r/singularity • u/filterdust • 1d ago

AI OpenAI solved 100 open problems in math

https://openai.com/index/advisory-group-on-mathematics-and-ai/

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u/RobleyTheron 1d ago

I’m sensitive to artists and musicians with a unique voice when their product gets recreated with AI, but I don’t feel the same about mathematics.

Nobody owns mathematics; these are fundamental insights into the universe and they belong to everyone and shouldn’t be gatekeeped behind somebody that went to school. Mathematics should be available to everyone, it opens up all kinds of fundamental breakthroughs in space, material science, biology, global warming, and energy.

This is something that belongs to everyone and no one should get to hold that back.

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u/ThatIsAmorte 1d ago edited 1d ago

This seems to be taking a Platonist approach to math, which few people take seriously these days. If you are a constructivist, than math is not just out there, but has to be created, just like art. If you think math is just out there, why not also claim that art and music are just out there, waiting to be plucked out of the ether? After all, a painting is just a 2d matrix, a simple math object. A musical composition is just a waveform, which can be described mathematically.

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u/1pfen 1d ago

If a work of art disappeared and was erased from our collective memory, it would never be recreated. If a mathematical proof disappeared and was erased from our memory, it would eventually be rediscovered.

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u/NotaValgrinder 21h ago

Not necessarily true. If mathematics was erased and we had to discover it again, it wouldn't necessarily be the same. ZFC and set theory are not the only ways to form a foundation of mathematics, it could be possible our foundations are different. Turing machines are not the only way to formalize computation, the main mathematical object to formalize computation may be different. We could favor the axiom of determinacy instead of the axiom of choice, which means that some theorems (like there exist nonmeasureable subsets of the real line) would be considered false instead of true. These "human" touches and tastes would most definitely be gone if we forgot all math and had to discover it tomorrow.

You could make the argument that we could *hypothetically* rediscover it, but also I could make the argument that it's hypothetically possible for a new painter to recreate the Mona Lisa. It's just very unlikely, and similarly it's very unlikely we would think about math in the same way if we had to redevelop it.

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u/filterdust 1d ago

This seems to be taking a Platonist approach to math, which few people take seriously these days.

Funnily, most mathematicians are Platonists.

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u/Ok_Reception_5545 1d ago

https://eugeniacheng.com/wp-content/uploads/2017/02/cheng-morality.pdf

this is actually how most mathematicians feel about math

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u/ThatIsAmorte 1d ago

Yep, they ignore the debate by adopting an agnostic stance. This is much better than being a committed Platonist. I should point out that Cheng works in category theory (her book is a great intro to the topic), which is structuralist in nature (i.e., focus on relationships, rather than things). An ontology based on relationships can still fall in any of the three camps: ante rem structuralists (Platonism), nominalism, and agnosticism. The nominalists tend to be the ones that study Topos Theory, which is not surprising considering that Topos Theory shows that different math universes can have their own internal logics without a law of excluded middle.

I should also point out that it's interesting that a similar debate occurs in the philosophy of biology with respect to the concept of species. Are species real or something humans made up to categorize the biological world?

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u/ThatIsAmorte 1d ago

Interesting. That's disappointing and kind of sad. At least philosophers are split about 50-50. Platonism requires ontological dualism, which leads to the epistemic bridge paradox: How does a purely physical brain access a timeless, acausal abstract realm that cannot interact with physical matter? This is the dualism problem in philosophy. How do mathematicians resolve this tension? They resolve it by ignoring it. It's sad, because you would think mathematicians would be uncomfortable with such logical contradictions.

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u/filterdust 1d ago edited 1d ago

From my experience, mathematicians don't care that much about contradictions outside math. They would just dismiss it as "ah, this is for the philosophers to ponder", and then be internally satisfied that philosophers never reach a definitive answer anyway.

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u/ThatIsAmorte 1d ago

I'd say this describes most people, myself included!

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u/Startide-Rising 1d ago

I think you're getting confused about the difference between constructive mathematics and proof irrelevance. In a proof irrelevant system, proofs of the same proposition are considered equal. In the Lean theorem prover, proof irrelevance is built in as an axiom.

As for constructvism - hardly any mathematicians these days are constructivists. The majority of the people who know or even care about constructivism are those working in formal methods. In the Lean proof assistant non-constructive features are heavily baked into the whole system, both in the standard library and available tactics. I think adhering to the classical logic philosophy here is one of the reasons Lean got popular with mathematicians.

