(Math) Blog

This is a place for me to write about mathematics and education.

Vibe Coding
learning
AI

I learned to program in C from two textbooks and no Internet. Something is lost when the AI writes all the code.

Dec 4, 2025

With or Without Order
probability
puzzle

A student asked whether choosing with order or without order changes a probability. My first instinct was wrong.

Nov 27, 2025

Self-Fibonacci Numbers
number theory
research
open
fibonacci
exploration

For which n does n divide the nth Fibonacci number?

Aug 11, 2025

Architects and Gardeners
philosophy
teaching

George R.R. Martin split writers into architects and gardeners. The same split applies to course planning, and I am firmly a gardener.

Jul 17, 2025

Learning is Remembering
philosophy

Plato’s anamnesis, the Pali sati, and mathematicians who ‘discover’ theorems. What if learning really is remembering?

Jun 29, 2025

Sperner’s Lemma - Geometric Proof
triangles
coloring
visualization
interactive
determinant

My new favorite proof of Sperner’s lemma: morph the vertices toward the cardinal colors and let the determinant do the work.

May 25, 2025

Sperner’s Lemma - Combinatorial Proof
combinatorics
triangles
coloring
visualization
interactive

The door-counting proof of Sperner’s lemma, as an interactive triangulation you can resize.

May 16, 2025

Sperner’s Lemma - Statement
combinatorics
triangles
coloring
visualization
interactive

What Sperner’s lemma says, with an interactive colored triangulation to play with.

May 14, 2025

Random points in a triangle
randomness
triangles

Randomness is hard to simulate. How to generate a uniformly random point inside a triangle, worked out so I could play with Sperner’s lemma.

May 12, 2025

Barycentric Coordinates
triangles
interactive
visualization

Every point in a triangle is a weighted average of its corners. An interactive look at what those weights mean.

May 11, 2025

Mir Publications
textbooks
russian

An archive of Mir Publications textbooks, and why I prefer their hundred-page directness to American doorstops.

Sep 10, 2024

Pythagoras using Hilbert 90
abstract algebra

Dummit and Foote classify Pythagorean triples using Hilbert’s Theorem 90, a surprisingly slick route to a classical fact.

Jun 8, 2024

Closed Convex Cones in LP
analysis
linear programming
convex analysis

A theorem I hit while formalizing linear programming in Lean, where the naive topological proof falls apart.

Jan 2, 2024

Combinatorial Nullstellensatz
combinatorics
problems
todo

A fun theorem I came across in a talk on tree colorings, and the polynomial trick behind it.

Nov 26, 2023

Logarithms and primes
todo
infinite series
number theory
riemann zeta

A NumberPhile video on the density of primes mod 4, and the passing remark in it that I found more interesting than the headline result.

Oct 26, 2023
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