think it’s pretty likely. Contrary to all the negative things said about mathematicians in this thread, in my experience they’re mostly not profit-driven (for the ones that are tend to filter out of academia during grad school, it’s a high-effort, low-reward environment).

Tao does not seem particularly threatened by AIs doing math, and I trust his judgment.

Re: Mathematics Without Mathematicians

#46

Post by pfdietz »

TimorousBestie wrote: post #45
bananaflag wrote: post #3

Earlier quoted context omitted.

I work in math and also believe in this stuff and have done so for years. You may call me sick if you wish so. My only cope among those was, using the author's words, "We will teach the mathematics AI discovers." This was back in 2018, before GPT-2. I abandoned it when I realized AIs will become better at explaining math before they become better at doing math. I still have some hope in the last one "mathematicians a…

> I still have some hope in the last one "mathematicians and the mathematically-inclined will still do math on their own". Maybe some limited communities of this sort will form. I think it’s pretty likely. Contrary to all the negative things said about mathematicians in this thread, in my experience they’re mostly not profit-driven (for the ones that are tend to filter out of academia during grad school, it’s a high-…

An alternate interpretation of Tao is that he has no illusions about where this is going and is trying the optimize his outcome. I wonder what he's telling his grad students and prospective grad students.

Re: Mathematics Without Mathematicians

#47

Post by pfdietz »

4bpp wrote: post #33
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]

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".

The mathematicians could make an argument that applies to everyone. But that probably leads to outright communism, and that well is still quite poisoned. Maybe AI ultimately gets powerful enough to give us Banksian full luxury communism. Alternately, it gives a world where corporations don't need workers and tyrants don't need citizens.

Re: Mathematics Without Mathematicians

#48

Post by [deleted] »

pfdietz wrote: post #46
TimorousBestie wrote: post #45

Earlier quoted context omitted.

> I still have some hope in the last one "mathematicians and the mathematically-inclined will still do math on their own". Maybe some limited communities of this sort will form. I think it’s pretty likely. Contrary to all the negative things said about mathematicians in this thread, in my experience they’re mostly not profit-driven (for the ones that are tend to filter out of academia during grad school, it’s a high-…

An alternate interpretation of Tao is that he has no illusions about where this is going and is trying the optimize his outcome. I wonder what he's telling his grad students and prospective grad students.

[deleted]

Re: Mathematics Without Mathematicians

#49

Post by Nevermark »

latexr wrote: post #40

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…

> it’s starting from an obvious base of “people who disagree are all wrong and their arguments aren’t worth taking seriously”.

Taking arguments seriously doesn't necessitate agreement.

Re: Mathematics Without Mathematicians

#50

Post by Twey »

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…

> Those "demons" didn't eat our lunch?

Tell that to the Europeans who were so afraid of naming the bear that its original name is still lost to us :) The Luddites also had a lot to say about the mechanical demons that were eating their lunches.

> Cognition is in the process of taking the leap from glacially slow biology under blind evolution, to lightening fast (scales of software in days, hardware in months) engineered self-optimization.

Yes-but, time scales are relevant only relative to other time scales (or the Planck time, if we get there). If the whole universe were to start running at 1,000,000× speed, you wouldn't notice. Speed is important to us humans currently because of our individual perspective and associated limited lifespan, but not in a universal sense (modulo some big hurdles like star lifetime and heat death). There are already self-replicating organisms with much faster iteration cycles than humans or human technology, like bacteria.

> Within 10 years, the robotics side will catch up with the speed of the software side. Biological cognition, bodies and economic status are all getting revolutionized within the next 10-15 years.

Just like it was in the 1980s, or the 1800s? I don't claim that these things _won't_ happen in the next ten years, but looking at it empirically people thinking that they will coïncides with every new technology and is a poor predictor.

> If there is reason in the short term to be discouraged, it is due to ourselves. But pushing for more ethical systems, hard, right now, is a better and right response.

I don't disagree, but it's not like we haven't been trying. Attempts to codify ethics go back about as far as human civilization, and it's not obvious to me that there's any faster road, and certainly not one fast enough to outpace our current rate of technological development (before you even start talking about AGI!).

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