Math – Apurva Nakade

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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

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

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