Mathematics

Reverse-Process Synthetic Data Generation for Math Reasoning

Training LLMs on mathematical reasoning by inverting easy-to-solve problems: generate derivatives, reverse them into integration exercises with full step-by-step solutions.

Watch: Calculus, The Big Ideas

Calculus as one idea examined from every side: a seven-episode animated playlist running from limits through the derivative, the integral, the fundamental theorem, gradients, and optimization.

On Intelligence: The Gap Where Safety Is Decided

There is a beautiful, settled theory of intelligence, and there are the crude systems we shipped. The distance between them is where safety is actually decided.

On Intelligence: and Its Specifications

We taught sand to think. We did it before we learned to say what we wanted it to do. There is a real, settled, and genuinely beautiful theory of what intelligence is: Bayes' theorem, Solomonoff's universal prior, and expected-utility maximization, …

From Mathematics to Generic Programming

Notes

History of mathematical ideas underlying generic programming. More accessible than EoP.

XTK: A Symbolic Expression Toolkit for Term Rewriting

A Python library for rule-based term rewriting with pattern matching, multiple input formats, and an interactive REPL.

Gödel, Turing, and the Mathematics of Horror

The formal foundations of cosmic dread. Lovecraft's horror resonates because it taps into something mathematically demonstrable: complete knowledge is impossible, not as humility, but as theorem.

Mathematical Structure in Software Design

How mathematical principles, generality, composability, invariants, and minimal assumptions, translate into better software.

Math Master's Done: Post-Mortem

I defended my mathematics thesis. Three years, stage 3 cancer, and a second master's degree. Here is what worked and what did not.

Going Back for a Second Master's, This Time in Math

I already have an MS in Computer Science. Now I'm going back for Mathematics and Statistics, because I kept hitting walls where I could use methods but not derive them.

The Beauty of Mathematical Abstraction

What makes mathematics beautiful: generality, inevitability, compression, and surprise. And why abstraction matters for software.