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After Math

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Re: After Math

#91

Post by charcircuit »

anonymouz wrote: post #88
charcircuit wrote: post #72

Earlier quoted context omitted.

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

You can, mathematicians generally don't. That's what the article is partially about - a purely formal proof doesn't get us much.

Because most mathematicians have not migrated to being AI native like most software engineers did. My post is trying to point out that these people's mind is still fixed in how the old world works and is not focused on the future where LLMs are doing a lot of the work.

Re: After Math

#92

Post by curt15 »

reisse wrote: post #82

The elephant in the room no one talks about yet, imo, is "should public funding of math studies be adjusted due to AI breakthroughs?" The sports comparison is wrong here because general public never paid for the specific match results. The value was always in the show, the advertising and betting around it, the health and educational value of doing sports, etc. And the sport mostly lives on what it earns, not on publ…

> Math, on the other hand, was paid for because people and states believed progress in math might lead to meaningful improvements in other branches of science, and, in turn, in our lives. If this is better served by AI, should we keep paying for the same number of tenure positions?

That is a pretty huge "if". The ultimate purpose of mathematics and really all scientific inquiry is human understanding of the natural world. It's not at all clear whether large language models can replace that any more than calculators can replace human mastery of arithmetic. Is society ready for engineers to design bridges and airplanes without understanding the underlying mathematics by simply handing off the entire process to a black box "AI architect"? Are people ready to ingest drugs "vibe-designed" by human drones pushing buttons on an "AI drug discovery" machine and just going "meh, seems about right!"

It might also be useful to take a step back from the hype that the frontier labs are obviously incentivised to incite. Before speculating about how "AI math" capabilities might supplant cutting-edge research in mathematics and other sciences, take a look at OpenAI's own job postings (https://openai.com/careers/search/?). Why doesn't OpenAI demonstrate its world-beating AI capabilities by automating more routine roles like "Account Associate", "Systems Architect" or "Android Engineer"?

Re: After Math

#93

Post by anonymouz »

charcircuit wrote: post #91
anonymouz wrote: post #88

Earlier quoted context omitted.

You can, mathematicians generally don't. That's what the article is partially about - a purely formal proof doesn't get us much.

Because most mathematicians have not migrated to being AI native like most software engineers did. My post is trying to point out that these people's mind is still fixed in how the old world works and is not focused on the future where LLMs are doing a lot of the work.

No, because knowing a proof exists is just a small part of math. It's value is rather limited to actual math, as the article explains quite eloquently and nicely.

Re: After Math

#94

Post by robotpepi »

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…

> 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!"

It's not about moving goalposts. What you're not understanding is that, even if for you is crystal clear that AI will be 100x smarter tomorrow, those in charge cannot simply bet all on that. Right now AI cannot really replace the core sauce of mathematicians (all the "understanting" and "asking the real questions" stuff), so it'd be unwise for, say, countries to start making decisions as if AI is capable of that.

Re: After Math

#95

Post by auggierose »

moralestapia wrote: post #90
justinparus wrote: post #84

"It is not the destination, but the journey that matters" For now, AI will be another tool in the toolbox of mathematicians. With humans driving the conversation to help understand the world better. If/when AGI is reached maybe we won’t be in the driver seat as much. I don’t think that matters. The goal of math is to achieve greater understanding of the world, regardless if humans are driving or if an AI is.

Why would my tax dollars go to fund someone's journey on what's essentially a hobby at this point?

You funded it before with your tax dollars, and it was already a hobby at this point. Mathematicians do what they do because it is fun. Well-paid-for fun, if they were able to get tenured.

Re: After Math

#96

Post by wffurr »

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…

Top comment on this post taking "reply to the title" to the next level.

Re: After Math

#97

Post by aaron695 »

emerongi wrote: post #59
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’d say Terrance has recently left the denial phase, the anger phase I’m sure he wisely kept off the Internet, and is currently in the bargaining phase - ie scrambling to change the goal posts. I wonder if he will wisely keep the depression / burnout phases also off the internet. You're making up a narrative about another person. You have no clue what's happening to him, without talking to him.

[dead]

Re: After Math

#98

Post by curt15 »

dash2 wrote: post #83

What I don’t see much of in the article - and still less in the comments that seem to see AI-led progress in mathematics as nothing but a disaster, because mathematics exists only to provide employment to mathematicians - is a sense that mathematics has a social purpose, or duties beyond the community of mathematicians. I thought the reason we were encouraging people to go into STEM, and providing clever people with…

> I thought the reason we were encouraging people to go into STEM, and providing clever people with large salaries, was that mathematical results were of practical value to the wider human race. In which case, it’s surely very good news that AI can get those results.

The impact of mathematics on other disciplines goes much further than specific results. Just as important, if not even more so, are the language and ways of thinking that typically come out of the process of establishing those results. Results without the accompanying conceptual understanding are about as useful as a mere oracle for math theorems.

Another point that seems to be frequently missed or mischaracterized is that mathematicians are not opposed to computational tools as a matter of principle and in fact do use them when they help their research. The current controversy is not about a hypothetical future where mathematicians have easy access to open-source, open-weight, auditable natural-language assistants to help them internalize a new result or search for counterexamples. It's primarily about the recent behavior of certain for-profit companies suddenly trying to disrupt mathematics by caricaturing it in the public eye as a game they can "solve" or "beat" for headlines and valuation.

Re: After Math

#99

Post by omnicognate »

wffurr wrote: post #96
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…

Top comment on this post taking "reply to the title" to the next level.

Quite. And unfortunately they opted for a clever, punny title that implies the exact opposite of what the article says.

Re: After Math

#100

Post by auggierose »

anonymouz wrote: post #93
charcircuit wrote: post #91

Earlier quoted context omitted.

Because most mathematicians have not migrated to being AI native like most software engineers did. My post is trying to point out that these people's mind is still fixed in how the old world works and is not focused on the future where LLMs are doing a lot of the work.

No, because knowing a proof exists is just a small part of math. It's value is rather limited to actual math, as the article explains quite eloquently and nicely.

The article is eloquent and nicely written, and it is also wrong.

To say that "1. AI really did solve a problem in mathematics." is wrong, is just wrong. No matter how nice and eloquent you try to explain it afterwards.

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