(mathoverflow.net)
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.
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.
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?
1. People will publish AI generated frontier math making it difficult to identify frontier mathematicians. 2. Trained frontier mathematicians will become scarce
" The National Security Agency is the largest employer of mathematicians in the U.S. "
https://www.scientificamerican.com/article/mathematicians-an...
Which makes total sense unlike the "too much frontier math" nonsense.
Which groups are those?
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".
Maybe we should start crediting and publishing our intermediate results and attempts.
Humans would gain credit for providing a part of the solution to tough problems, LLMs would profit from the resulting data flywheel.
> Maybe we should start crediting and publishing our intermediate results and attempts.
All mathematical results are "intermediate results". What would it mean for something to be a final result?
Just, without the aliens, space travel, or mech-suits.
Got half the other downsides though!
Your joke overestimates the intelligence of real life humans.
https://warhammer40k.fandom.com/wiki/Tech-Priest:
> Despite the never-ending thirst for knowledge of all branches of the order, most Tech-priests of the Adeptus Mechanicus have lost the ability to innovate or carry out basic scientific research.
> No longer the master of its creations, the Cult Mechanicus is enslaved to the past. It maintains the glories of yesteryear with rite, dogma and edict instead of true discernment and comprehension.
> For instance, even the theoretically simple process of activating a vehicle's engine is preceded by the application of ritual oils, the burning of sacred resins and the chanting of long and complex hymns.
Take a good look at the textbooks that teach mathematics and tell me I am wrong.
The simple short-term solution is just don't feed all your work into the IP theft machine?
Prior to LLMs there was some minimal effort required to snipe someone and possibly your reputation was attached otherwise there would have been no point in publishing to begin with.
Now anyone with a few dollars can do it, many who don't have a reputation to worry about.
It's the same problem as YouTube AI slop, AI-generated music, and everything else. Don't you dare tweet or blog about a video idea or hum a few bars from a song - within an hour 27 people will have posted AI slop rip-offs. There's something uniquely depressing about being beaten to the punch by a thief that doesn't deliver the same soul-crushing impact as having someone copy you after the fact.
See this amusing reddit post. https://www.reddit.com/r/IndieDev/comments/1wfl64l/game_went...
I'm sure there's a named concept for this: the idea of the game is its selling point, and has to be revealed to consumers to market itself. But the market has low friction (via Steam distribution, and by copies being cheap to make w/ LLMs), so you can't reliably establish your product before masses take over, especially if you don't have reputation built up from previous games.
You have to be bringing in something else for this not to happen, trade secrets not present to the consumer being one such factor.
Universities can host the llms just like they hosted any other computer lab or web service on campus. This is what universities are supposed to be doing. Universities should be involved in open model research and should offer models that are not datamined.
And I really doubt university ITs would be able to run these, at least in an up to date and stable manner. High performance computing is typically run totally separately from everyday user systems, and tend to be extremely painful to use (hello slurm!).
— Mitch Hedberg
Muddling through with markets, democracy and welfare.
Global life expectancy was 34 in 1913. Today it's 70.
https://ourworldindata.org/life-expectancy
Global GDP was less than 1Trn until about 1800. In 1950 it was 11.7Trn . Today it's 157 Trn. In a life time it's gone up by more than 10 fold.
https://ourworldindata.org/grapher/global-gdp-over-the-long-...
People are living longer, richer lives all over the world.
The world's largest country grew at 7.8% last year.
https://www.reuters.com/world/india/why-indias-strong-gdp-gr...
Things are getting better. Look at the data, work at what you do and ignore the doom sayers.
I know lot of folks on Hacker News hates patents but that was the whole point of them: the patent holder got exclusive rights to the invention for 20 years. But the trade off was that specific details about the invention, how it worked and how it's made were entered openly for anyone to look up. The patent holder would basically benefit it for the majority of his or her life but then after that it was permanently part of the public domain.
