This will not happen. The fear comes from the real problem: publication as a measure.

The mathematics itself will only benefit from the discovery of cross links from the human created literature. Think about these LLM as infinitely patient and very long attention experts in what was already done.

So on one side, for a few years at least, it will become normal to publish tens of articles. The article inflation is what scares the present system.

On the other side, after a while, when all the existing mathematical corpus will be mined and most of buried connections will be explored, we shall have a much more better foundation for future mathematics.

It is very naive or misleading to think about mathematics as if it were chess or go.

In few year these (future) tools will be in standard use.

I have seen two worries recently:

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.

Make the proof from LLMs with the same constraints as human mathematicians have:

The proof must be as succinct as possible so that it's reviewable. It's ok for the same LLM to publish repeatedly, but it's not Ok to drop a bulk 600kb Lean proof.

The proof must build on other works that are similarly bite sized and published before (so that it's incrementally reviewed)

The proof must be published as soon as fully formed, and not in bulk like current LLMs proofs.

I devised an algebraic representation of music composition. This enables me to mass produce musical scores without ever touching artificial intelligence.

It took me 10 years to develop the system, and I intend to ride it out as much as I can. By act 3 of my life sure I will publish the math. But in this economy, I would be a damn fool to publish my equations just to let the LLMs write better music.

https://monictheory.com/developer-api

Universities should be providing university hosted llms to their faculty and students. No student or faculty member should be using public llms for their work. They can share info directly with other people or in non-public forums to keep it away from commercial llms. It is going to have to be against the rules to submit anyone else's work to a commercial llm. Businesses are going to have similar policies.

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.

In science and math, too often only the final result gets credited or published.

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.

anyone else already experiencing this in a corporate environment? I know I am. Its not just between teams either, its within them.

As the famous British mathematician Alfred North Whitehead wrote 111 years ago, "Civilization advances by extending the number of important operations which we can perform without thinking of them."

This now includes the proving of theorems.

He went on to write "Operations of thought are cavalry charges in a battle - they are limited in number, they require fresh horses, and must only be made at decisive moments."

Mechanization also demolished that institution, which had also survived for thousands of years.

Part of the controversy here is that now the skill advantage that some Field Medalist had is much narrower. The fact that fields medals have an age limit implies that it favors brain power over understanding. And that was the guiding light award of the community. So i find it "funny" (and natural) when they are offended by AI.

That is the main "crisis" of mathematics.

In my opinion there has never been a better time to be a mathematitian, and there has never been a better time to be a software builder.

But there has never been a worst time to have the need to prove your economic value as a mathematitian or software developer alone. Because "understanding" is not something you can prove in one afternoon, its something that you prove with a life.

you don't worry about it for a couple years and check back to see if its a real problem or a panic induced engagement generator

We don't.

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.

There is a financial incentive to selling access to the leading LLMs needed to find whatever secret result there is out there. See the play station hypervisor 0day from the other day. If a LLM can find someone's secret 0day they are flaunting around they can find a math proof someone else says they have.

This is a simple matter of intellectual property. A tool or technique for doing a thing can be patented. A legal monopoly is granted to the originator. The public is made aware of the technique but is legally forbidden from using it for a period of years/decades.

Talking about frontier mathematics? Even the common for-mere-mortals version of mathematics is totally inaccessible to most people. Even to those who want to really learn it.

Take a good look at the textbooks that teach mathematics and tell me I am wrong.

The problem here is that AI isn't just a problem, it also revealed a problem: too much emphasis on publishing papers and churning out new results. The name of the game right now is just that: make something new and significant. AI itelf is a problem around the world right now because we've set up some seriously bad incentives. Same with art - it devolved into content creation for money, so AI snaps that up.

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.

Similar principle applies to open source or any other creative endeavor put in the public domain.

> Regardless of the true cost, it seems that professional mathematicians now need to wary about what they put into a LLM and think hard about how to disclose and publish a result.

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.

I'd guess universities might starting hosting open source models. They can probably actually afford to, unlike individual mathematicians.

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.

I welcome the era of secrecy. After living so much in this era of open information where everyone seems to know everything, secrets may be a way to make things more interesting again.

Like we can prevent the rest of our society from devolving into the Medieval Era of secrecy: by treating individuals with respect and dignity and not as the ore from which resources can be profitably extracted.

Ctrl + F, "open journals", 0 results. There has been an explosion of open access journals in the last decade. Is everyone basically LARPing on YCombinator?

Stop treating AI companies and their software as somehow unconstrained, above-the-law actors. It's delusional that anyone buys that. Regulate them appropriately.

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.

Simple: if you don't publish your work, we don't fund you. Why is this even a question?

wouldn't it be dystopian secrecy cause a flock camera is equally capable of watching the mathematicians as it is the public citizens.

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Seems rather a dramatic notion for a single incident...

The simple short-term solution is just don't feed all your work into the IP theft machine?

All of life proceeds effectively with a right brain and a left brain. A fast loop and a slow loop. A general and a scout. A melody and a base. The evolutionary moments involve moving the melody into the base and making way for a new melody. But there is always an overseeing element and a work element. A manager or coach and an employee or athlete. It's just an effective pattern of growth. You see it everywhere in nature. In generations of animals and plant life (the more experienced parent, the growing child; the central 'brain' and the rest of the body; the queen ant and the ant colony; the trunk and the leaves).

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.