From the Editors, Volume 5
Welcome to the fifth volume of the Pittsburgh Interdisciplinary Mathematics Review (PIMR)! Thank you to the unrelenting and passionate work of everyone involved in making this volume possible, including but not limited to our authors, editors, referees, our advisory board, the mathematics departments at the University of Pittsburgh and Carnegie Mellon University, and the University of Pittsburgh Library System, who allow us to publish our work. This volume features articles from a wide variety of pure and applied subjects, ranging from analytic number theory to analytic philosophy.
Our volume begins with a variety of exposition and survey articles. We are introduced to Thomas Hales’ Simple matroids and Alfred North Whitehead’s theory of dimension (1906), where geometric matroids are thoroughly explored and serve to elaborate on Whitehead’s theory of dimension. It is followed by returning author Thomas Gilton’s When a set theorist hears “combinatorics”, Part 2: Trees, where in this sequel, countably and uncountably infinite trees are studied to understand combinatorial questions. Finally, we conclude with Gruesome predictions by Sven Neth, who takes a Bayesian approach to inductive reasoning to understand a question involving predicting the next color in a sequence.
PIMR has the honor of including an interview with Professor June Huh of Princeton University, a 2022 Fields Medalist and 2022 MacArthur Fellow whose groundbreaking research explores bridges between algebraic geometry and combinatorics. While in Pittsburgh for a guest lecture, Huh sat down with our editors to discuss his introduction to mathematics, his research experiences, and his outlook on the future of mathematics given current advancements in AI.
In our undergraduate research section, we feature the work of researchers from Haverford College as they explore modeling elephant and poacher populations, utilizing a predator-prey model to flesh out a high-risk, high-reward situation involving poachers and elephants. Following this article, Khintchine's theorem and related topics in Diophantine approximation from an undergraduate at the National University of Singapore discusses the monotonicity assumption of Khintchine’s theorem across various analytic perspectives.
We conclude our volume with our usual lighthearted columns, including Jason Wein’s Beach Math depicting a terrifying story involving comforting mathematics, and Prof. Paul Gartside’s Proofs Without Words.
We are also excited to announce that PIMR editor Bridget Vaughan will be stepping up as a new Editor-in-Chief for the PIMR, with Leonardo Finzi and Nina McCambridge staying on for the foreseeable future. We hope you enjoy perusing our articles and encourage you to submit to our future editions, be it exposition, undergraduate research, or Beach Math problems. We look forward to reviewing your submissions!
