encyclopediai

But what if the fundaments of all these, in the human produced literature, actually contain hidden circularities and holes which make very hard the progress?

IMO for the moment the greatest value from these AI tools is that we can start an audit and hopefully proceed on a saner foundation, after we use the tools and think about it.

This is different than too many AI generated proofs or panic reactions from the academic system with its stupid incentives.

Thanks, I noticed it, see also possible relations with RNA in RNA based combinators, so it is indeed relevant. https://chorasimilarity.wordpress.com/2024/03/11/rna-based-c...

You can play with it. Equivalence with Turing machines is not the point of interest

Sorry about this "not A but B", now is one of those situations where is needed.

Is not:

- cellular automata, - Turing machines

implemented chemically.

The goal, first of UPIM, then chemlambda or chemSKI, is simply to: - find chemical complexes, - or to make them

(though I suspect that we shall discover them in our cells)

so that they enter in random chemical reactions which are akin the graph rewriting inspired by lambda calculus or SKI combinators or Interaction Combinators.

The thesis is that this chemical translation still can do "anything" despite the lack of control of reactions or the combinatorial explosion of possible reaction networks.

Under this thesis we are graph quines.

Every day now I expect that they or somebody alike will discover in our genes that we (ie life) are lambda terms, combinators or something similar to Universally Programmable Intelligent Matter https://web.eecs.utk.edu/~bmaclenn/UPIM/UPIM3.pdf or chemSKI https://imar.ro/~mbuliga/talks/chemski-with-tokens.html

All it takes is to identify the syntax, so to say.

A bit more developed, here:

https://chorasimilarity.wordpress.com/2026/09/22/a-mathemati...

A mathematician's suggestion:

I would push for an audit of the whole mathematical corpus (all articles etc ingested by the present AI) as soon as possible. Since there are of the order of 10^7 articles, compared with the progression of results announced, this might be possible in less than a year.

All these results exploit the existing corpus. With enough time and maybe several orders more attention, we humans would discover these results.

So instead of producing heaps of new proofs (but be welcome to do this IMO), make an audit, OpenAI or Anthropic or anybody who listens.

The title communicates a different idea than the body of the text. I'd rather give a quote from the body, which is very reasonable:

"We believe the recent developments have profound implications for mathematics but the systems are likely to be comparably strong in other technical domains, including cyber security, autonomous weapons, biological and chemical agent development and the spread of misinformation.

I have previously compared the arrival of these new AI tools to the moment Galileo picked up a telescope for the first time and was able to see things in our solar system that we’d never seen before. It is an exciting and transformative moment to be doing science. But it is also a very dangerous period and we need to be careful about our use of language when describing these dangers."

So the "problematic" part is not about mathematics, really.

Yes. The main idea visible through this pile of problems is that human ingenuity (of the management) will find a way to use anything for more money (publishers) or more prestige (academic researchers).

The mathematicians who complain now had no worries about the way the generous idea of open access turned into the gold open access, where the author pays for publication.

These people have no problems with the phd students who are forced to publish or perish and even if they survive there is no future for them.

Now the problem is IMO that for the first time the interest of the publishers and academics are not aligned.

Publishers want more articles to sell back to the academics.

Academics are pushed by the system to publish more.

But all the work is done by academics who write and review the articles.

And also a huge inflation of articles devalue the publication unit.

So a CAPTCHA idea is only natural, even if the kind of a malefic idea a manager could have.

Thanks. IMO the most fun is in the CAPTCHA, which turns on its head the Turing test.

But it goes even further than their greCAPTCHA and it solves their consumed time problem.

Indeed, in their proposal they have a human bottleneck, but in the june 2026 proposal is suggested that one could use an AI to generate the results without the knowledge of the submitted article.

If the AI can generate a pretty close result, with the article fed gradually as a prompt, then reject.

And even further, that it might be not even a need to publish anymore.

Just use the article for training and make a public database with some numbers about the successful researcher, where we see an influence score (how many times an idea from an accepted article are used by other accepted articles), a publication score (how many articles the author had).

I wonder if the reality will be more or less surprising, my bet is on "more".

In June 2026 I proposed a CAPTCHA for scientific publications

https://chorasimilarity.wordpress.com/2026/06/13/a-captcha-f...

At the moment this was seen as a tongue in cheek proposal.

Yes. AI is a useful tool and we are going to adapt and use it.

The phd student will be forced to publish 10 breaktrough articles, the university department which does not offer "free" access to AI (for its members) will see the its ratings going down, when compared with the other universities.

