There are many conjectures that we know are almost surely true, but we don't know why, and explaining why is the main purpose of the mathematician when publishing a proof.
The fact that we don't know why is a clue pointing at some area of math that we haven't discovered yet. The hope is always that it will uncover some hidden fertile valley that will lead to lots of new discoveries. But the proof of the conjecture itself, without understanding, is really not that valuable.
My point is that even if AI discovers many new truths, there's still plenty to do for the mathematical community, in dissecting it and building useful abstractions to understand it, abstractions that can be leveraged for further exploration and uncovering new questions.
> 1. People will publish so much frontier mathematics, humans won't be able to understand it all
That already happened before AI.
> 2. Frontier mathematics will all be kept secret
Gauss kept lots of frontier mathematics in his drawer. In the 20th centuries government spy agencies developed public key cryptography long before that was known to the public. To give just two examples.
It's not the end of the world.
And what do you care, if someone keeps frontier mathematics a secret, if you can ask DeepSeek version 10 in 2030 to prove the Riemann hypothesis for you?
About 4-6 years earlier, depending what you want to count, although the inventors may also have been less clear on its importance or applications compared to the later public inventors.
It's been in use far longer than LLMs. Thought I'm not exactly sure when it came into common use. I'm pretty sure I've heard the term on Nova decades ago.
1. People will publish AI generated frontier math making it difficult to identify frontier mathematicians.
2. Trained frontier mathematicians will become scarce
Seems perfectly possible to get the worst of both worlds: more mathematics than anyone can read, and less access to the mathematics people actually care about.
That's also what the gerrymandering discourse is like. Gerrymandering is a threat to civilization because it means political parties will minimize their electoral margins, and because it means politicians will maximize their electoral margins.
The whole point of gerrymandering is to split districts so that votes for the other party are diluted. The whole point is to create many districts where your party is majority and then a few districts for the rest of the opposition.
If you are good at it, end result is that minority can keep majority of the seats and power. So, as there are two parties, the groups are "likely to voted republicans" and "likely to vote democrats".
Yes, quite well in fact. This lecture was in 1939. In the 50's, Lie groups (previously just a pure, beautiful mathematics) were used in particle physics. Gell-Mann used SU(3) to predict some new particles before anyone observed them.
And then similar stuff happened later in quantum mechanics, with gauge theory, but I understand that only at a handwavy level. I think overall the "standard model" is a perfect example of what Dirac predicted.
Whether this still holds up in the past 40 years is another question. I don't have a great example from my lifetime.
1) Dirac actually developed big parts of Lie Theory and its application in relativistic particle physics, without using the mathematical formalisms at all (until later on).
His work was subsumed/beautified by mathematicians after the fact (30s), an 'optimization' really which helped to extend and understand it further, not to discover it. The Gell-Mann prediction mirrors Dirac's own positron (non)prediction closely but was done without Lie formalisms.
The applications of Lie theory in relativistic fields theories began even earlier, with the Noether/Klein/Hilbert/Einstein collaboration in 1910s.
2) Continuous symmetries are a convenience and not essential to particle physics IMHO.
e.g. It's obvious we can swap positive and negative charge and get the same physics. That's a discrete symmetry. But in gauge theories the symmetry is not +ve <-> -ve, but rather the continuous rotation of the unit circle in a complex plane. electron becomes positron via complex numbers. It doesn't mean there's a complex electron with +-ie charge, but it does work better with relativistic Lagrangian fields theories where phase changes are continuous and frame dependent. Noether's methodology of using an invariant action integral leverages the Lie theory very effectively, but there are other ways to skin that cat though.
3) Beauty is in the eye of the beholder, but I doubt the standard model and the perturbative methods (renormalization, etc) underpinning it would be to Dirac's liking.
Recently I showed my 7-yr-old son and a friend of his how they could build their own little video games with the Claude app. Simple stuff, make me a maze game, make the walls move sometimes, make it bigger, make there be a score.
The delight they have at, video games aren't just a thing to play, it's a thing they can design and change, share with each other... I think that dream of a truly malleable experience is still there, I think this "explosion of new forms" you talk about is happening right now with AI, and I think this time it is going to be bigger than ever.
