Partial orders for Counter data structures
Multisets can be partially, but not totally, ordered by inclusion. Here’s a quick bugfix for the
counter crate.#mathematics
Apostol's Solution to the Basel problem
A neat solution to the Basel problem: $\sum_{n=1}^\infty \frac 1 {n^2} = \frac{\pi^2}{6}$. The solution is by Apostol, and relies on using vector calculus.Factorial overflow
Exploring the factorial function and determining the first $n$ such that $n!$ exceeds the maximum size of an unsigned integer, for various bitwidths. We’ll take a look at Stirling’s approximation and the Lambert W function.Writing an eigenvalue solver in Rust for WebAssembly
We build an eigenvalue solver in Rust and compile it to WebAssembly, to build an interactive demo of the Gershgorin Circle Theorem that bounds the region of the complex plane matrix eigenvalues live in.Talk: Implementing Efficient Language Models under Homomorphic Encryption
A summary of a talk on implementing efficient language models under homomorphic encryption by Donghwan Rho at Seoul National University.Heuristics for Minimum Euclidean Skeletons
A retrospective look at my 2021 University of Melbourne vacation research project on minimum Euclidean skeletons, a geometric graph theory optimisation problem.Can a regex match valid card numbers?
We construct a Deterministic Finite Automaton that recognises the set of arbitrary-length valid card numbers as per the Luhn check digit algorithm and abuse reality to derive an (executable!) regex with millions of characters.Hard problems: the Hadamard matrix problem
It’d be a bit imprecise to define a measure on the set of open problems, but I’d wager that it is much larger than the set of solved problems.
One such open conjecture is the Hadamard matrix problem, an unsolved problem in mathematics that keeps me up at night. Do square matrices $H$ with entries $\pm 1$ satisfying $HH^T = nI_n$ exist for all $n = 4k$? The smallest unknown case is of order 668; like Order 66, but for mathematicians instead of Jedi.
Building animations in Manim with LLMs
Building animations in Manim with LLMsPaper: Step-by-Step Diffusion: An Elementary Tutorial
Paper: Step-by-Step Diffusion: An Elementary Tutorial2025 Australian Election Forecast Model
2025 Australian Election Forecast ModelInverse UMAP transforms
Inverse transforms with UMAP dimensionality reduction