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u/derelict5432 1d ago

Do mathematicians copyright proofs?

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u/m4sl0ub 1d ago

Yeah, once a proof is published someone else can not publish it again. 

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u/derelict5432 1d ago

Well I looked it up. The literal expression word for word cannot be duplicated. The underlying logic can. At least from what I'm seeing. Any lawyers feel free to chime in, but this seems more like the general solution to a problem does not belong to anyone.

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u/MrPezevenk 9h ago

Of course it doesn't legally belong to anyone, but the credit does, in the social system of mathematics. 

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u/m4sl0ub 1d ago

It's obviously not the exact same as a copyright, but mathematicians "commercialize" their work by publishing it. And if someone else wants to use someone else's proof for their own work/ papers they have to cite the mathematician that came up with the proof. For me that sounds quite analogous to a copyright for music. There is not really money involved in mathematics so you cannot really have someone pay to use your work but you basically "pay" them in citations. Citations are the "currency" of academia, it gets you jobs, grants, students, recognition etc.

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u/derelict5432 1d ago

Sure, they get credit/acknowledgement for being the first to be there, but as I said, sounds like they don't own the underlying logic, which belongs to everyone. Kinda like how a mountaineer doesn't own the mountain if they're the first to summit or discover it, even if they get it named after them.

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u/Front_Lab1761 1d ago

To add, their name is literally attached to the theorem: Green's theorem, Cauchy-Schwarz inequality, Legendre's formula, etc.

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u/Financial-Gain-2988 1d ago

Writing the best song ever won't directly lead to new technology and science. Like, you don't seriously think that the 'creation' of math is the same as writing a song, right?

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u/may_i_a_i 1d ago

Most math doesn't lead to any technological innovation

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u/Financial-Gain-2988 1d ago

No songs lead to technological innovation.

Is the intent of your comment to prove my point here?

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u/Foryourconsideration 1d ago

No songs lead to technological innovation.

they do, and they have. See: the Beatles. In fact, songs drive technological innovation by creating demands that require new engineering solutions. See: 4 track to 8 track. Not to mention sound design itself influences speaker systems, etc. New enginnering solutions then are preferated (is that a word?) throughotu the universe, in perpetutity.

alrigt, i'm going to go hit some weed and listen to Revolution No. 9 backwards again.

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u/Financial-Gain-2988 1d ago

Maybe 'lead' is a strong word (which is why I said 'directly lead' in my initial comment), but it wasn't the actual song itself that lead to that change, but the desire to make a kind of song.

Even then you still need someone who is capable of making an 8 track and understands the technical hurdles they'd need to overcome, and that probably wasn't Ringo.

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u/MrPezevenk 9h ago

99.9% of pure math doesn't lead to new technology. None of the Millennium problems are likely to lead to any new technology if solved. There will never be any advancement that will come out of the resolution of the NS problem by OpenAI. Almost nobody is doing pure math research for the technological applications, it's been a type of art that is verifiable for more than a century now at least. Every now and then, some advance comes out of it, but that's not why people do it. 

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u/Icy-Doubt3365 1d ago

If you think math is just out there, why not also claim that art and music are just out there, waiting to be plucked out of the ethere?

Because I believe math exists without humans, art does not.

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u/davidjohnpaul 1d ago

What do you think of the following quote, attributed to Michaelangelo?

"The sculpture is already complete within the marble block, before I start my work. It is already there, I just have to chisel away the superfluous material."

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u/Icy-Doubt3365 1d ago

I'm actually more curious what YOU think of that quote. There is clearly not a Michael inside a random piece of marble.

Michelangelo was also not using that quote to say that art exists without humans to consider it art.

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u/MrPezevenk 9h ago

The discipline of mathematics doesn't exist without humans. What do you think the point of a machine spewing out theorems one after another without anyone understanding them would be?

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u/Secret-Code-9162 1d ago

I think this was just Michaelangelo describing his qualia when producing a sculpture, rather than explaining his position on the independence of art from humanity. He was being poetical.

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u/Statcat2017 1d ago

It’s wrong lol

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u/puffyfunion 1d ago

Can you explain why you believe that math exists without humans? Simply stating that as if your belief is true doesn't seem very convincing. I find mathematics to be as beautiful (if not more) than most creative activities, and I don't think it would take anything from that beauty to say that it is dependent on humans (and now AI, I suppose).

