This idea of AI filling in results only in the convex hull of known math. I don't know, man. Almost everything new is a recombination of old ideas. For example, given enough time and the right pressures, multicellular life develops from simple molecules. terrytao.wordpress.com/2026/10/08/w...

What should we tell our students?

[This is a guest post by Álvaro Lozano-Robledo. This blog post was initially written in a different file format and converted using AI. — T.] TL;DR: Keep calm and carry on studying math. I wo…

terrytao.wordpress.com

x.com/itsolelehman... I have to dunk on this post even if it's from the wrong site. Somehow this person (or their AI) appears to have a deep understanding of what 10+ different results in the openAI proof dump means for science...

Just when you think the US administration has bottomed out, they find a new low. www.bbc.com/news/article...

Fort Hood attacker's execution by firing squad will be livestreamed, Pentagon says

Pete Hegseth says the execution will be public, but a legal expert says the "unprecedented" decision is on "uncertain legal terrain".

bbc.com

I would have to assume there is currently an army of AI agents at OpenAI and Anthropic working on AI research using massive resources, constrained only by the time to run computational experiments. I would also have to assume they are quite successful at it. And publishing none of it.

arxiv.org/abs/2610.08144 "Hence, informally, providing semantically faithful AI autoformalisation is harder than any computational problem including the Halting problem" This does not invalidate the Navier-Stokes Lean proof, but it could an entirely different argument compared to the writeup.

Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs

Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this pro...

arxiv.org

www.ahmath.org/statements "Mathematicians did not ask for this work to be done." I get the feeling, but this sounds super gatekeepy. Isn't mathematics supposed to be open so that anyone can contribute? OpenAI's proof dump is a contribution. There is still a lot of work for humans to understand it.

Looks like this already came true today? We might have actually overshot: Lance Fortnow wrote in his blog: "Now these proofs haven't been fully verified but if they hold up, we've seen more progress in theoretical computer science in the last 24 hours than in the previous three decades combined!"

Jarno N. Alanko@jnalanko.bsky.social · 3w ago

It is really starting to feel like at least a decade worth of pure math/TCS results is going to be happening in Q4 2026. Human understanding, digestation and dissemination is going to take a while. But wow.

github.com/openai/math/... Discrete Fourier transforms faster than O(n log n)? Means also faster polynomial multiplication?

math/preprints/An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026 at main · openai/math

Contribute to openai/math development by creating an account on GitHub.

github.com

github.com/openai/math/... Subset sum faster than the textbook meet-in-the-middle algorithm! What a morning!

math/preprints/Subset-Sum-in-Time-2-power-0-49n-October-4-2026/subset-sum.pdf at main · openai/math

Contribute to openai/math development by creating an account on GitHub.

github.com

github.com/openai/math/... 2-approximation for the shortest common superstring! Better than greedy!!

math/preprints/A-Polynomial-Time-2-Approximation-for-Shortest-Common-Superstring-September-24-2026/paper.pdf at main · openai/math

Contribute to openai/math development by creating an account on GitHub.

github.com

github.com/openai/math/... Really bold claim in the OpenAI proof dump: matrix multiplication can be done in O(n^(9/4)), with a *non-constructive* proof.

math/preprints/Matrix-Multiplication-Nine-Fourths-October-2-2026 at main · openai/math

Contribute to openai/math development by creating an account on GitHub.

github.com

arxiv.org/abs/2610.067... O(n^1.9992) algorithm claimed for 3SUM! Huge if true! Lots of conditional lower bounds are based on the assumption that 3SUM takes quadratic time.

Truly Subquadratic 3SUM and Truly Subcubic APSP via Triangles in Sparse Lopsided Graphs

We give the first polynomial improvements over the textbook algorithms for $3$SUM and All-Pairs Shortest Paths (APSP): we show how to deterministically solve $3$SUM on $n$ integers of polynomial size ...

arxiv.org

I used AI to comb through Franklin's notebook to find the part where she thinks DNA might be a double helix. It found it! "... suggests that there is an integral no. (or simple fractional no.) of residues per turn of helix (if there is a helix) ... "

Elizabeth Anne, PhD@lacksauthority.bsky.social · 6d ago

never the wrong time for this classic

never the wrong time for this classic

Science Magazine@science.org · 6d ago

Exclusive: A new analysis refutes James Watson’s claim that he was the first to recognize the significance of the famed photograph 51. https://scim.ag/4rTKck8

People say Claude Opus 5.5 is amazing. I find it infuriating. It constantly tries to be one step ahead of me. If I ask for some simple plot, it tries to infer what I *really* want and adds all sorts of things that I never asked for. I does not feel like I'm in charge.

www.anthropic.com/news/claude-... 950 Claude agents spent 21 hours looking at sequences encoding reverse transcriptases and noticed nearby spaced repeats like in CRISPR. It's cool but.... how come the string matching community had not found this before? Embarrassing.

