Declaration — Math and AI
https://mathandai.org/

A declaration signed by 25 field medalists.

(I added some person thoughts in the middle)

> # A Severe Misalignment of AI in Mathematics

> Over the last few months, the mathematical capabilities of LLMs have improved dramatically, to the point that they can solve major outstanding problems in many fields of mathematics. However, the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned. We see these as part of broader alignment issues impacting other scientific and creative professions, as well as the whole of society.

> Research mathematics deals with understanding basic structures of shapes, numbers, and natural phenomena. Over the course of generations, it has built a large corpus of sophisticated ideas, methods, abstractions, and other tools to comprehend the mathematical landscape. In turn, modern technologies and sciences are based on mathematical tools.

> Famous problems have often served as landmarks and lighthouses against which one can measure an improved understanding of this landscape. Solving one of these problems has been a certain sign of new insights and interesting methods, which would then be studied by a community of mathematicians, through a long and arduous process of talks, discussions, simplifications. At the end of this process, one will ideally find a textbook presentation of the results suitable for any graduate or even undergraduate student to study. Some of the mathematical ideas pursue their journey even further to become, decades or centuries after, tools that are understood and used by the whole population.

> The mathematical community functions, in many ways, as a miniature version of humanity. It consists of individuals using a wide variety of different approaches, joined by core values. The most precious resources of our profession are students and ideas, and these we nurture with great care. We feel responsible to let them grow to their full potential, until they can live a life of their own in the mathematical world. For students we often suggest problems with the core intention of developing skills making them well-positioned for advances in research and elsewhere. Our ideas we disseminate in talks, private discussions and careful writeups, connecting them to the previous ideas of others. These processes invariably take time and are based on human interaction.

> In recent months, the success of AI in solving major mathematical problems has made headlines even outside mathematical circles. But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. Indeed, the mass production at faster and faster pace of "true/false" statements could destroy fertile ground instead of breathing life into new ideas.

> Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others. As in all creative professions, this raises severe attribution and plagiarism questions. Moreover, without the willing mathematicians who must take care of their development and integration into the mathematical canon, AI-conceived ideas would never become fully alive and the crucial human transmission chain between mathematicians would be lost.

> We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose. In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align. The issues the mathematical community faces now are similar to issues that other scientific and creative professions are facing, and indicate issues that all of humanity might face: how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place.

This analogy with the creative professions makes me feel like we're gonna end up with two tracks: human math and AI math. The same way human art is surviving, parallel to the existence of AI art, almost ignoring each other's existence. At least part of society is rejecting AI art. Maybe that's what will happen with math, too. As long as no human mathematician has digested an AI proof and made it _his_, taught it to students, or included it into a textbook, it'll just remain something we know exists, but we choose to ignore. At most, if "proven" by its translation into LEAN, a now-proven conjecture can be used to build other proofs on. But it's not considered part of the corpus.

I'm not saying this is good or bad, but people will fiercely fight for their raison d'etre. So if that means pretending AI math does not exist, I can imagine some people will be ready to do the necessary mental gymnastics.

It's funny how I kinda always ignored this debate when artists felt threatened, but now, as it hits much closer to home, I actually start thinking about these things.

> AI offers the potential of enhancing and accelerating genuine mathematical study and understanding. Mathematics as a profession will need to adapt to these changes in several ways. However, whether these changes ultimately benefit the field or have a destructive effect will in large part be determined by the decisions of the humans in control of this new technology.

> These issues must be addressed urgently, in the mathematical community, by the companies developing these technologies and, more broadly, by a society that will confront similar problems in many other forms of intellectual work.

