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AI isn’t outthinking mathematicians, it’s out-remembering them

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Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#191

Post by chongli »

a2ff6eeb0 wrote: post #174
chongli wrote: post #164

Earlier quoted context omitted.

So you concede the point then. The age of humans comprehending things is not coming to an end . And therein lies the rub. When it comes to intellectual labour: Understanding == Value If a mathematician produces something incomprehensible then it has no value. It's meaningless. Indistinguishable from random noise. An AI which produces incomprehensible text is producing no value. We didn't need to spend trillions of do…

You may have missed the present tense. I didn't say it's over, but that it will be. Please pay attention and don't make straw men. Again, do you believe that there are documents, of any value, that humans don't understand? Maybe an LLM could help you notice what I was saying, since it's clearly beyond at least one human's comprehension!

Again, do you believe that there are documents, of any value, that humans don't understand?

There is no value in an undeciphered document until understanding is achieved, just as a lode of gold ore in some asteroid orbiting a distant star has no value until we can fly there and extract it.

If an LLM can help us understanding something then it was not incomprehensible, by definition.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#192

Post by tcp_handshaker »

aurareturn wrote: post #100
tengbretson wrote: post #82

Earlier quoted context omitted.

String theory is a great example of a dead end kept alive by ego and sunk cost fallacy. An AI would have declared it dead and moved on 10 years earlier.

When people make these comments about string theory, are they at the forefront of quantum physics theory and have spent years on modern string theory? Or did they just watch a YouTube video and then keep parroting this?

Sabine has been at the forefront and has the goods: https://youtu.be/1mgxuVVUz40

And for the inevitable critics of Sabine...maybe Leonard Susskind is good enough for you: https://youtu.be/2p_Hlm6aCok

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#193

Post by a2ff6eeb0 »

chongli wrote: post #183
akiselev wrote: post #129

Earlier quoted context omitted.

> Can you give an example of an incomprehensible piece of writing (any writing, never mind a proof) that has commercial value commensurate with the costs involved here? It depends on what exactly you mean by "commercial value commensurate with the costs involved" but I'd volunteer the 3G/4G/5G specifications and the other documentation required to implement the mobile network protocols. 5G is currently sitting at ove…

Read the rest of the discussion. The claim is about text which is in principle incomprehensible to humans. If there exists a text which only one person can understand, that person can communicate their understanding to others, even if that doesn't help them with the original text. That dissemination of knowledge is what provides the value, not the mere existence of the text. If that person forgets or dies before they…

> If there exists a text which only one person can understand, that person can communicate their understanding to others, even if that doesn't help them with the original text.

If there exists a text which only an AI can understand, that AI can communicate their key conclusions to others, even if that doesn't help them with the original text.

The only difference here is the amount of meat involved. Perhaps tossing a few steaks on the server racks could help with that.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#194

Post by nobodyandproud »

devmor wrote: post #160
Arainach wrote: post #140

Earlier quoted context omitted.

Spending your life's work on a theory that is widely agreed to be untestable is certainly a form of ego, or at least is more philosophy than science.

This is a pretty silly belief to hold about science. Plenty of strong, well held standards of the modern era were considered ridiculous fringe beliefs a century ago.

They were testable, no?

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#195

Post by alterom »

philipfweiss wrote: post #102

One thing about human mathematicians is that they only publish positive results. Professors etc might have file drawers full of "negative results", but the incentives and bandwidth of human mathematicians makes publishing these useful results impossible. But AI agents have no such limitations and can publish and re-use negative traces easily. There have been some recent projects ( https://www.theoremdb.org ) aimed at…

The bandwidth is absolutely there ("we tried this and it didn't work" is totally the stuff of conference discussions).

The incentives are not.

The incentives are skewed towards "a magician never reveals her secrets". The results are presented as if a rabbit got pulled out of a hat, with a maximum ta-da! effect, and little backstory of how the hell did we get there.

Don't get me wrong, these things are discussed, often over beers (you better drink it you want to make a career in the field).

But not published.

The younger mathematicians are trying to change that with the blogging culture. But the professional incentives aren't there. (In corp-speak: can't put blogging on perf). They burn out.

That's why math blogs usually come from either the top dogs in the field, like Terrence Tao, who don't need to care about perf, or people outside academia.

That's one thing that I hope the disruptive/destructive effects of LLMs will force mathematicians to face.

As one of my fellow mathematicians sarcastically wrote¹, we've reached a point where we should become a cult because we're acting like one anyway.

The other possibility is, of course, that the shake-up will take us precisely into that direction.

My point here is that the real problem here is not mathematical; it's a social one: incentives and politics, organizational structures, policies, allocation of jobs and funding.

All of this directly impacts how we do mathematics, who we do it with and teach it to, how we teach and communicate, and, of course, what math we even do and look at.

Given that, I'm neither too worried about humans vs. AI standoff, nor hyped about the Glorious New Future full of AI-assisted discoveries.

AI or not, the organizational issues in the field are still there, as are the incentive structures (including the infamous publish-or-perish).

