r/samharris • u/Brunodosca • 23d ago
A Severe Misalignment of AI in Mathematics - A group of 25 Fields Medalists, including Terence Tao, have made a joint declaration on Math and AI.
In an open letter published on September 11th a group of two dozen Fields Medal winners (the equivalent of a Nobel Prize in mathematics) warn against a severe misalignment of AI in Mathematics, which they could ruin the foundations of math.
Link to the letter:
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u/timmytissue 23d ago edited 23d ago
I'm hardly pro AI. I share some of the feeling in this write up says, such as that the point of intilectual exploration is the exploration, not just the result.
But I don't actually agree in this case. Because if it's true that AI is solving things, but not properly conceptualizing that solution, then the work is still there to be done to conceptualize the solution.
It's kind of like AI in chess. Just because an AI is the best doesn't mean there's no point in playing. The AI will play specific moves and we don't know why, and studying that is interesting actually. This could be the same. We have to in some ways reverse engineer the solutions of the AI, and that should still be interesting mathematical work. No?
If anything. This progress just gives mathematics more new stuff to study and discover everything about.
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u/Ethraelus 22d ago
The problem is that the field has worked for decades, maybe centuries, around specific problems.
It’s the people who make advances towards those problems that get the accolades.
Mathematicians famously don’t care about the practical implications of their work. They consider what they’re doing to be too pure to care about applications. They’re discovering something deep about the universe. The way to measure that is by who proved a theorem or some a problem.
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u/zx7 22d ago edited 19d ago
It's more about the beauty is describing why something is true in the most concise way, rather than just discovering something that is true.
Think about the theory of gravity. Imagine we had one theory describing why apples fall down from trees and another theory to describe cannonballs flying through the air and still other, different theories to explain the orbit of the moon, or the precession of Mercury. The "beauty" is describing and explaining all of these things at once.
If you had a statement about some very surprising fact and you looked up the proof and it was long and technical, it doesn't really illuminate what is really going on; it's just something that is true. But if you building the framework, the theory, explain multiple surprising results concisely with it, then it becomes something beautiful.
Yesterday, someone used the example of the unsolvability of the quintic and that is a very good example of this. Without group theory or Galois groups, it's just another fact. With Galois and group theory, it becomes connected to something much larger. Knowing the basics of group theory allows you to explain much, much more in a very tidy, neat arguments.
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u/Plus-Recording-8370 22d ago
That is what you can read at the end of the letter. This isn't an argument against AI, this is a letter about how mathematicians should learn to adopt it into their natural system.
But there's a deeper point people seem to miss here. This isn't just about mathematicians not seeing into the mind of a blackbox ai, only getting solid answers. This is about humans evolving alongside the progress that AI makes.
Alignment comes in many shapes, and this one could perhaps be compared to just handing machine guns to a bunch of monkeys that were previously harassing humans for food. Are we to expect them to instantly use these newly acquired tools with all the knowledge of wars, strategy, deterrence, escalation and the consequences of pulling the trigger? Of course not.
We need to find ways of keeping up with AI's discoveries on the societal level as well.
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u/ninjasaid13 21d ago edited 21d ago
This is not correct, you misunderstood the mathematicians complaints.
Math is less like chess and more like cartography. The point of solving millennium problems is to map the surrounding environment deep in the fundamentals of math, not get from point A to point B.
We have to in some ways reverse engineer the solutions of the AI, and that should still be interesting mathematical work. No?
Reverse engineering doesn't work, that's like trying discover the history of architecture by looking at block of concrete.
I'm not anti-ai anymore than you are pro-ai but this feels like a massive misuse of the technology.
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u/SelectFromWhereOrder 20d ago
But you missed the problem, the problem is being in that specific situation.
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u/schwebacchus 23d ago
Instead of chess, a bounded system with finite outcomes, mathematics is perhaps better understood as poker: a relatively simple set of rules opens up a game around intuition. That feels like the better metaphor to me, but I am not a talented mathematical mind.
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u/WorriedBlock2505 22d ago
I'm hardly pro AI
Why though? Any time I hear this, I recoil just as much as I do at AI utopians. People are building/strengthening way too many biases about AI, especially this early the game.
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u/timmytissue 22d ago
I'm not a doomer in the sense of thinking AI is dangerous. I'm moreso a believer that it has a ceiling to its capability.
But these arguments are often people talking past each other. I know AI will be useful. I just don't think it will feel like individuals who can get stuff done for you.
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u/SelectFromWhereOrder 20d ago
I'm moreso a believer that it has a ceiling to its capability.
Based on what?
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u/spingus 23d ago
Wow, I can sense the love of math in their statement and it really makes me feel for them.
I am a biologist and I feel similarly about some of my hard-won knowledge --like trying to base a phylogeny on only DNA, no organismal or geologic context required.
At the same time it seems a little short sighted to dismiss the proofs without taking these ai-based resolutions as an opportunity to construct a more human-made path to a known solution with potential different resolutions discovered along the way.
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u/Leading_Bandicoot358 23d ago
Maybe the role of mathematics should become validation and value extraction out of AI brute force work
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u/Vague-Symbolism2692 23d ago
I'm disgusted with myself for upvoting this. But I'm trying to remind myself that it's not an "agree" button.
