Thomas Bloom on Twitter / X

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

An OpenAI model has disproved a central conjecture in discrete geometry

An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.

Text rendering and effects using GPU-computed distances

Text rendering is cursed. Anyone who has worked on text will tell you the same; whether it's about layout, bi-directional, shaping, Unicode, or the rendering itself, it's never a completely solved problem. In my personal case, I've been working on trying to render text in the context of a compositing engine for creative content. I needed crazy text effects, and I needed them to be reasonably fast, which implied working with the GPU as much as possible. The distance field was an obvious requirement because it unlocks anti-aliasing and the ability to make many great effects for basically free.

The Distance

If you’re seeing this, you’re here early. Thank you for trying things out. I’m building this in public and appreciate any and all feedback. With that, there are two main things I ask you to keep in mind.

Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms

Nicole Feng

We introduce a method for approximating the signed distance function (SDF) of geometry corrupted by holes, noise, or self-intersections. The method implicitly defines a completed version of the shape, rather than explicitly repairing the given input. Our starting point is a modified version of the heat method for geodesic distance, which diffuses normal vectors rather than a scalar distribution. This formulation provides robustness akin to generalized winding numbers (GWN), but provides distance function rather than just an inside/outside classification. Our formulation also offers several features not common to classic distance algorithms, such as the ability to simultaneously fit multiple level sets, a notion of distance for geometry that does not topologically bound any region, and the ability to mix and match signed and unsigned distance. The method can be applied in any dimension and to any spatial discretization, including triangle meshes, tet meshes, point clouds, polygonal meshes, voxelized surfaces, and regular grids. We evaluate the method on several challenging examples, implementing normal offsets and other morphological operations directly on imperfect curve and surface data. In many cases we also obtain an inside/outside classification dramatically more robust than the one obtained provided by GWN.

Defining the Dimensions of the “Space” of Computing

The first computing machines were so large they filled entire rooms. Today they are ubiquitous, built invisibly into our environments. While it's tempting to view this change within a predetermined space of progress, we can still shape the future on our own terms.

Direct Consequences of the Three-Dimensional Counterexample to the Jacobian Conjecture

Expository writing following an explicit three-dimensional Keller counterexample.

5000 Feet is the Best

5000 FEET IS THE BEST is based on two meetings with a former drone operator which were recorded in a hotel in Las Vegas in september 2010. On camera, the drone operator agreed to discuss the

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

Addressable Space Web - Summer of Protocols

Addressable Space Chenoe Hart 1. Hidden Floors You may not notice in everyday life when a building you walk into is constructed of words and numbers in addition to bricks and mortar. Consider the composition of One Burrard Place, a condominium in Vancouver. It was described as

The case of the 500-mile email

The following is the 500-mile email story in the form it originally appeared, in a post to sage-members on Sun, 24 Nov 2002.:

Cosine similarity

In data analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the cosine of the angle between the vectors; that is, it is the dot product of the vectors divided by the product of their lengths. It follows that the cosine similarity does not depend on the magnitudes of the vectors, but only on their angle. The cosine similarity always belongs to the interval [ − 1 , + 1 ] . {\displaystyle [-1,+1].} For example, two proportional vectors have a cosine similarity of +1, two orthogonal vectors have a similarity of 0, and two opposite vectors have a similarity of −1. In some contexts, the component values of the vectors cannot be negative, in which case the cosine similarity is bounded in [ 0 , 1 ] {\displaystyle [0,1]} .

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

Chris Peikert on Twitter / X

WOW!! 🤯Among many jaw-dropping results, this proves NP-hardness of the Closest Vector and Nearest Codeword Problems for *polynomial* approximation factors, for the first time ever, and via a totally new approach (Reed-Solomon techniques). Amazing! https://t.co/3yh3scLX5R— Chris Peikert (@ChrisPeikert) August 1, 2026

How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer. | Quanta Magazine

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.