We are doomed, yes, but by our own hands and committees. And it's up to us, not the AI, to get us out of there.

The little shove from the AI might be just the thing we need.

____

¹ https://www.mcsweeneys.net/articles/an-open-letter-to-the-ma...

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#196

Post by chongli »

scarmig wrote: post #168
chongli wrote: post #90

Earlier quoted context omitted.

You've moved the goalposts. The original claim was about producing mathematics that are in principle impossible for any human to understand . All the stuff you've listed is understood by some person, and that understanding is the source of its value. Now that we've cleared that up, can you furnish an example that satisfies the original claim of incomprehensibility and value?

There are plenty of artifacts that, if not impossible for humans to understand, then at least no human has ever completely understood. To start with, the universe as a whole. Despite that, we are able to choose legible pieces of it to model and perform useful actions from. This will shift your argument--that doesn't count! etc., to the point where it's by construction unsatisfiable and vacuous. And it doesn't matter:…

One person need not completely understand something for it to have value; it's sufficient for there to exist a shared understanding.

an LLM might e.g. break some cryptographic algorithm in a way utterly unintelligible to humans, but the fact that it works would be sufficient on its own to make all of us choose to abandon that algorithm and choose different ones.

No, that is the entire point. If it is an algorithm which accomplishes something useful, then it is intelligible as such. That which is incomprehensible cannot be understood even in part, so it provides no value as a bit of knowledge (unless you're looking for a strong random number source, I suppose).

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#197

Post by OroPla »

aurareturn wrote: post #100
tengbretson wrote: post #82

Earlier quoted context omitted.

String theory is a great example of a dead end kept alive by ego and sunk cost fallacy. An AI would have declared it dead and moved on 10 years earlier.

When people make these comments about string theory, are they at the forefront of quantum physics theory and have spent years on modern string theory? Or did they just watch a YouTube video and then keep parroting this?

I also just keep parroting that the Earth is not flat and a bunch of other things I've been told and then never questioned, since it seems to make sense.

When the flath-earth craze started I've been trying to at least get that bit actually personally verified. Haven't managed to do it to this day, though. So I'll just keep parroting various things without properly understanding them.

C'est la vie.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#198

Post by hibikir »

I suspect that a lot about what we call being very intelligent is ultimately out-remembering people around us. I think of all the times in my software career when I did something that others considered very high performance, it either came down to either having more energy than others at tackling a problem they thought was more trouble than it was worth, or just bringing back random knowledge from previous jobs or self study, and being able to apply it to the problem at hand.

I don't think I've had a truly original idea in my life. Combine A + B, when it's rare for people to know A and B at the same time. So from that perspective, what LLMs are doing is basically the same thing. Sometimes I am faster than the LLM because my context might be better organized, but it typically needs just a hint from me to steer itself correctly. It claims something is a memory leak, but smelling a rat, I suggest it to double check the garbage collection statistics too, at which point it's clear it's no leak, but a tuning error, at which point the LLM is better at tuning than me, because it has more energy than I do.

Maybe there's true brilliance out there, when something doesn't come out of combining data and building hypothesis until you get really lucky. My experience is not comprehensive. But I look around me, and it sure seems I've not been lucky enough to see it. Even the shiniest people I've worked with, which most of the audience here would recognize, have never shown me that they can go past this.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#199

Post by chongli »

atleastoptimal wrote: post #97
chongli wrote: post #26

Earlier quoted context omitted.

We don’t trillions of dollars in LLM investment to build things mathematicians don’t understand. We already have plenty of those, even from ancient times. As to your second point, Terry Tao already has an answer [1]: the proof isn’t the contribution, shared understanding is. This issue was already raised back when the four-colour theorem was proved. Machine proving and machine proof checking are useful tools but they…

If humans have nothing to contribute then shared understanding is a pointless endeavor. It makes sense now in the "centaur" period where human + AI > AI alone, but when AI mathematicians are both more rigorous and more elegant, then taking the time dumbing down their proofs to a human level of understanding is like requiring that we ensure all our current proofs be understandable by a monkey.

Where is the value in an unintelligible gibberish proof?

We already have countless examples of such filling up the arXiv, written by hacks long before LLMs started writing proofs. No one cares about them. You might as well build a box blasting radio static into the void. You could save a lot of electricity that way.

Re: AI isn’t outthinking mathematicians, it’s out-remembering them

#200

Post by OroPla »

AustinDev wrote: post #73
EA-3167 wrote: post #59

Earlier quoted context omitted.

Robots in labs already exist, but mercifully they're not hooked up to anything as unpredictable as an LLM. Robots tend to work best as specialists doing high-throughput, extremely repetitive tasks which nonetheless require a degree of precision. Giving a robot a "human" body makes very little sense if we're talking about the needs and productivity of a non-human; humanoid robots are marketing for humans.

Humanoid robots are obviously more than marketing. The entirety of human civilization is human shaped. Making robots that are human shaped is easier and more efficient than redesigning and rebuilding everything that exists.

Historically this has never been correct. Turns out you get more efficient systems when designing them without how a human would accomplish a task in mind.
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