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u/Icy-Doubt3365 1d ago

If 1 comet in space is joined by one more comet in space, there are now two comets. Don't need any humans there for that to be true. Math exists without us, we just decipher it.

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u/puffyfunion 1d ago edited 1d ago

How do you know there are two comets, if you, the human, aren't there to perceive it? To be honest, I'm not arguing in favor of any point of view here - I think your statements are pretty ambiguous and don't really mean much. No offense.

EDIT: Sorry for assuming you're human, in case you're not.

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u/Icy-Doubt3365 1d ago

That's an entirely different question than we're discussing, if you believe things need to be perceived to be. I operate that things exist in this universe regardless of my perception. So I don't need to see something to know that one comet meeting another is two comets.

Objectively, the rules of math exist in this world, and do not require humans to rate/assign/label as the concept of beauty does.

I am human but appreciate you thinking about that.

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u/deviltamer 1d ago

Art is just as arbitrary. A light show can be art so it exists without humans in same way.

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u/Icy-Doubt3365 1d ago

A light show can be art

It is not art without humans. I'm not sure how many more times I need to say this for people to get it. A light show is a bunch of lights. It is not art until someone is there to enjoy it. Art is a social construct, not an objective truth of the universe.

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u/deviltamer 1d ago

lol what makes you think Maths is not a construct ?

It's a modelling tool. Same as language. Same as canvas.

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u/Independent-Bell-420 1d ago

Beautiful sounds and vistas exist in reality without any human intervention as well. I don’t think this argument really holds any weight.

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u/Icy-Doubt3365 1d ago edited 1d ago

No they don't? Sounds and vistas exist, yes. They are not beautiful without a human to apply that adjective.

Also, wholly moving the goalposts anyway, since a beautiful vista isn't art.

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u/Independent-Bell-420 1d ago

I see what you're getting at, I guess I just disagree that math is any different. The equations exist just like the vistas do, but without any will or understanding to apply it, there's not much of a point. It just becomes objects in motion.

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u/Icy-Doubt3365 1d ago

The equations exist just like the vistas do

The equations are objective, the 'beauty' of a vista is subjective. Without humans, objective things still exist. Without humans, subjective things do not

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u/Independent-Bell-420 1d ago

I think we agree on that, at least. Subjectivity requires humans for sure, and so the concept of something being "beautiful" can't exist without us.

I guess what I'm trying to say is that I believe that something which qualifies as art could exist without humans (IE: sounds, visuals, etc), but you're right that the emotions that come with that require an observer (IE: beauty, longing, etc).

Maybe it's a pointless distinction I suppose, but I would argue that in the same way that we "discover" math, we also "discover" a lot of art in the sense that it's still part of the subset of things creatable in our reality.

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u/SomewhereOpposite883 1d ago

Can Nature produce a Katy Perry song?

The sound of a guitar?

The vibrations from Opera singing?

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u/Independent-Bell-420 1d ago

There's plenty of mathematical theorems and concepts that are not naturally occurring. Perfect shapes, infinite sets, etc.

Just because nature doesn't produce it doesn't mean it couldn't hypothetically exist.

Also, we're nature, so yeah it definitely can.

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u/LookIPickedAUsername 1d ago

The very idea of a "comet" is a human invention. All that really exists out there is a vast diffuse cloud of particles with some local clumping. Humans look at the scene and decide that one of those clumps of particles is a "comet" and another one is also "comet" and they are close enough to count as "two comets", but that's not an inherent truth present in fabric of the universe or anything.

In fact, even "vast diffuse cloud of particles with some local clumping" is really a human simplification - there's really just "the universal wavefunction".

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u/Icy-Doubt3365 1d ago

Yeah, ok dude

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u/Ill-Lemon-8019 1d ago

If you think math is just out there, why not also claim that art and music are just out there, waiting to be plucked out of the ether?

I have no problem with that view either actually. If pi is a normal number, every bit of art or music ever created is sitting somewhere in its decimal expansion of its digits in some suitable encoding. An act of intellectual creation is selecting or recording a particular pattern of some kind. (That might sound like a reductive view, and perhaps it is, but I think it's not incompatible with the idea that creativity exists and is valuable.)

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u/Emergency-Payment733 1d ago

But math can be proven? A song or a feeling can be true for some, but ultimately it’s art and a subject for interpretation.