It will be "use AI or perish" for academic management so on the side of academic management the ones with vision will thrive and the ones without will perish.

But what about the publishers? In the last decades the academic research was made into a feeder for publishers. The main goal of a researcher is to write articles, which are later sold back to other researchers.

This economic system is under big stres now, because for a while at least the academic management and publishers will have contradictory goals.

And that is why this scare which is induced by those who profit the most from the present system.

The last days we are served these high goals about understanding, "digestion" and so on.

But if you look at the practice of present mathematics, in the last 20 years it is all about publishing solutions to problems.

There are famous problems to be solved, there is a hierachy of conjectures to be solved. A quick search here on HN gives pearls like "Theory building papers are dime a dozen and don't get published in high tier journals unless they solve a problem".

And all of a sudden it turns out that problem solving can be automatized.

So then what will problem solvers do? Well, from now on they will "digest" problems solved by AI.

In a way or another they will find a way to stay on top.

That's the goal, at least, but mathematics as a living practice does not have much to do with these games of power.

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.

Most mathematicians do compete for funding, based essentially on how many articles they can publish and where. Publication strongly favors problem solving. Universities are ranked on the same criteria.

What we see is a panic reaction to the fact that problem solving is "easy", which affects the future of the management of mathematics, not of mathematics itself.

Mathematicians are not luddites afraid of AI, is the academic publishing industry mixed with management interests speaking here.

If you look at the Leiden Declaration https://leidendeclaration.ai/ then you notice two weird IMO facts:

- that it was stirred by the International Mathematical Union Committee on Publishing

- that is a mixture of the older San Francisco Declaration on Research Assessment DORA https://sfdora.org/read/ and recent fear of commercial AI competition

I feel like Randy Waterhouse in the scene where he was trying to (not) participate to a discussion at the table concerning the internet.

Everybody knows what eating the seed corn means.

There is no seed corn analog in mathematics.

Since the fashion that mathematics is problem solving there are lots of farmers ploughing their own field, that I concede.

The is no "the mathematicians". Some mathematicians, very influent ones, are mad at AI, for social reasons, because it shows problem solving is "easy".

Mathematics is fine and will be fine in the future.

I disagree with this scarcity point of view.

Concrete example: Navier-Stokes. I don't make any claims about the truth of the announcement of the proof. But for the sake of the argument le't just suppose we know now that there is a smooth solution with smooth boundary and initial data which blows out in finite time.

Navier-Stokes is the simplest among evolution problems for continuum media, because it has maximal material symmetry (that's the mathematical meaning of a fluid).

If this is solved then go to a harder one, Coulomb friction. As a real life phenomenon, friction is very interesting to explore and mathematically is much harder than NS.

So it is not like we will ever be left without things to think about.

Oh, you want another? The present AIs are things made of mathematics. I would like to understand as a mathematician how and why they can beat human problem solvers?

Is that because mathematics is in some precise, interesting sense, more "computable" than it seems?

Mathematics called and says she's fine. She's curious about how is that possible.

Misaligned are the present academic merit system hand in hand with financial interests of academic publishing industry.

The system will be exploited and there will be an inflation of problem solving articles produced with AI. Nobodies will be more productive than 10 Fields medal recipients, each year.

So of course that the ones at the top of this system are scared.

This is a social problem of the present system, not a problem of mathematics.

Mathematicians will do mathematics and politicians will do politics, what's new?

I run such tests since a long time at chorasimilarity open notebook.

I always used guest non login accounts.

As a mathematician I was able to check two plagiates (by humans) with even such primitive means.

But I have to mention that some things irk me in this conversation about math or science and AI.

First, I see lots of attribution and other related problems, with certain impact for the researcher proffesion.

But I don't see the most natural question: wouldn't you like to know the answer to _open-problem_ ?

I mean, is research now only about publishing and solving famous problems?

From this point of view I think the links from this recent post are depressing

https://terrytao.wordpress.com/2026/09/10/crowdsourcing-a-li...

Second, I think very relevant that the original meaning of "encyclopedia" is "recurrent education".

So I arrived to think that the present and future forms of AI in mathematics and sciences should be seen as modern day encyclopedic efforts.

Once we pass over the flurry of solving famous open problems (and wouldn't you like to know?) the next natural step is an audit of the ehole corpus of mathematics and sciences accumulated until now.

And then pass further on a saner basis and damn about problem solvers and unhappy publishers and management.