When Adam Tobin-Williams ’26 enrolled at Johns Hopkins University as a Chemical and Biomolecular Engineering major, he didn’t expect to fall in love with mathematics. But a single course—Linear Differential Equations with Mario Micheli, senior lecturer of applied mathematics and statistics—sparked an entirely new academic path.
“That class really drew me in,” he says. “I realized I was more fascinated by the math behind engineering than by the engineering itself.”
Now pursuing a dual bachelor’s/master’s degree in both applied mathematics and statistics and chemical and biomolecular engineering, Tobin-Williams is blending two disciplines that share a common goal: using theory and computation to solve complex, practical problems.
Tobin-Williams says that the rigor of applied math at Hopkins became a defining challenge—and a source of motivation.
“AMS courses are consistently the hardest I’ve taken,” he says. “The concepts come quickly, the workload is demanding, and exams really test your understanding. But that’s what makes it exciting. You’re constantly learning how to think more critically and how to collaborate more effectively.”
The academic rigor of his coursework provides benefits that extend beyond the classroom.
“In some courses, the class average might be 50%, so you have to get comfortable not knowing everything right away. That process of struggling, failing, and then understanding—that’s what gives you the skills needed for real technical challenges, whether in research.”
Tobin-Williams’ passion for applied math goes beyond equations. After his freshman year, he joined a research team at the Johns Hopkins Applied Physics Laboratory, where he helped integrate large language models into a system designed to assist military medics in high-pressure environments.
“We were building a tool designed to provide quick, accurate guidance for medics and warfighters treating specific battlefield injuries,” he explains. “I analyzed how well the system performed using data science tools like confusion matrices in Python. It showed me how powerful well-designed algorithms can be in high-pressure situations.”
That experience deepened his interest in the interconnectedness of mathematics, programming, and optimization—an interest he is continuing to pursue in his master’s thesis.
Working under Mahyar Fazlyab, assistant professor in the Department of Electrical and Computer Engineering, and Mateo Díaz, assistant professor in the Department of Applied Mathematics and Statistics, he’s developing and implementing a new algorithm in semidefinite programming to help estimate Lipschitz constants—a key part of understanding how stable deep neural networks are.
“Our goal is to create a faster, more efficient way to determine how stable a neural network is,” he says. “It’s still early, but I love that I get to help test and implement theories that could improve the performance and reliability of AI systems.”
Across his courses and research, Tobin-Williams continually finds ways to merge applied math with engineering.
“Graph theory, Monte Carlo methods, and optimization—these all show up in my chemical engineering work,” he says. “For example, I’ve used graph theory to study crystal structures, figuring out which crystals connect and how particles move across surfaces. It’s amazing how these abstract concepts become tangible when you see them applied.”
He’s also shared his enthusiasm as the head teaching assistant for the course, Linear Differential Equations for five semesters. His leadership earned him the Professor Joel Dean Excellence in Teaching Award, presented by the applied mathematics and statistics department.
“Helping other students find their footing in math has been one of the most rewarding experiences I’ve had at Hopkins,” said Tobin-Williams.
His time at Johns Hopkins has inspired him to continue his studies and he now is planning to pursue a PhD in chemical engineering, with a focus on optimization.
His advice to students? “Talk to your professors. Explore everything. Applied math can seem abstract, but once you start making connections to hands-on problems, you realize it’s everywhere.”