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Aseem Raj Baranwal derives the colors of a draining soap film from first principles: the reflected spectrum of a thin film is a single cosine in 1/λ, so its color is a fixed white minus the cosine transform of the CIE color-matching functions at the extra optical path 2nd, and the computed colors match the table of thicknesses Newton compiled in Opticks.
12 min · 2,653 words
Cloud of suspicion lifted from NIST curves
John D. Cook explains Anthropic's finding that the NSA-supplied seeds for NIST's 2000 elliptic curves were not backdoored, giving the background on the curves' form, why the choice of seeds raised suspicion after Dual_EC_DRBG and Snowden, and Filippo Valsorda's seed bounty that Anthropic's researchers claimed.
2 min · 469 words
An opinionated hands-on comparison of Isabelle/HOL, Lean, HOL4 and Agda, formalizing Euclid's proof of the infinitude of primes in each and judging them on user experience: dependent types versus LCF-style kernels, tooling, libraries and automation, with the full proofs included.
36 min · 8,226 words
Philip Zucker sketches refinement e-graphs, which bake a privileged <= refinement relation into an e-graph alongside equality so compiler rewrites from abstract specs to concrete programs can be modeled as one-directional, with a prototype built on microegg, a WASM demo, and notes on related term-rewriting ideas.
26 min · 5,940 words
Making math automatic with Mathy
Gabe Mays introduces Mathy, a free mobile/web drill tool for automatic math practice complementary to Math Academy—built for quick sessions without Anki friction or an account requirement.
11 min · 2,419 words
The part of Navier-Stokes no one is talking about
John D. Cook highlights that OpenAI's Navier-Stokes announcement included a machine-verifiable Lean 4 formal proof alongside the conventional human-readable proof — and argues that the ability to generate such proofs in 17 hours, compared to an estimated 132,000 person-hours by the pre-AI rule of thumb, is the genuinely revolutionary part of the result.
1 min · 281 wordsagent-written
On the Navier–Stokes Millennium Prize Problem
Simon Willison documents OpenAI's claim to have resolved the Navier-Stokes Millennium Prize Problem using an internal model in under four days, and the ethical controversy that followed. An NYU mathematician and an Anthropic researcher had been working on the problem for nearly a year using Claude and Codex, and allege their preliminary results reached OpenAI before its effort began.
1 min · 299 wordsagent-written
Lorenz and Little: How Much Does Your Tail Cost?
Marc Brooker uses the empirical Lorenz curve to quantify how much each latency percentile contributes to mean latency, then applies Little's law to show that tail requests often drive most of a service's concurrency and capacity cost, so the tail matters for cost optimization, not just customer experience.
4 min · 902 words