The cultural divide between mathematics and AI • Hacker News Board

Re: The cultural divide between mathematics and AI

#41

Post by chasd00 » Wed, Mar 12, 2025, 6:34 PM UTC

bluefirebrand wrote: post #25

Henchman21 wrote: post #15

Earlier quoted context omitted.

I’ve worked in tech my entire adult life and boy do I feel this deep in my soul. I have slowly withdrawn from the higher-level tech designs and decision making. I usually disagree with all of it. Useless pursuits made only for resume fodder. Tech decisions made based on the bonus the CTO gets from the vendors (Superbowl tickets anyone?) not based on the suitability of the tech. But absolutely worst of all is the arro…

> Move fast and break things!! Even when its the society you live in. This is the part I don't get honestly Are people just very shortsighted and don't see how these changes are potentially going to cause upheaval? Do they think the upheaval is simply going to be worth it? Do they think they will simply be wealthy enough that it won't affect them much, they will be insulated from it? Do they just never think about co…

Humans like to solve problems and be at the top of the heap. Such is life, survival of the fittest after all. AI is a problem to solve, whoever gets to AGI first will be at the top of the heap. It's a hard drive to turn off.

Re: The cultural divide between mathematics and AI

#42

Post by oersted » Wed, Mar 12, 2025, 6:35 PM UTC

xg15 wrote: post #22

> One question generated particular concern: what would happen if an AI system produced a proof of a major conjecture like the Riemann Hypothesis, but the proof was too complex for humans to understand? Would such a result be satisfying? Would it advance mathematical understanding? The consensus seemed to be that while such a proof might technically resolve the conjecture, it would fail to deliver the deeper understa…

Serious theorem-proving AIs always write the proof in a formal syntax where it is possible to check that the proof is correct without issue. The most popular such formal language is Lean, but there are many others. It's just like having a coding AI, it may write some function and you check if it compiles. If the AI writes a program/proof in Lean, it will only compile if the proof is correct. Checking the correctness of proofs is a much easier problem than coming up with the proof in the first place.

Re: The cultural divide between mathematics and AI

#43

Post by bo1024 » Wed, Mar 12, 2025, 6:35 PM UTC

woah wrote: post #20

> Perhaps most telling was the sadness expressed by several mathematicians regarding the increasing secrecy in AI research. Mathematics has long prided itself on openness and transparency, with results freely shared and discussed. The closing off of research at major AI labs—and the inability of collaborating mathematicians to discuss their work—represents a significant cultural clash with mathematical traditions. Th…

AI is undergoing a transition from academic research to industry engineering.

(But the engineers want the benefits of academic research -- going to conferences to give talks, credibility, intellectual prestige -- without paying the costs, e.g. actually sharing new knowledge and information.)

Re: The cultural divide between mathematics and AI

#44

Post by tech_ken » Wed, Mar 12, 2025, 6:36 PM UTC

Mathematics is, IMO, not the axioms, proofs, or theorems. It's the human process of organizing these things into conceptual taxonomies that appeal to what is ultimately an aesthetic sensibility (what "makes sense"), updating those taxonomies as human understanding and aesthetic preferences evolve, as well as practical considerations ('application'). Generating proofs of a statement is like a biologist identifying a new species, critical but also just the start of the work. It's the macropatterns connecting the organisms that lead to the really important science, not just the individual units of study alone.

And it's not that AI can't contribute to this effort. I can certainly see how a chatbot research partner could be super valuable for lit review, brainstorming, and even 'talking things through' (much like mathematicians get value from talking aloud). This doesn't even touch on the ability to generate potentially valid proofs, which I do think has a lot of merit. But the idea that we could totally outsource the work to a generative model seems impossible by definition. The point of the labor is develop human understanding, removing the human from the loop changes the nature of the endeavor entirely (basically to algorithm design).

Similar stuff holds about art (at a high level, and glossing over 'craft art'); IMO art is an expressive endeavor. One person communicating a hard-to-express feeling to an audience. GenAI can obviously create really cool pictures, and this can be grist for art, but without some kind of mind-to-mind connection and empathy the picture is ultimately just an artifact. The human context is what turns the artifact into art.

Re: The cultural divide between mathematics and AI

#45

Post by [deleted] » Wed, Mar 12, 2025, 6:41 PM UTC

nicf wrote: post #21

lordleft wrote: post #19

Earlier quoted context omitted.

I'm not a mathematician so please feel free to correct me...but wouldn't there still be an opportunity for humans to try to understand why a proof solved by a machine is true? Or are you afraid that the culture of mathematics will shift towards being impatient about this sorts of questions?