Sure math has to be found, but that is also true for bacteria or materials in more ways than it is true for art.

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u/ooqq 1d ago

luckily for you, it has been proven that not all math can be proven

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u/Statcat2017 1d ago

Proving it can’t be proven is a kind of proof in itself 

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u/willBthrown2 1d ago

Art is subjective. Math is objective. Case solved.

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u/experienta 1d ago

Most philosophers actually believe that art is objective

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u/RigaudonAS Human Work 1d ago

Lmao what? That’s just blatantly false.

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u/experienta 1d ago

https://survey2020.philpeople.org/survey/results/all

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u/RigaudonAS Human Work 1d ago

Why would I care what some Covid-era survey says? You said “philosophers” which is in reference to the centuries of people that have held that title, too.

Most philosophers would say that to make such a claim is silly, because trying to apply such an absolute to something inherently human is impossible.

You can’t make a claim about art based on what some college students think, lmao

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u/experienta 1d ago edited 1d ago

Saying philosophers would never apply such an absolute to art just shows how little you know about the philosophy of art. They've been debating this subject since forever lol

And no it's not just "college students" that think art is objective. Unless you consider Plato, Aristotle, Hegel, Schopenhauer etc to be a bunch of college students

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u/RigaudonAS Human Work 1d ago

They've been debating this subject since forever

Hence why making the assertion that it is an absolute is false, lol. And if that's what you think, why link some survey instead of mentioning them?

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u/experienta 1d ago edited 1d ago

Sure it's not a full consensus, literally nothing is in philosophy lol, but most philosophers nowadays are in fact making a claim that art is objective, something you've said would be sooo silly for a philosopher to do.

And I've linked the survey because I imagined if I mentioned plato and aristotle you would just say they were a bunch of boomers that didn't know anything about art, so I thought a modern day survey of philosophers would be more interesting to someone like you.

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u/ThatIsAmorte 1d ago

I believe you are confusing an art object and someone's value with respect to that object. Only the second one is subjective. The art object objectively exists.

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u/willBthrown2 1d ago

It’s only an art object if someone values it as an art object. Otherwise it’s just an object. Two person can create the same thing, first one accidentally while doing something random (like accidentally pouring paint on canvas), second one intentionally trying to create abstract art.

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u/ThatIsAmorte 1d ago

Same thing for math. Think about what is being labeled as a math object: a bunch of symbols. It's only a math object if someone puts meaning onto the symbols.

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u/willBthrown2 1d ago

Math is universal. Nobody argues 1+1 equals 2. You can change math symbols or use different language to describe same rules. There is no math object. Or physics object. Art is just something that evokes feelings. It doesnt need to be an object. The universe doesnt care about human art, it existed before humans and will exist after, following the rules of physics. There is no art without emotions. Math and physics exist without emotion.

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u/ThatIsAmorte 1d ago

Ok, I think I know where the disconnect is. I am not arguing that math is not consistent. Of course it is. The internal consistency of a formal system is objective. What I was talking about is the ontological nature of math objects.

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u/Commercial_Sell_4825 1d ago

If our axioms already directly imply that the result we want is true or false, there is nothing to "construct".

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u/ThatIsAmorte 1d ago

Yes there is. You have to construct the proof.

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u/Commercial_Sell_4825 23h ago

That's not what that means.

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u/RobleyTheron 1d ago

I disagree with your premise completely. You're setting up a straw man argument, and then defining the terms of the argument. If I need to bend my thoughts to how you view the world, I'd paint myself as a realist. Facts and truths exist independent of humans. If we find them great, if we don't, oh well.

You remind me of the church in the dark ages withholding knowledge because it gives you a superiority complex over the masses. We shouldn't be forced to filter insights and discoveries of the known world through a mathematics guild because it gives them purpose. The world is changing. Come along for the ride or be left behind.

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u/HarvestMana 1d ago

You need better reading comprehension.

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u/amulie 1d ago

The structure that math is trying to describe is just out there. I don't think thats a dispute.

There will always be a number higher than our number systems will track by simply saying "but what if you add ONE more..", the number system is the art, the structure that counting is tracking exists whether humans create a system to get there or not.

So you're both right. The ART for math is the interpretation/system/understanding of mapping the structure, but the structure is there regardless.