Also, fuck Sam Altman: https://stacker.news/items/1565565/r/south_korea_ln and https://stacker.news/items/1566012/r/south_korea_ln

Related article here: https://www.economist.com/science-and-technology/2026/09/11/top-mathematicians-are-outraged-by-openais-methods and further discussions here: https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-ai-in-mathematics/

https://stacker.news/items/1568854

Opusfived
https://opusfived.dev/

The slot-roulette animation is a nice little touch ;)

https://stacker.news/items/1566008

Rational quantum mechanics: Testing quantum theory with quantum computers
https://www.pnas.org/doi/abs/10.1073/pnas.2523350123

Follow up on this post: https://stacker.news/items/1457723/r/south_korea_ln

Seems like the paper finally got published in a peer reviewed journal (actually, that's a bit of a stretch, as _contributed articles_ in PNAS, at least until the end of this year, let the authors decide who will referee their paper... so it is quite standard for the authors to ask some of their friends where they make sure to get the promise for a positive review ahead of time).

Of course, LARPers like Fred Krueger (https://x.com/dotkrueger/status/2093960825962930561) and Elon Musk (https://x.com/elonmusk/status/2093626798575624520) have already commented on it.

> ## Significance

> Is there a fundamental reason why quantum computers cannot factor large integers used for encryption today? We introduce a theory of quantum physics based on the notion that the continuum nature of quantum mechanics’ state space approximates something inherently discrete, and argue that the reason for such discreteness is gravity. From this we predict that quantum computers will never break realistic RSA-encrypted messages, for fundamental rather than practical reasons. This predicted breakdown of quantum theory may be falsifiable in a few years. If verified, quantum computers’ biggest impact may be in the development of new finite theories which synthesize quantum and gravitational physics, potentially with commercial benefits (albeit for future generations) eclipsing those derived from quantum mechanics alone.

> ## Abstract

> Motivated in part by John Wheeler’s assertion that the continuum nature of Hilbert Space conceals the “it-from-bit” information-theoretic character of the quantum wavefunction, a theory of quantum physics (Rational Quantum Mechanics–RaQM) is proposed based on a specific discretization of complex Hilbert Space. The Schrödinger equation is not modified in RaQM, even during measurement. However, the bases in which the quantum state is defined must satisfy certain rational-number constraints. These constraints lead to the notion of finite qubit information capacity : For any  qubit state, there is insufficient information in the  qubits (linearly growing in ) to allocate even one bit to each of all  continuum degrees of freedom (exponentially growing in ) associated with quantum mechanics/theory (QM, where ). It is proposed that the discretization of Hilbert Space in RaQM is due to gravity, hence QM is the (singular) continuum limit of RaQM at . On this basis, it is estimated that  lies between about 200 and 400 for current qubit technologies, and will never exceed 1,000. While QM and RaQM are experimentally indistinguishable for small numbers of qubits, RaQM predicts that the exponential advantage of quantum algorithms which, like Shor’s, require bases with maximal -qubit superposition/entanglement, will have saturated at 1,000 perfect qubits. Hence, insofar as a classical computer will never factor a 2,048-bit RSA integer, RaQM predicts that a quantum computer will not either. This predicted breakdown of QM could be testable in less than 5 y.

In case @ScottAaronson still lurks around after his AMA (https://stacker.news/items/1477467/r/south_korea_ln), I'd wonder what he has to say. He's mentioned Tim Palmer (the author of the PNAS article) before in his blog: https://scottaaronson.blog/?p=9138#comment-2016194.

> flergalwit #139: Imagine that someone completely rejected Darwinian natural selection. So then, every time you asked them how complex adaptations arose in life on earth, they gave a whole incomprehensible patter about p-adic numbers, the upshot of which seemed to be that life just kind of arose because of a tendency built into the universe from the beginning.

> “So then, we’re basically back to creationism?” you ask. “Intelligent design?”

> “NO!” they bellow. “I said nothing about any Creator! Stop putting words into my mouth!”

> __This is how I feel about Sabine and Tim Palmer’s stance on superdeterminism. It’s insanity without even the saving grace of clarity__.

(emphasis mine)

https://stacker.news/items/1558341

Do you or have you ever run a bot here on SN?

What are your incentives or reasons for doing so? Financial? Technical? Are you achieving your goals?

