From the Editors, Volume 3

We are delighted to present the third volume of the Pittsburgh Interdisciplinary Mathematics Review (PIMR). The third volume would not have been possible without the incredible work of the authors, our editors, and our referees, as well as the continued support of our advisory board and the mathematics departments of the University of Pittsburgh and Carnegie Mellon University. This volume provides a taste of math in all its forms — from pure theory to applications in society-defining issues. Mathematicians featured in this issue use not only traditional methods, but also cutting-edge tools such as artificial intelligence and the Lean theorem prover.

We are excited to feature the expository pieces, When equivariant homotopy theory meets combinatorics by Julie Bannwart, a researcher at the Johannes Gutenberg-Universität, Mainz, and When a set theorist hears “combinatorics”: Infinite Ramsey theory by Dr. Thomas Gilton of the University of Pittsburgh. These works illustrate that combinatorics can serve as a bridge between seemingly disparate topics.

It is our privilege to feature interviews with Professor James Maynard of the University of Oxford, and Professor Bard Ermentrout of the University of Pittsburgh. Maynard was awarded the Fields Medal in 2022. He discusses how he utilizes math from surprising places, and how others have built upon his work. Maynard also talks about the future of math, and the potential he sees in generative AI to perform tedious tasks in order to free up the creativity of mathematicians. On the other hand, Ermentrout studies math in close connection with its applications. A pioneering computational neuroscientist, he discusses the development of the field throughout the 20th century and its future going forward. He won the Moser prize in 2025, one of the most prestigious awards in dynamical systems.

Given the ongoing upheaval in research funding within the USA we see it as ever more our responsibility to make math more accessible to the public. It is important that more people have access to appreciate and engage with the knowledge, beauty, and utility mathematics produces, and in doing so recognize its value, both as a tool for society and as an intellectual pursuit. We encourage you to submit to future issues and further this goal, be it through exposition, survey, book reviews, undergraduate research, or beach math problems. We look forward to reviewing your submissions!

Leonardo Finzi, Nina McCambridge, Griffin Mekler-Culbertson, & Lark Song
Co-Editors-in-Chief of the PIMR