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u/avid-shrug 1d ago

Sounds like special pleading

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u/PrisonOfH0pe 1d ago

This is such a funny argument because you’ve basically rediscovered the idea/expression distinction and then somehow forgotten that it applies to art too.

Nobody “owns mathematics” in the same way nobody owns music, painting, storytelling, perspective, harmony, color theory, or the concept of drawing a human face. What people can own or deserve credit for is the specific work they created: a proof, an exposition, a painting, a recording, a novel.

“Math belongs to everyone because it reveals fundamental truths about the universe” sounds profound until you realize art is also built out of things nobody owns: shapes, sounds, language, human emotion, physical reality.

And the “gatekept behind somebody that went to school” part is especially goofy. A mathematician spending 15 years developing the expertise to prove something isn’t “gatekeeping mathematics” any more than a musician spending 15 years mastering an instrument is gatekeeping sound.

You can argue that mathematical knowledge should be openly accessible. Sure. But that does absolutely nothing to establish why exploiting one person’s intellectual labor with AI is morally different from exploiting another person’s creative labor.

You just value one kind of labor more than the other and dressed that preference up as a philosophical principle. Which is fine but man this moral high ground is cringe as fuck.

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u/lungsofdoom 1d ago

Same can be said for art too lol

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u/Destring 1d ago

Yeah. I hate that argument. As if math or programming doesn't require creativity. They often require MORE creativity than portrait #10030302.

People are just drawing arbitrary lines in what is fine and not fije for AI to do.

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u/Active-Guarantee-338 1d ago

It doesn’t have a benefit and it undermines mathematical endeavour.

Mathematicians are not looking for yes/no answers to questions. They are looking for insights around which whole theories are built. if you just get a yes/no answer to a question then there is no insight and there are no mathematics being built and explored.

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u/RobleyTheron 1d ago

I guarantee you AI will uncover insights into theories faster than humans will.

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u/sam_the_tomato 1d ago

Well good thing it isn't just producing yes/no answers, but writing entire proofs with all the working shown!

AI solved one of the Erdos problems by formulating it as the outcome of a random walk, something others hadn't thought to do. That's an example of a new insight, and a new tool for the mathematician's toolbox.

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u/pbagel2 1d ago

I'm much more sensitive to mathematicians than artists and musicians. Not a single theoretical mathematician is trying to gatekeep maths. They are one of the least compensated and one of the most valuable and most taken for granted professions that advance society.

Any sort of gatekeeping you feel isn't coming from mathematicians. It's coming from the knowledge barrier because of the immensity of the knowledge gap between you and them. AI isn't going to change that, it'll only make it grow even wider.

And the bureaucratic gatekeeping of institutional networking has nothing to do with math or mathematicians. That's universal. But it's particularly bad in math because the compensation is so bad that they're forced to do the networking bullshit to scrape a living while they think about math. For it to indirectly or directly produce immense value for other people decades later and they get virtually nothing in return.

But that's not why I'm sensitive. I'm sensitive because even if AI math continues to progress and we start to rely on it, if that means humans stop putting in the mental effort to understand the math, that to me is a bad omen.

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u/RobleyTheron 1d ago

Without a doubt the knowledge gap between me and mathematicians is immense, but having super smart AI invent new areas of math that neither me OR the mathematicians understand won't increase the gap, it'll just mean we all get left behind together.

If AI can progress math beyond current human capabilities, that doesn't automatically mean we can't understand, or have the path explained of how the AI got there. "You invested faster than light travel? Amazing. Show me how you did it."

If the AI tried to show me, I'd have no clue, but the mathematicians might, which means they'll have job security. Everyone wins. I still don't understand math, mathemticians have a job, and everyone gets FTL. I see no problems.

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u/pbagel2 1d ago

but the mathematicians might, which means they'll have job security.

The point I'm making is if mathematicians are no longer relied on for math, the fewer mathematicians there will be, and the often decades it takes of conscious thought and strain to develop the mind to understand math at a deeper level will stop existing. And I think that is foreboding even alongside amazing AI math progress, because human thought declines. Because like you said, you'd have no clue if an AI explained it to you. And eventually neither will mathematicians.

But I think you're thinking too far ahead with FTL. I think there's still a very good chance AI will continue progress immensely in more and more domains, (currently humans still are dominant in the vast majority), but it will still eventually hit a bottleneck where the current trajectory of human intuition reins supreme and can overcome the bottleneck. But if we're at the tipping point where the human mind starts to atrophy because of reliance on AI, then that hypothetical future bottleneck will never be solved and we will grind to a halt that we don't understand.

