Proved, Certified, Swept, Sampled
A claim in a paper can be backed by very different things. It can have a written proof. It can have a theorem the Lean kernel has checked. It can ha…
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Count the Rings or Sear the Squid
Drop a handful of squid rings into a frying pan and you have already made a decision, whether or not you noticed making it. You can lay them out so…
Navier–Stokes Blows Up, and the Blow-up Is a Vortex You Can Picture
On 8 September OpenAI published a proof that the three-dimensional incompressible Navier–Stokes equations can develop a singularity in finite time:…
An AI System Claims a 90-Year-Old Math Prize Problem. The Real Story Is Messier
On September 8, OpenAI announced that an internal AI system produced a solution to the Navier-Stokes existence and smoothness problem. If you are no…
Part 6 - STATISTICS
Bernoulli, Binomial Distribution & Central Limit Theorem Explained from First Principles When I first started learning probability, I came acros…
AdvancedMathBench: A New Benchmark for LLM Advanced Mathematical Reasoning
What Changed Large language models (LLMs) have demonstrated proficiency in high-school and olympiad-style mathematics. However, their performance in…
The Quantum Math Talent Shortage: Why Good Mathematicians Hate Working at Quantum Companies
There's a quiet crisis happening in quantum computing that nobody wants to talk about. Quantum startups are desperate to hire mathematicians. They'r…
Making Equation (2.2) of the OpenAI Erdős Result Executable
Why a proved theorem still needs reproducible claim custody On May 20, 2026, OpenAI announced that an internal reasoning model had produced a counte…
How I Use an Online TI-84 Calculator for Quick Math While Coding
Many developers don't think about calculators until they need one. Whether it's debugging formulas, checking statistics, verifying algorithm outputs…
The Merging Was Always the Point
Yesterday, an internal model at OpenAI disproved the Erdős unit-distance conjecture. The conjecture is from 1946. It is, depending on which discrete…
How I Built a Vedic Panchang Engine in TypeScript — Swiss Ephemeris, Meeus Fallback, Zero External APIs
Sub-arcsecond planetary positions, sunrise for any location on Earth, and an entire astronomical calendar — all computed server-side in a Next.js ap…