Obviously this doesn't scale, but I chose to send this junior researcher a (hopefully polite) email with some of my thoughts (written hastily in 30 minutes, not polished). More practicing mathematicians & researchers should advocate for the culture they want, so here's my bit.

Gautam Kamath@gautamkamath.com · 4d ago

I saw someone post a dozen+ AI slop papers purporting to solve niche open problems. This is antisocial behaviour and worse than if the problems stayed open. 0 people understand the solution, and there is no readable writeup. Also, incentive for either is removed.

Three years ago, we proposed "overlapping qubits" as a description of information encoding in quantum gravity. In our new paper with Charles Cao's group at @virginiatech.bsky.social, we finally apply overlapping qubits to evaporating black holes! arxiv.org/abs/2608.10085

Claude is getting watermarks. I presume GPT will need to implement this too to comply with EU regulations support.claude.com/en/articles/...

How Claude marks AI-generated content | Claude Help Center

support.claude.com

Like many others I was feeling the lack of a platform where the full spectrum of opinions (in particular also lesser heard voices) on "math and AI" may get an audience. Now here it is! Think about contributing and share it widely! proofsandprompts.com #math #mathsky #llm #AI #mathandai

Proofs and Prompts

Notes from the common room

proofsandprompts.com

I'm pleased to share our #ICML2026 tutorial on machine unlearning! Presented by Vinith Suriyakumar and myself, it includes a full set of videos recorded and posted to YouTube! Please check it out: unlearning-tutorial.github.io

In summary, it seems like two of the biggest results in their big list of 10 was just putting two things together and not citing them properly paywall-free link: www.yahoo.com/news/science...

OpenAI’s latest math breakthroughs commit research misconduct, experts say

OpenAI’s newest chatbot may be a whiz at math, but it seems to be lagging far behind humans in its academic rigor. Last week the company announced 10 more artificial-intelligence-generated math advan...

yahoo.com

Exactly how i feel about writing myself semi-rad.com/2026/08/do-i...

Unverified but BIG if true eprint.iacr.org/2026/1591

A Polynomial-Time Quantum Algorithm for the Dihedral Coset Problem

We present a polynomial-time quantum algorithm for the Dihedral Coset Problem (DCP). The algorithm is based on Regev's polynomial-time reduction of the Dihedral Subgroup Problem (DSP) to the modular ...

eprint.iacr.org

Some initial thoughts, and a complicated mix of feelings. Wow. I mean, Erdos problems are cool (I genuinely mean that), I didn't know about the Jacobian conjecture before it got disproved. But this newest batch from OpenAI hits home in a way the previous announcements did not.

I tend to agree with Tobias. It will be interesting to see near-term changes in the valuation of certain aspects of research. An important problem I see is who can afford access to frontier models and how the scientific community should address this. tjoresearchnotes.wordpress.com/2026/07/28/p...

Proof inflation

I have been thinking a lot about how social dynamics are going to shift in the new era of cognitive abundance. I don’t pretend to have any kind of crystal ball, but there are numerous histori…

tjoresearchnotes.wordpress.com

While the Fields Medal celebrates the under-40s, the mathematician Joan Birman has, at the age of 99, solved a major open problem in representations of the Braid groups, a topic she has worked on for more than 60 years.

Belief propagation is reshaping how we think about tensor networks, and now it can be improved systematically. Check it out! “PEPS is hard” may be becoming less absolute. Using these techniques in practice? I’d love to hear what works, what doesn’t, and where they break down.

APS journals@apsjournals.aps.org · last mo.

A theoretical framework for belief propagation in tensor networks introduces an innovation called a cluster expansion based on statistical mechanics, allowing it to overcome longstanding limitations on accurate approximation. Read more in PRX Quantum: https://go.aps.org/4gvmeI6

The Coherence Principle Back into the swing of things in Maynooth, getting ready for the repeat examinations that start next month, I realized that I had forgotten to pass on an interesting paper that I found out about a few weeks ago but was reminded of while in London so I'm remedying my…

The Coherence Principle

Back into the swing of things in Maynooth, getting ready for the repeat examinations that start next month, I realized that I had forgotten to pass on an interesting paper that I found out about a few weeks ago but was reminded of while in London so I'm remedying my omission now. The title is The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories…

telescoper.blog

How far can we compress billion-parameter LLMs? We introduce requential coding, which achieves < 1-bit per param compression, and explains why scaling doesn't hit a generalization wall! arxiv.org/pdf/2607.11883 w/ Shikai Qiu, Marc Finzi, Yujia Zheng, Kun Zhang 1/🧵

new favorite diagram shortlist entry

After 20 years, researchers finally have strong evidence that “quantum proofs” are more powerful than ordinary classical ones. The results suggest that at least in computation, there’s no way around the complexity of the quantum world. Read more in @quantamagazine.bsky.social:

Researchers Reveal the Power of ‘Quantum Proofs’ | Quanta Magazine

When checking that solutions to certain problems are correct, it turns out, you can’t get around the inherent complexity of the quantum world.

quantamagazine.org

I am happy to announce that our newest work on non-local quantum computation (NLQC) has made it to the arXiv: scirate.com/arxiv/2606.2.... For me personally, the main motivation to study these tasks comes from quantum position verification, but it has links to diverse areas such as quantum gravity.

