Abstract Nonsense

A place for long-form blog posts.

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.

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.

An Afternoon Reading the Dictionary

I scripted the extraction of dictionary definitions from macOS’ built-in Oxford Dictionary archive to automate my new-vocabulary blog page. As all good automation projects, I probably spent more time automating the process than it would’ve taken to do it manually.

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.