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.

From Mathematics to Generic Programming

Notes

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

CBT: Computational Basis Transforms

A C++17 header-only library that formalizes a pattern behind FFT, logarithmic arithmetic, and Bayesian inference: transform to a domain where your target operation is cheap.

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.

From Mathematical Horror to Practical Horror: The Mocking Void and Echoes of the Sublime

How The Mocking Void's arguments about computational impossibility connect to Echoes of the Sublime's practical horror of exceeding cognitive bandwidth.

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.