Equivalence of non-local computation tasks beyond Clifford operations

Non-local quantum computation (NLQC) studies how two collaborating players can implement channels on distributed systems using a single simultaneous round of quantum communication and shared entanglem...

scirate.com

a bit late, but as of this month, I’ve joined QMATH @qmath-copenhagen.bsky.social as a postdoc in @dansfranca.bsky.social 's group! i'll be working on quantum algorithms theory and quantum info more broadly. if anyone in the copenhagen area wants to collaborate, hit me up!

Bayesian Inductive Inference and the Anthropic Cosmological Principle Many moons ago I wrote a paper with a person called Antony J.M. Garrett with the title Bayesian Inductive Inference and the Anthropic Cosmological Principle (the full reference is A.J.M. Garrett and P. Coles, Comments on…

Bayesian Inductive Inference and the Anthropic Cosmological Principle

Many moons ago I wrote a paper with a person called Antony J.M. Garrett with the title Bayesian Inductive Inference and the Anthropic Cosmological Principle (the full reference is A.J.M. Garrett and P. Coles, Comments on Astrophysics 17(1) 23-47 (1993). It got a few citations here and there, and has been discussed in a few books and other texts. In 1999, the journal&hellip;

telescoper.blog

The alpha version of my new book "Optimal Transport for Machine Learners" is out, with in particular an online version with interactive figures www.gpeyre.com/ot4ml/

I'm so happy to share this paper, we put a lot into this one: arxiv.org/abs/2606.12539 If you have ever wondered what the quantum-information literature has to say about temporal correlations and time itself, check out our unifying picture: all you need are spacetime states.

Unifying spacetime approaches to quantum mechanics

Recent efforts to formulate quantum mechanics in a way that treats space and time on a more equal footing have led to a large variety of spacetime-oriented approaches. In this work we present a detail...

arxiv.org

Big update: the EC Zoo is now a handbook. It spans codes, sphere packings, lattices, designs, groups, and phases of matter. Extensively checked, but not perfect—feedback very welcome: arxiv.org/abs/2606.11484

Handbook of Error-Correcting Codes

Barcode scans, clear phone calls, reliable data storage, satellite communication, and large-scale quantum computation are all made possible by error correction. We present a handbook version of The Er...

arxiv.org

The Erdos unit-distance conjecture disproof was achieved using the publicly available GPT 5.5 Pro by Yichen Huang. github.com/yichenhuang/...

GitHub - yichenhuang/unit-distance

Contribute to yichenhuang/unit-distance development by creating an account on GitHub.

github.com

Amazing paper!

Sophie Huiberts@sophie.huiberts.me · 3mo ago

Recently I've been obsessed with this 1994 paper by Hooker. Among other things, he explains the (largely unexamined) empirical content of NP-completeness theory. More theorists need to read it

Tonight in the ai reading group i was reminded of something that happened in 2006 after I dropped out of college, when I was living in a run-down old house next to jb alberto's in rogers park with a bunch of dudes. it was, as you can imagine, not clean.

I read Dirac’s original paper on the Dirac equation and I must say it is really beautiful. He comes from an experimental question (that the electron has spin-1/2) and derives the equation from a simple relativistic argument. The presentation is honestly better than any I’ve seen in modern textbooks

Found this goldmine in arxiv.org/abs/2602.09665

Apparently there's a quasi-polynomial time classical algorithm for the unknot problem which was announced in a talk in 2021 and is summarized in this slide, but there's not actual writeup of it anywhere. www.maths.ox.ac.uk/node/38304

After grumbling for years in our substacks about uses and abuses of probability in machine learning, @beenwrekt.bsky.social and I decided it's finally time to put down some concrete ideas in a manifesto with a DOI. Here it is, give us your best feedback. (1/4)

Separating Geometry from Probability in the Analysis of Generalization

The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for ...

arxiv.org

new paper! energy is one of the simplest and main quantum observables: it is experimentally friendly and theoretically simple. can we witness magic by looking at energy/heat measurements? well, "every little heat is magic"! arxiv.org/abs/2604.08663 1/n