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:…
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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…
Algorithmic Logo Design: Building Numerical Integration into the CyArm SVG
When we approach logo design as a form of systemizing, we move beyond the limitations of manual vector tools and embrace the beauty of repeatable, a…
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…
The 10 free books I recommend to every engineer learning ML math (and why order matters)
After teaching hundreds of engineers learn machine learning last 5 years, a pattern becomes hard to ignore. Most people don’t struggle because machi…