Well, it depends on exactly what future you were imagining. In a world where the model just spits out a totally impenetrable but formally verifiable Lean proof, then yes, absolutely, there's a lot for human mathematicians to do. But I don't see any particular reason things would have to stop there: why couldn't some model also spit out nice, beautiful explanations of why the result is true? We're certainly not there…

[deleted]

Re: The cultural divide between mathematics and AI

#46

Post by GPerson » Wed, Mar 12, 2025, 6:43 PM UTC

nicf wrote: post #21

lordleft wrote: post #19

Earlier quoted context omitted.

I'm not a mathematician so please feel free to correct me...but wouldn't there still be an opportunity for humans to try to understand why a proof solved by a machine is true? Or are you afraid that the culture of mathematics will shift towards being impatient about this sorts of questions?

Well, it depends on exactly what future you were imagining. In a world where the model just spits out a totally impenetrable but formally verifiable Lean proof, then yes, absolutely, there's a lot for human mathematicians to do. But I don't see any particular reason things would have to stop there: why couldn't some model also spit out nice, beautiful explanations of why the result is true? We're certainly not there…

I don’t think the advent of superintelligence will lead to increased leisure time and increased well-being / easier lives. However, if it did I wouldn’t mind redundantly learning the mathematics with the help of the AI. It’s intrinsically interesting and ultimately I don’t care to impress anybody, except to the extent it’s necessary to be employable.

Re: The cultural divide between mathematics and AI

#47

Post by nicf » Wed, Mar 12, 2025, 6:49 PM UTC

GPerson wrote: post #46

nicf wrote: post #21

Earlier quoted context omitted.

Well, it depends on exactly what future you were imagining. In a world where the model just spits out a totally impenetrable but formally verifiable Lean proof, then yes, absolutely, there's a lot for human mathematicians to do. But I don't see any particular reason things would have to stop there: why couldn't some model also spit out nice, beautiful explanations of why the result is true? We're certainly not there…

I don’t think the advent of superintelligence will lead to increased leisure time and increased well-being / easier lives. However, if it did I wouldn’t mind redundantly learning the mathematics with the help of the AI. It’s intrinsically interesting and ultimately I don’t care to impress anybody, except to the extent it’s necessary to be employable.

I would love that too. In fact, I already spend a good amount of my free time redundantly learning the mathematics that was produced by humans, and I have fun doing it. The thing that makes me sad to imagine --- and again, this is not a prediction --- is the loss of the community of human mathematicians that we have right now.

Re: The cultural divide between mathematics and AI

#48

Post by anon291 » Wed, Mar 12, 2025, 6:51 PM UTC

daveguy wrote: post #40

anon291 wrote: post #35

Earlier quoted context omitted.

I work with the ones that made the jump to industry, so no, I'm confronted with the divide day in and day out. The academics that either switch to industry or maintain close industry ties, typically do not seem to share these concerns, or at least, can contextualize them.

Academics that decided they didn't really want to be academics, but instead switched to industry. Seems like a significant sample bias, no?

They're still academics...

Re: The cultural divide between mathematics and AI

#49

Post by gopher_space » Wed, Mar 12, 2025, 6:54 PM UTC

anon291 wrote: post #23

woah wrote: post #20

> Perhaps most telling was the sadness expressed by several mathematicians regarding the increasing secrecy in AI research. Mathematics has long prided itself on openness and transparency, with results freely shared and discussed. The closing off of research at major AI labs—and the inability of collaborating mathematicians to discuss their work—represents a significant cultural clash with mathematical traditions. Th…

[flagged]

I miss when money people treated my motivations like a black box.

Re: The cultural divide between mathematics and AI

#50

Post by EigenLord » Wed, Mar 12, 2025, 7:01 PM UTC

Is it really a culture divide or is it an economic incentives divide? Many AI researchers are mathematicians. Any theoretical AI research paper will typically be filled with eye-wateringly dense math. AI dissolves into math the closer you inspect it. It's math all the way down. What differs are the incentives. Math rewards openness because there's no real concept of a "competitive edge", you're incentivized to freely publish and share your results as that is how you get recognition and hopefully a chance to climb the academic ladder. (Maybe there might be a competitive spirit between individual mathematicians working on the same problems, but this is different than systemic market competition.) AI is split between being a scientific and capitalist pursuit; sharing advances can mean the difference between making a fortune or being outmaneuvered by competitors. It contaminates the motives. This is where the AI researcher's typical desire for "novel results" comes from as well, they are inheriting the values of industry to produce economic innovations. It's a tidier explanation to tie the culture differences to material motive.