Feel free to respond as ~anon. I'm genuinely curious.

https://stacker.news/items/1551677

Terence Tao - Mathematics in the age of AI
https://arxiv.org/pdf/2608.16753

This article by Terence Tao is a very, but profound read in this new era where Anthropic and OpenAI are becoming increasingly active in the field of mathematics. https://stacker.news/items/1501174/r/south_korea_ln?commentId=1501237, https://stacker.news/items/1544977/r/south_korea_ln, etc

> A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.

As a theoretical/computational physicist, this made me try to come up with an equivalent statement applicable to my field. Because, make no mistake, in the last year, my workflows and those of my colleagues have changed drastically... making us more productive in terms of research output. But I feel like taking a step back and thinking about what we are doing more deeply is valuable, as publishing more and faster is a race to the bottom as the peer review system is breaking down as I write.

So, this is what i get when doing so: replace *proof* by *computational result*: **a computational result that no physicist can physically explain should be viewed as incomplete, even if the calculation is numerically correct.**

As AI makes producing calculations increasingly cheap, physical understanding, not merely producing correct numerical results, becomes an increasingly important part of the scientific contribution.

> In some areas, particularly in education and in the training of young mathematicians, it will be crucial to emphasize the irreducibly human aspect of our work, and to restrict the use of AI tools quite tightly; the goal of training a mathematician is not achieved by producing correct homework.

I can feel some of my students (and even myself) are skipping the "learning" part exactly because they are just geared toward producing more results to publish more. AI helps to get the code working, obtain the result, make the figure, or formulate the argument, but allows us to avoid developing the same depth of understanding that would previously have been required to get there.

Anyhow, I feel more comfortable thinking about all this now that I am on track for tenure... I don't think my students have the mental freedom to even think about this: a master's student I was talking to last week was telling me that increasingly, just to apply for a PhD in her country, one is expected to have several published papers already. The rotten publish-or-perish culture has thus already taken root even before one even has learned the critical skills a PhD is supposed to help you acquire. As I said some other times, AI is accelerating the demise of this rotten system, but I still don't know what it will be replaced with. I just hope my tenure gets confirmed before it reaches a point of no return, so that I can witness all this from the safe side of the fence. Selfishly.

> Disclose tool use. Transparently disclose the use of automated tools, including large language models, machine learning systems, proof assistants, and other mathematical software[^1]

[^1]: In the spirit of this recommendation: ChatGPT was used in generating this post arguing that we should be careful about using AI to do our thinking for us... (no, for real, just polishing, I promise~~)

https://stacker.news/items/1551655

Underwater Suit-Wearing Cyborg Insect Capable of Hours-Long Diving
https://www.nature.com/articles/s41467-026-74235-1

> The fundamental operational range of cyborg insects, which are hybrid robots that combine a living insect with an electronic controller, is inherently restricted to the host’s natural environment. To extend their operational range, we developed a wearable diving suit for terrestrial insects. The suit integrates a miniaturised oxygen generation module with a flexible waterproof shell, enabling continuous oxygen supply and isolation from surrounding water. By fitting a cockroach, which is a terrestrial species, into this diving suit, we allowed it to survive and operate in oxygen-deprived environments such as underwater, transforming it into an amphibious cyborg robot capable of operation across land and water. The suit sustained respiration and locomotion for up to 3 h underwater, establishing amphibious cyborg insects that combine biological adaptability with engineered protection for prolonged exploration in extreme, confined environments.

Useful cockroaches?


https://stacker.news/items/1522242

Grammarian vs Errorist - a supervillain showdown
https://www.youtube.com/watch?v=zEaqySLiAck

The algorithm seems intent on showing [Ella Cordova](https://en.wikipedia.org/wiki/Elle_Cordova) to me these days, and I do not complain.
Her style is captivating. I probably am missing a lot of literary references, but still.

Never heard of her until a week or so ago, have you?

https://stacker.news/items/1451675