Games that allow custom map is not that new. Minecraft also allows you some basic boolean mechanism that you can build surprisingly complex stuff. I don't know why do you need AI for this
I think the tech companies would be supporters of new rules that would let builders create more housing all throughout San Francisco. We need a big tent, with all pro-housing groups coming together, to change the rules, and start allowing new housing again.
If you own a lot in San Francisco you should be able to build an apartment building on it.
This is like giving you three outputs from md5sum and asking you to guess for which one the input ended in a "q". There's no way to tell unless you break the RNG.
I think the point is probably to help convince people that the watermarking doesn’t perceptibly impact quality, which is a concern some people have (whether well founded or not).
Maybe some sort of blockchain could make it so that you don't have to verify the whole proof yourself, to know that it's true. Because some of these proofs could take a long time to verify. Similar to a Merkle tree, but you'd have to make it respect the laws of mathematical proof in some way.
edit: Yes I think this should be possible, using a "recursive SNARK".
I don't think the mathematicians are going to be able to make that work, because journals are already struggling to keep up with their review load, and AI seems like it will make that harder. So a solution that involves "journals will do a lot more effort to review each paper" doesn't seem practical.
It would work better as a bar for hiring, rather than as a bar for publishing.
It will be interesting to see the evolution of journals in the next ten years for sure. Have they outlived their usefulness? Maybe everyone will just upload papers to arXiv, along with a copy of the formal proof.
My conclusion is the opposite. If benchmarks were meaningless, surely Meta would be able to find some benchmark that shows they are better than Sol and Fable. The fact that they can't do that tells me that benchmarks still do mean something.
Muse 1.1 performed relatively well according to benchmarks, putting it within spitting distance of the premier models. However, based on the results I got from it and the review videos I watched, it wasn’t even close.
Opus 5 is incredible at making games. Almost like a generation better than other models from my experience. You won't see that if you just look at the popular benchmarks..
You have to test each model on your actual use case to see how well it really performs.
Yeah, totally. But... the problem is that I don't have time to test every single model that comes out. So I rely on reports like this to decide, should I even bother testing out Muse?
My son was gifted an old Mac from his grandparents. It only supports OSX 10.13. I’ve been able to make several games that he genuinely likes (7 yo) Opus built them on my workstation and then pushed them to his computer and tested them over SSH. It handled all the asset creation or collection from CC0 licensed sources. I believe everything is built on the Godot engine. It’s really amazing to me. I don’t know what it would cost me to get someone to build custom games on a long deprecated computer architecture, but I paid Anthropic $20.
I don't think it is vague in the slightest. Take the most simple examples, how many LLM's have you tested making them? There are stylistic choices pertaining to games that is well beyond a 0/1 reward. Even something as basic as breakout or flappy bird can have wildly different quality between models. Yeah, you could call this animal on a bike benchmarking, but I don't think it is. IMO the problem space occupies an interesting area where you can ignore the pass/fail and focus on the actual level of the model to do something beyond that.
I doubt the OP meant something like creating the whole tech stack for WOW.
Right, but the point is that you can't conclude that a model is necessarily bad because it's not hitting the same scores on benchmarks. I just don't agree with lacker's conclusion, because their logic doesn't seem to consider that. Scoring lower on a benchmark doesn't strictly mean they have a bad model, but it may be the case. Like you said it's one data point, but being the easiest, and obviously most gamed, means you should probably weigh them less heavily.
Personally, I end up throwing away a decent amount of books that the book donation people won't take. Especially old technical books. Textbooks from 2001. These headlines just don't tell me anything useful. "Rare" doesn't mean anything.
Please, give me one example of an interesting and unique book that the AI companies have destroyed.
You really don't think know they are selling endless counterfeit products? Don't know they are taking part in massive return fraud against small sellers? You don't think they know they totally ignore sellers with problems even if their livelihood depends on it?
1. People will publish so much frontier mathematics, humans won't be able to understand it all
2. Frontier mathematics will all be kept secret
Fortunately, these seem like they can't both happen at once.
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