In 200-dimensional word embeddings such as gensim's glove-twitter-200, a cosine similarity of 0.656 — corresponding to an angle of about 49° — counts as a large similarity, according to an analysis by…
AI acts as an intelligence multiplier, disproportionately boosting the productivity of top-tier programmers and mathematicians, who use it to settle long-standing conjectures, according to the article…
OpenAI announced a proof that settled a long-standing question about the Navier-Stokes equations from fluid dynamics, and simultaneously posted a Lean 4 formal proof of the result. The formal proof as…
AI-powered coding agents such as OpenAI's Codex, used with GPT-5.5 and GPT-5.6, generate code that is often 2-3 times longer than necessary, lacks structural simplification, and fails to break large f…
John D. Cook, a mathematician and blogger, tested Anthropic's Claude AI's ability to generate ASCII diagrams, finding that the first attempt to reproduce a graph from his post on the graph imbalance t…
Levent Alpöge and colleagues used Claude AI to discover a new Hadamard matrix, prompting a series of posts by John D. Cook on Hadamard matrices and their applications, including NASA's use of a Hadama…
A 225-bit cryptographic key can be stored as a permutation of a standard 52-card deck, according to an article by Stephen Hewitt in Paged Out! issue 9. SymPy's Permutation class provides O(n²) ranking…
Levent Alpöge, a mathematician at Anthropic, discovered a counterexample to the Jacobian conjecture using Claude Fable 5, disproving a long-standing open problem in algebraic geometry. The counterexam…
Grok 4.5 successfully generated SWI Prolog and Lean 4 code to solve a chess puzzle: placing five white queens and three black queens on a 5×5 board so that no queen of one color attacks a queen of ano…
John D. Cook published a blog post on September 23, 2022, detailing regular expressions for matching HCPCS (Healthcare Common Procedure Coding System) Level II codes, which follow the format of one le…
A blog post by John D. Cook connects central Delannoy numbers, which count king moves on a chessboard, to DNA sequence alignment. The Delannoy numbers D(m,n) represent the number of possible alignment…
Claude generated Z3/Python code to solve a chess puzzle placing all pieces on a 6x5 board with bishops on opposite colors and no attacks. The solver found 192 raw solutions, deduplicated to 24 unique …
A user tested Claude's ability to generate Lean 4 code to formalize a ring theorem, achieving a proof after 11 iterations but with five unproven 'sorry' sections. The experiment highlights challenges …
John D. Cook used Anthropic's Claude (Sonnet 4.6 Medium) to find a typo in a blog post about quaternion rotations by asking it to write Lean code verifying the post's theorems. After four iterations, …
ChatGPT successfully generated a SWI Prolog program to solve a chess puzzle placing five pieces on a 4x4 board without attacks, finding all 16 solutions. The experiment suggests LLMs can effectively h…
Claude AI generated a Prolog program to solve a Martin Gardner chess puzzle requiring placement of two rooks, two bishops, and two knights on a 4x4 board without any piece attacking another. The progr…
Anthropic's Claude AI generated a Lean formal proof for a Fourier coefficient calculation involving Bessel functions, requiring eight iterations to fix errors and produce a working proof with four 'so…