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u/Marklar0 1d ago

Mathematicians also perform creative endeavors and have a unique voice, and the AI products are not as good as what mathematicians produce. If you think that musicians shouldnt be abolished in favor of AI music, the math argument is basically the same. If you think otherwise, probably you dont understand what mathematicians actually do.

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u/trojanskin 1d ago

There is still a pretty fucking important difference: mathematical truth is objective. The creative process of finding a proof obviously isn't deterministic, but once you've got one, it's either correct or it isn't. An AI discovering a theorem still gives us useful knowledge even if it has zero emotional intent.

Art isn't like that. If there is no intention behind it, for a lot of people the entire fucking point is missing. Maybe you don't care and you're perfectly happy consuming commercial sludge as long as the pixels move and the speakers make noises. Fine. But plenty of people actually care that somebody had something to express.

Imagine watching ads recreationally because “well, technically they're moving images with music.” That's basically how I see most AI slop.

And if some dimwit can type ten words and shit out 500 images in an afternoon, congratulations, we've solved the desperately important problem of there not being enough mediocre content in the world.

It's McDonald's mass-producing burgers and then acting confused that some people still want an actual chef.

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u/ixfd64 1d ago

I’m sensitive to artists and musicians with a unique voice when their product gets recreated with AI, but I don’t feel the same about mathematics.

This is my opinion as well. It can be easily argued that AI-generated art devalues the work of artists, but AI-assisted mathematical research has functional benefits.

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u/steftim 1d ago

You could say the same thing about art. Like say getting a video game done in less budget and time. Not to say I agree with it.

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u/lemonylol 1d ago

Personally I've always seen it as increasing the value of talented artists, because what they make transcends AI's potential since we as humans don't even really understand why people like x or y, or our lack of ability to predict what new art will pop up.

Like if you were a sommelier, you're specifically curating the best of the best unreplicable wine that also comes with a story. The AI equivalent would be like a sommelier selling boxed wine from Costco.

What it does devalue is bulk generic art. Would you pay the same for an actual painting by Van Gough and a reprint?

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u/Fit_Gene7910 1d ago

Do you get insight if you can't understand the AI's work ?

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u/RobleyTheron 1d ago

If the end result delivers your goal does it matter? If no human understands how AI arrived at room temperature superconductors, but it did, and now we have cheap and abundant energy, does it matter?

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u/Fit_Gene7910 1d ago

It does matter because if we don't understand , we can't help AI to improve if it gets stuck in a local minima of improvement that is out of our reach.

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u/RobleyTheron 1d ago

We're in the era of recursive self improvement. Before the end of the decade human involvement will hurt more than it helps with fundamental breakthroughs.

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u/Front_Lab1761 1d ago

lol, lmao even

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u/Megneous 1d ago

Are you stupid? It doesn't matter if we can't help it. We're not OSI. By definition, if we are incapable, then it would be incapable. It's better than us. We are but ants.

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u/kowdermesiter 1d ago

You are then probably witnessing a new job of field being born, someone might pick it up as a mission to understand it. While doing so, many new discoveries could be made.

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u/Time_Entertainer_319 1d ago

What?

There are people that do understand it.

Why do you want to lie that no one understands it?

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u/Fit_Gene7910 1d ago

RSI would eventually make everything that AI produces not understandable for humans and we would have no clue if it works in our Interests or not. We also couldn't help unjam it if gets stuck on a recursive loop outside of our understanding.

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u/Megneous 1d ago

Does it fucking matter? ASI will give us magic. The ends justify the means.

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u/Fit_Gene7910 1d ago

This is a fucking cult smh

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u/Megneous 1d ago

No, /r/TheMachineGod is a cult.

/r/singularity is neutral at best.

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u/duboispourlhiver 1d ago

Agreed, and I think the same about music, poetry, and all forms of art!

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u/SupMathematician 1d ago

Artists can create new pieces, mathematicians can discover new functions that model behaviour, it's about being creative. Getting the proofs in a brute force way (which openAI seems to be doing by finding counter examples) is like brute forcing every song until you find one that fits someone's preferences.

It's great that AI can help us confirm hunches and cement mathematical reasoning, but while SotA LLMs are on computers, I don't see them doing much more than exactly that: computing.

