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After Math

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Re: After Math

#71

Post by anonymouz »

charcircuit wrote: post #31

>The first assumption is wrong because to really solve a mathematical problem, providing a mere answer (even if formally certified) is not sufficient. What is missing is an intelligible proof that human mathematicians can understand and use to advance the aims of mathematics. This makes a bad assumption that humans need to be the one to advance the aims of mathematics. LLMs could be what advances the aims of mathemat…

The authors discuss the dual roles of proofs, and the new need to differentiate them better, clearly in the article.

Re: After Math

#72

Post by charcircuit »

anonymouz wrote: post #71
charcircuit wrote: post #31

>The first assumption is wrong because to really solve a mathematical problem, providing a mere answer (even if formally certified) is not sufficient. What is missing is an intelligible proof that human mathematicians can understand and use to advance the aims of mathematics. This makes a bad assumption that humans need to be the one to advance the aims of mathematics. LLMs could be what advances the aims of mathemat…

The authors discuss the dual roles of proofs, and the new need to differentiate them better, clearly in the article.

I disagree with the idea that they require serving both roles in order to be considered a proof.

Re: After Math

#73

Post by oliculipolicula »

svara wrote: post #67

I'm a bit worried that this line of reasoning is assuming its conclusion, in stating that mathematics is for human understanding. This is not something that's just true on its own; it's on us as a species to make sure that it remains that way, for the sake of our dignity. However, this position will be extremely difficult to defend, against the economic value of not caring.

It points to a possible alignment: math helps humans to _discover_. So can AI.

You're right though; the economic and emotional impact of OpenAI's executives are much more obvious today. In comparison, the actual implications of Navier-Stokes blow-ups on the epistemological landscape will take at least two years to become obvious to any intelligence, if ever.

I'm optimistic that the Joe in the street will soon be able to make earth shattering discoveries with the help of AI, at least once a week, when universal basic tokens come to pass. Then the nihilists will also keep their existential or otherwise depression to their AI therapists. Hopefully then the puritan billionaires can only helplessly compare the profligate blooming of a thousand new avenues to unrestrained moral depravity

Re: After Math

#74

Post by icepush »

yazaddaruvala wrote: post #12

I think as a civilization we need to postulate a new term: “purpose death” Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence. I truly think because of the pace of innovation this will be a universal feeling for every hu…

I, on the other hand, don't want to be a permanent serf to whoever manages to merge their brain with ASI first and think it's high time we begin decommissioning datacenters through direct action.

Re: After Math

#75

Post by rdedev »

yazaddaruvala wrote: post #12

I think as a civilization we need to postulate a new term: “purpose death” Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence. I truly think because of the pace of innovation this will be a universal feeling for every hu…

> AI will run and trample anything that stays in front of it.

Right now that entirely depends on the whims of a few people. We can try to make it not be that but I don't have much hope in that area. See climate change

> As a software engineer, I myself have only recently recovered from it

Can I ask you how you came here? Right now I am getting closer to "purpose death" as you call it. Software engineering is one of the few things I am good at and the only thing that I can rely on to put food on my table. Even if I end up being someone who gives minor suggestions to the AI, it always feels like C level execs can't wait to get rid of me

Re: After Math

#76

Post by qbit42 »

stabbles wrote: post #7

Wouldn't AI make the field of mathematics more ambitious? In software development it feels that way: there are often tasks I can take on that would have been too risky in 2025, because it was unclear if they were worth it. Now you generate a prototype and can make much better judgement calls what is possible and what is worth pursuing.

Maybe, but what remains of the human professional mathematics will be unrecognizable (at least for those without tenure I guess). All of our credit assignment systems are breaking and access to computational/financial resources is becoming way more important. Math has been one of the most open academic fields but everyone is becoming afraid of sharing their ideas. Personally, my job has slowly been moving from open-ended brainstorming to prompting/digesting LLM output (or LLM output transmitted by grad students). And the students are so demoralized! Also, the academic funding structures which have supported math departments are looking less and less stable - I imagine many of them will shrink.

Re: After Math

#77

Post by rdedev »

icepush wrote: post #74
yazaddaruvala wrote: post #12

I think as a civilization we need to postulate a new term: “purpose death” Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence. I truly think because of the pace of innovation this will be a universal feeling for every hu…

I, on the other hand, don't want to be a permanent serf to whoever manages to merge their brain with ASI first and think it's high time we begin decommissioning datacenters through direct action.

I hope what happens in the original deus ex game happens here then, that the ASI does not want to merge with a human who wants it only for base desires

Re: After Math

#78

Post by alansaber »

sigmoid10 wrote: post #68

This kind of argument is always dangerous, because it essentially resorts to moving goalposts. "Oh, AI can now do X? Sure it is amazing, but it can't do Y yet, so we're totally safe!" Just because humans can't process the proof or see the advancements, it doesn't mean that it will remain that way in the future or that it will not change the field. If you only define yourself by things AI can't do yet , you're about t…

Technology advances, but extrapolating the value of human labour to 0 is equally invalid.

Re: After Math

#79

Post by alansaber »

zkmon wrote: post #51

It shows that the human quest has been in wrong direction since the industrial age began. Domains like math and other inter-connected or inter-dependent domains - all exist in modern times only to keep people employed outside of basic work such as farming and survival. All of these domains can be removed and humans can still continue with their lives taking care of what really is needed for their survival and sprawl.…

Why draw the line at the industrial age? Humans subsisted for millenia before the ready preparation of fire.

Re: After Math

#80

Post by qbit42 »

zarzavat wrote: post #28

The hand wringing is premature. Thus far AI has only shown a superhuman aptitude for brute forcing proof of existence: - Disproof of the Jacobian conjecture by example - Construction of a non-sofic group - Existence of singularity in Navier-Stokes Mathematical conjectures tend to be universally quantified, especially those conjectures that are used as building blocks (e.g. RH). If anything, AI models are currently pe…

You can also brute force the existence of a proof...

It is true that the biggest splashes have been from counterexamples and such, but I have seen many smaller examples of proving positive results in my own field.

Perhaps not superhuman yet but sufficient to completely upend the status quo. And I'm supposed to believe that this won't change in a year? or two?

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