Chris Peikert on Twitter / X

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 in $O(n^{1.9992})$ time and APSP on directed $n$-vertex graphs with polynomially bounded integer weights in $O(n^{2.9995})$ time. This refutes the $3$SUM and APSP hypotheses. Using known reductions, we also refute the real-valued versions of the $3$SUM and APSP hypotheses, the Exact Triangle hypothesis, the Zero-Weight $k$-Clique hypotheses, and the three rectangular hinted Online Matrix--Vector conjectures of van den Brand, Nanongkai, and Saranurak, and we give polynomial speedups for a variety of other problems. All of these results follow from a single new algorithm for thin matrix products. Let $X$ be an $N\times D$ integer matrix and $Y$ a $D\times N$ integer matrix with $D\le N^{1/18}$, and let $W$ be any set of at most $N^2/\sqrt D$ positions. We compute the entries $(XY)[I,J]$, $(I,J)\in W$, in $O(N^2/D^{0.063})$ operations, which is polynomially less than the time needed to write down $XY$ or to compute $N^2/\sqrt D$ inner products one by one. We design this algorithm by modifying a variant of Coppersmith's rectangular matrix multiplication algorithm, built from a ten-multiplication identity of Schönhage, to perform only the operations needed for the entries in $W$, and show that few operations are needed. Interpreted as a graph algorithm, this solves the All-Edges Sparse Triangle problem in truly subquadratic time on sparse lopsided tripartite graphs where two parts have $n$ vertices but one part has $n^{\varepsilon}$ vertices for $\varepsilon<0.12$. By known reductions, Exact Triangle, and hence $3$SUM and APSP, reduce to this problem. We also give a data structure version that answers queries for single entries of $XY$, not known in advance.

Timothy Gowers @wtgowers on Twitter / X

AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried.https://t.co/SD1vVPkrHR— Timothy Gowers @wtgowers (@wtgowers) May 20, 2026

"GPT 話你知": Thoses tasks surpassed by LLMs - Blog - Qingyu✨'s blog

We are publishing a list of QOJ problems for which LLMs, mostly GPT, have found solutions that are significantly faster than the authors’ intended solutions. If you would like to submit additional problems for inclusion in this list, please write an editorial on QOJ in the problem forum, mark it as anonymous, and leave a comment below.

Ten advances in mathematics and theoretical computer science

OpenAI shares new results on long-standing open problems in mathematics and theoretical computer science, including advances in geometry, cryptography, and complexity.

Noam Brown on Twitter / X

And yes we did try other major problems without success. Sadly no Millennium Prize problems (yet).But also, we didn’t spend a lot on each problem. It’s possible to push test-time compute much further.— Noam Brown (@polynoamial) August 1, 2026

Przemek Chojecki | PC on Twitter / X

The Growing Map of Open Mathematical Problems.We mapped 15,000+ conjectures from UnsolvedMath to show potential links between concepts.It also shows how under formalized the frontier is (less than 10%). pic.twitter.com/nm0PCpXVPf— Przemek Chojecki | PC (@prz_chojecki) August 28, 2026

Michael Truell on Twitter / X

We believe Cursor discovered a novel solution to Problem Six of the First Proof challenge, a set of math research problems that approximate the work of Stanford, MIT, Berkeley academics. Cursor's solution yields stronger results than the official, human-written solution.…— Michael Truell (@mntruell) March 3, 2026

NP-overrated

If you learned about NP-hard problems in university, your takeaway was probably this:

Tiny Code Christmas

LoveByte

Qdrant

Qdrant is an Open-Source Vector Search Engine written in Rust. It provides fast and scalable vector similarity search service with convenient API.

Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms

An Introduction To Robust-First Computation

Did you know there's an entire field of computer science barely yet explored? Join me at the entrance to a deep rabbit hole as we take a look at Robust-First Computation.

SciPy 1.0: fundamental algorithms for scientific computing in Python

SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments.

A 16× Smaller Index for EmbeddingGemma 2

EmbeddingGemma 2’s one advertised way to shrink its vectors, keeping 128 of 768 dimensions, loses about 0.06 nDCG@10. Storing all 768 at 2 bits each is 16× smaller with no measurable loss on SciFact or NFCorpus.