We are often asked whether pangenomes are worth the hassle. The files can be large and methods to explore them are much more challenging than linear references. Earlier this week, we preprinted a clear example of how and why pan-genome graphs are so important for trait discovery.

bioRxiv Genomics@biorxiv-genomic.bsky.social · 5mo ago

Dissecting the regulatory and genomic drivers of the dichogamy determining G-locus in pecan https://www.biorxiv.org/content/10.64898/2026.05.14.725045v1

I'm starting to believe in the labor theory of value for TCS/math papers. That is, given equally skilled workers, with equal tools, and equally important problems, the value of a paper is roughly proportional to the amount of (human) labor that has gone into it.

It is really starting to feel like at least a decade worth of pure math/TCS results is going to be happening in Q4 2026. Human understanding, digestation and dissemination is going to take a while. But wow.

Exciting news regarding the SBWT rust API! We now have an implementation of the subset rank method in this preprint, written Anastasia Diseth. It takes the space down from 5 bits/kmer to 2.5 bits/kmer (double that if both strands are indexed). About 4-5 times slower. www.biorxiv.org/content/10.6...

New Space-Time Tradeoffs for Subset Rank and k-mer Lookup

Given a sequence S of subsets of symbols drawn from an alphabet of size σ , a subset rank query srank( i, c ) asks for the number of subsets before the i th subset that contain the symbol c . It was r...

biorxiv.org

The world’s largest battery-electric aircraft flew for the first time on the 12th of August, a 27-minute test flight over upstate New York that cost about five dollars in electricity. Heart Aerospace’s 30-seat prototype is a big step toward a commercial version. buff.ly/i3f0PhR #ShareGoodNewsToo

The largest all-electric plane ever flew for 27 minutes, on $5 of electricity

Heart's X1 demonstrator flew for 27 minutes from a regional airport in upstate New York, running on battery power the entire time. The aircraft reached 1,100 feet...

techspot.com

3Blue1Brown posted a great exposition of the proof of problem 6 of IMO 2025. This problem is brilliant. It's insane that some contestants managed to solve it. www.youtube.com/watch?v=Nbwv...

The last IMO problem AI could not solve

YouTube video by 3Blue1Brown

youtube.com

This race to be the first to publish an AI-generated result is getting silly. If the answer is just a prompt away for anyone, why should *any* human get credit for it? The value is in the quality of the exposition. Racing to be the first to publish is detrimental to that.

www.anthropic.com/research/cla... Anthropic optimizes open-source models for protein design, gets a 4x speedup and a low-memory mode. That's actually... pretty underwhelming? With their resources I would have though they can do better than small constant speedups.

How Claude is uplifting biomolecular modeling

Anthropic is an AI safety and research company that's working to build reliable, interpretable, and steerable AI systems.

anthropic.com

developer.nvidia.com/blog/introdu... Native GPU programming support in Rust from Nvidia!

Introducing CUDA Rust: Two Tracks for Writing GPU Kernels | NVIDIA Technical Blog

In September 2026, NVIDIA announced it is leaning into native GPU programming in Rust. CUDA C++ and CUDA Python are mature, enterprise-grade toolchains, and NVIDIA will be growing and maturing CUDA…

developer.nvidia.com

STOC is fighting AI-generated submissions by requiring a proof-of-human 20-30 minute video explaining the work. Seems reasonable to me. Otherwise the PC will drown in submissions.

Lance Fortnow@lance.fortnow.com · 3w ago

STOC call for papers is out. Deadline is November 2. acm-stoc.org/stoc202... New rules for the AI era: limited submissions, public posting and a required video. Is it a coincidence that the camera-ready deadline is April Fools Day?

⚠️ We believe that there is an ongoing campaign targeting owners of popular crates and rust-lang team members that is attempting to compromise devices and accounts in order to use them to publish malware. See our blog post for details: blog.rust-lang.org/2026/09/17/t...

Be alert: targeted attacks on prominent Rustaceans | Rust Blog

Empowering everyone to build reliable and efficient software.

blog.rust-lang.org

terrytao.wordpress.com/2026/09/16/l... >Since research papers are the standard currency in math, a currency that is being rapidly devalued by AI, perhaps we should find ways to inject more humanity into them. For instance, we could add a “backstory” section... Yes!! Do it! Make math human.

Let the Diners Into the Kitchen

[This is a guest post by Noah Giansiracusa. This blog post was initially written in a different file format and converted using AI. — T.] Imagine a tech company announces new robot workers th…

terrytao.wordpress.com

I think that the year of the Linux desktop is finally coming. AI is really good at debugging obscure issues that used to require lots of technical expertise to solve. It already fixed an issue with my Bluetooth headphones, and another one with my USB audio card.

People say that viral genomes are tiny. Not all! Today, I learned that this exists: en.wikipedia.org/wiki/Pandora.... It's a giant virus that spans 1 micrometer and has a genome with 2.5 million bases and 2500 genes. Discovered in 2013.

Pandoravirus - Wikipedia

en.wikipedia.org