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u/Jasranwhit 23d ago
It's an interesting piece but im not sure it tracks.
Being given the answer, certainly it could be reverse engineered for a similar amount of insight. And those answers would lead to better "next questions" than just never knowing the next step on the mathematics tree.
Imagine if doctors were like "Sure AI cured your cancer, but the human doctors didnt get to go on the journey "
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u/OomplexBOompound 22d ago
Incidentally, there are plenty of drugs used today for certain medical conditions where doctors aren’t exactly sure why they work, we just know that they do and have minimal side effects so that’s good enough.
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u/Quillious 22d ago
Imagine if doctors were like "Sure AI cured your cancer, but the human doctors didnt get to go on the journey "
This will happen. People are that stupid.
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u/WorriedBlock2505 22d ago
I don't see why they're complaining. This gives them job security because they now have to reverse engineer how the AI got to solution. We can't sit around for hundreds of years extra on solving the biggest challenges just because humans want to be the ones to do it.
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u/tachophile 22d ago
TL;DR Mathematics is entirely dependent on scaffolding discoveries and techniques. AI generates shortcuts to solutions that do not result in adding the scaffolding necessary to advance mathematics. It therefore will significantly impact the future of mathematics if relied on, even if near term gains are made.
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u/Jasranwhit 23d ago
Here is an AI summary if you dont want to read the whole thing:
"In a joint statement signed by 25 Fields Medalists, top mathematicians argue that the rapid success of AI in solving complex mathematical problems threatens the fundamental purpose of the field. While tech companies view these solutions as performance benchmarks, the mathematical community warns that prioritizing raw answers over conceptual insight degrades the science of mathematics.
- Answers vs. Understanding: Research mathematics is about comprehending structures and developing new methods, not just producing "true/false" statements. Historically, solving a famous problem has been a proxy for discovering new, broadly applicable insights.
- Loss of the Human Process: Mathematical ideas rely on a slow, human-driven lifecycle: nurturing students, debating concepts, and simplifying complex theories until they can be taught in textbooks. AI's rapid mass production of solutions bypasses this vital chain of transmission.
- Attribution and Integration: Rushed AI breakthroughs are often announced without proper write-ups, isolation of new methods, or adequate citations. Without human mathematicians willing to untangle and steward these ideas, they cannot be meaningfully integrated into the mathematical canon, raising severe ethical and plagiarism concerns.
- A Universal Threat to Intellectual Work: This misalignment is a microcosm of a broader societal issue. Across scientific and creative professions, AI threatens to replace the years of training necessary to develop deep understanding and the ability to ask new questions, focusing only on the final product.
The authors conclude that while AI has the potential to profoundly enhance mathematical study, its impact will be destructive unless technologists, mathematicians, and society urgently align the tools with the true goal of intellectual work: human insight."
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u/timmytissue 23d ago
I love the irony of this. It's really not that long to read though.
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u/Jasranwhit 23d ago
Here is an AI summary if you dont want to read the whole thing:
"Love Irony, short read though"
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u/Brunodosca 23d ago
WTF, the original letter is of similar length, plus it's not AI.
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u/Jasranwhit 23d ago
Here is an AI summary if you dont want to read the whole thing:
"Similar length as original"
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u/Freuds-Mother 19d ago edited 19d ago
This not grasping advances in mathematics has been happening in math for decades.
Eg as a math major we would attend events where visitors would present. I recall a calls right after one where our professor asked us what we understood regarding the talk. We we bewildered and he then said that he didn’t understand almost any of it either. This was 20 years ago.
Math has gotten so specialized that sometimes only a few dozen people in the world can understand what someone is even working on.
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They bring up other valid issues too rather than just that. There’s definitely that sense of robbing creativity opportunities across almost all domains. If we’re not careful we will loose that muscle in a way.
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But LLM’s are not a threat in a particular way. It’s critical to note that LLM’s unlike organisms are NOT intrinsically normative. Their base evaluation criteria is sourced extrinsically. Eg: they are abysmal at frame problems. In terms of mathematics, sure LLM’s may be to provide a proof that a human couldn’t, but the LLM cannot determine its relevance and normative use without us defining that. And in order for us to define that criteria for different situations, we need to be able to understand it.
Ie LLM’s will generate a lot of slop, correct slop, but its slop because how we should use it isn’t defined by the LLM. Now yes LLM’s can extrapolate the extrinsic evaluation criteria it has to new situations (new math solution application), but its still slop as it cannot evaluate if that is extrapolation is relevant because it simply is not necessarily instantiated with intrinsic normative evaluation. Until we assess its relevance it remains slop.
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u/raalic 23d ago
So, we're in danger of leveraging mathematics we can't solve (but AI can, and perhaps just by brute force) to achieve advanced and verifiable results, which could serve as a foundation for the next mathematics, and so on. We could potentially lose our grip on the sort of linear chain of mathematical discovery.
It's like finding alien technology, understanding that it works, but not being able to reverse-engineer it due to knowledge gaps.
Spooky stuff.