AFAIK it was the reason why the patent system was invented, otherwise the best option jealous guarding of trade secrets that ideally (for the secret holder) died with them.
Some methods are more realistic than others, but I don't see a requirement for any outlandish ideas.
In a sane society it should be easy to argue against that claim, but looking around in the US at least, it turns out you’re correct: that doesn’t seem to be the norm under US-style capitalism.
Luckily we have other countries to provide an example here.
Though maybe if there's a flurry of math-optimized agents coming up, like there are small coding agents, those might be feasible to host personally.
Analogously with software development, it's always been good practice to write things down, but since the start of this year it's become dramatically more important for everyday work.
What we need to do is make mathematics about understanding, rather than churning out results. People should be rewarded for reaching an ability to explain mathematics without the aid of computers, to teach people for the sake of their learning.
I do think AI also needs to be eradicated because of its destructive properties, but I think that at the same time it also is a manifestation of the sickness in our society to go after the wrong incentives that are detrimental in the long run.
I wonder how life was while the Butlerian Jihad was raging through the universe.
Jihadis were fighting opponents with thinking machines. Did they win because the machines were not capable enough?
The idea that this genie is going back in the bottle is, imo, very wishful thinking. The thinking machines can rip off your software ideas completely, in days.
Automated spreadsheets and PPTs won't get people fired.
"Eradicated" is a pretty strong word. It's also completely unfeasible.
Wrong incentives can maybe be adjusted for. Shutting down the pursuit of one of the most astonishing things we've ever created is simply not going to happen short of a cataclysm, and I'm not a big fan of those.
I wonder how it revealed it... oh, right, because AI labs rushed to churn out new results for marketing purposes. Mathematicians didn't make them do it. So I'm not sure it's really an indictment of the field.
In fact, how often does mathematics feature in university press releases, how often do mathematicians compete for multi-million grants, how many of them are interviewed on TV?... This discipline is less afflicted by weird incentives than most other fields. It's mostly just a small clique of nerds publishing abstract "open source" work.
> Maybe mathematicians are smart enough to never ever buy such piece of shit on higher principle
They are not. Mathematicians are as human as most of the rest of us here.
This is all but guaranteed now.
Mathematicians/Scientists/Researchers need to stop sharing freely with "AI Companies" and have explicit clauses in place in their publications about not using their research without their explicit consent.
There should be a clear legal distinction between using research data for AI model-training vs. another researcher using it.
Come up with a legal framework, establish procedures for sharing and using others work and have a single scientific body in charge of enforcing it.
The frontier LLM vendors do sell enterprise licenses which contractually guarantee that your prompts won't be used for training. (Maybe they'll secretly violate the agreement but in principle it's legally enforceable.) Scholars and universities who care about credit and attribution will either have to purchase those licenses or run their own private open-weight LLM instances.
risk of prescient theory is more important than dismissive ablation.
edit: to wit, facebook google and anything else not e2e.
it's not like the ai is homomorphic.
"government intelligence agencies" ARE 'AI'.
I hate this but I don't think there's any going back now that LLMs exist.
Two people can keep a secret if one of them is dead.
At the same time, mathematicians should be using sophisticated, specialized LLM tools in much more sophisticated ways than lay people. There should be no way lay people can compete. There are new tools to master and if you use your slide rule, you won't keep up. It's a chance for mathematics productivity to boom.
With apologies to Baudelaire: The greatest trick exploitative powers ever played was convincing the people that it was impossible to imagine anything else.
Sometimes blinkering people so that they never ask the question "why is this being done to me" or "why is justice not possible" is much easier than finding an answer that will get them to go away.
The friction in math right now is you have the fast moving melodic bits racing faster than the base can understand always or keep up with. So you start to need AI for both the left brain part that is executing and the right brain part that is synthesizing. That's just the friction right now. You reduce the friction by using AI to help with understanding AI and getting back to a more normal rhythm of scouting out (with AI) and (what is still developing more and more) synthesizing with AI.