I’m a student in the Maryland area who does independent mathematics research, mostly in analytic number theory and approximation theory. Most of my work starts in Desmos: I build a graph to look at a question, try an idea against it, and keep the ideas that hold up when the numbers are checked. Several times this has led me back to known results from another direction, among them Stirling’s formula, Chebyshev nodes and Nadaraya–Watson regression.

The question I return to most is how well smooth functions can describe the primes: how closely the logarithmic integral Li(x) and Riemann’s R(x) follow the prime counting function π(x), how to build curves that stay above π(x), and whether there is a natural way to define π(x), or the n-th prime, between whole numbers. Alongside that I like building approximations by hand: fit a formula, study what is left over, and fit that.

Outside of pure math I co-founded TrXon with Rodrigo Cartagena, an off-road self-driving vehicle project. Its path planner interpolates sensor checkpoints on both sides of a trail and averages them to find the centre line, which is where several of the interpolation pages here come from. I’m also in The Knowledge Society’s Activate program and take dual-enrollment courses at the College of Southern Maryland.

If you’d like to talk about any of this, or you’ve spotted a mistake in a graph, email is the best way to reach me.