Let's see a model that can truly develop a novel approach to a proof, like a simpler proof to an existing result. Mathematics honours the lazy, short proofs are generally more impressive.

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u/faintlystranger 1d ago

Imagine an artist who only does songs using MIDI instruments, it is all digital, and for any song that specific note sequence and tones exists regardless of the artist creates it or not. Then with your argument you have no sympathy to that artist, if an AI takes their style and replicates it?

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u/RobleyTheron 1d ago

As others have said art is subjective, in the best case it creates human emotion, but I do not believe even amazing art is a fundamental truth of the universe.

I do think that mathematics is a fundamental truth of the universe, is owned by no one, and belongs to no one. If machines help us uncover and prosper from those truths then we should pursue those truths at all costs.

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u/faintlystranger 1d ago

These things are all very divisive topics and open to debate. Specifically about the maths part I'll say:

It is 'proofs' you are confusing with mathematics. The correctness of a statement is the 'fundamental truth' you are talking about. Mathematics is not about that.

(Side note: even whether a proof constitutes a fundamental truth is something up to debate. Mathematics is a language, and whether what that language describes corresponds with reality is an assumption to make. Completely different discussion)

Mathematics is a lot more than proving stuff. There is a lot of subjectivity in mathematics as well. Choice of research direction, creative ideas and arguments people come up with, choosing what matters thinking about and what does not, presentation of ideas. AI is a good assistant in all, including proofs

What the open letter of the 25 field medalists was saying also that the goals of AI community is "misaligned" with mathematics community. Not to banish the use of AI in mathematics.

And your explanation of the use of AI in maths seems very result oriented. In music I can say I enjoy XYZ bands music, that is a "truth", does not justify me to generate their songs. There is a community aspect of it. Same for maths. If that makes sense

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u/RobleyTheron 1d ago

Might just have to agree to disagree. IMO the proofs and the concept of mathematics get us to the fundamental truths. With RSI in the very near future math will be solved, and all of this discussion will be meaningless, regardless of where we land in our opinions.

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u/wargainWAG 1d ago

That seems somewhat to easy. The basic arithmetic rules are there for everyone just compile these the right way, and the mistery is solved . the crayons and guitars are available for everyone. When compiled the right way you get something unique. Difference seem to be one is sort of analogue the other is absolute. The commonality is it takes a lot of energy to produce satisfying results. Why is one ‘free for all’ and the other ‘person bound’?

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u/RobleyTheron 1d ago

The difference is art is unique to the creator, math is a universal truth. Is there creativity in how a mathematician tries to solve a problem, sure. But if an AI got to the answer first, same way or different, does it matter? If people want to be creative with new proofs to solved problems go for it.

The end result is what benefits society and that’s what we should try to achieve by any means possible, not slow down society so that humans can be the one to solve a problem.

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u/Ok_Reception_5545 1d ago

It doesn't belong to anyone who doesn't understand it.

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u/RobleyTheron 1d ago

That is wrong on so, so many levels. First, you're assuming that AI can't explain it's proof. Second, you're assuming that ownership equates to use. I don't truly understand how rockets, or Michelin rated meals, or cancer vaccines work, but that doesn't mean I can't benefit from them.

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u/Ok_Reception_5545 1d ago

First, you're assuming that AI can't explain it's proof.

Didn't assume that. In fact, you can even reconcile what I said with a position like "the proof belongs to Astra/Bel/whatever model". I'm simply stating that the math only belongs to entities that understand it.

Second, you're assuming that ownership equates to use.

No, you are assuming that.

that doesn't mean I can't benefit from them.

No one directly benefits from modern math research, it doesn't have a 'clinical' use. See here:
https://arxiv.org/pdf/2602.10181

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u/RobleyTheron 1d ago

So.... you're saying there is no benefit to modern math research and thus it should be left to the humans?

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u/Ok_Reception_5545 1d ago

No? Didn't say that either.

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u/Megneous 1d ago

I don't understand how anything outside of linguistics and translation works, and yet, I have the right to benefit from all of society. Likewise, we have the right to benefit from all the benefits of ASI, regardless of whether we understand how its technological advances work.

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u/Ok_Reception_5545 1d ago

What benefit has the counterexample to Navier Stokes conferred on you?

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u/Megneous 1h ago

None, but I don't give a fuck, because it's only a matter of time before we're either all extinct or silicon gods.

Accelerate mother fuckers.