Turán's theorem is the founding result of extremal graph theory: among all graphs on $n$ vertices with no clique on $r+1$ vertices, the balanced complete multipartite graph has the most edges. We pres...
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.
Notes for a Theory | Alberto Garutti
Tim Berners-Lee, Giant Global Graph (2007)
A new vision for the web where the users master their data and link them to everybody's benefit in a giant global graph.
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.
Maximum power principle
The maximum power principle or Lotka's principle has been proposed as the fourth principle of energetics in open system thermodynamics, where an example of an open system is a biological cell. According to Howard T. Odum, "The maximum power principle can be stated: During self-organization, system designs develop and prevail that maximize power intake, energy transformation, and those uses that reinforce production and efficiency."
Chomba Bupe on Twitter / X
It appears OpenAI Astra's mathematical feat was more of surface level stitching of components."The LLM-generated proof hinges on a particular mathematical argument that it presented as its own but that actually first appeared in a 2016 paper by Miller and a collaborator." pic.twitter.com/labUnQMRab— Chomba Bupe (@ChombaBupe) August 7, 2026
Open Graph protocol
The Open Graph protocol enables any web page to become a rich object in a social graph.
(PDF) Maximum Power: The Ideas and Applications of H. T. Odum.
PDF | "Maximum Power" is a synthesis of the creative genius of Howard Thomas Odum as seen through his own words and those of his students, many of whom... | Find, read and cite all the research you need on ResearchGate
General Theory of Natural Equivalences
Samuel Eilenberg, Saunders MacLane, General Theory of Natural Equivalences, Transactions of the American Mathematical Society, Vol. 58, No. 2 (Sep., 1945), pp. 231-294
Read OpenAI’s latest internal memo about beating the competition — including Anthropic
The memo directly mentioned OpenAI’s intensifying competition with Anthropic.
Interesting footnote on math arXiv arxiv.org/abs/2608.16066v1
Unsorted interesting articles/papers
Male-like ornamentation in female hummingbirds results from social harassment rather than sexual selection
