Mathematical journeys begin in unorthodox ways. This was the case for Eric Ramos, assistant professor in the Department of Mathematical Sciences at Stevens, who gained an affection for mathematics in high school through a TV show. Numb3rs is a typical police drama with the added twist of one of the main characters being a math genius who uses his talents to solve crimes. Referring to this as his “supervillain origin story,” Ramos’ curiosity from the show would lead him to explore the field of mathematics and become a professional mathematician, earning his second grant from the National Science Foundation (NSF).
Ramos began his graduate-level studies in the field of number theory, the study of integers, citing that it was “the oldest field and theoretically rich.” This took him to the University of Wisconsin-Madison, where he completed his Ph.D. under Jordan Ellenberg, professor of mathematics and accomplished author of titles such as How Not to Be Wrong: The Power of Mathematical Thinking. Serendipitously, Ellenberg was the math consultant for the first season of Numb3rs, a fact that Ramos did not discover until later.
Combinatorics, the branch of mathematics concerned with counting, is where Ramos would take his talents next. “It might sound simple, but there are still deep questions about counting,” he said. This would largely intersect with the research he was doing as an assistant professor at Bowdoin College in 2021 to earn his first grant from the NSF, LEAPS-MPS: The representation theory of combinatorial categories. The funding backed studies of networks of connected points to see their use in understanding how large groups of points with no direct connections can exist, and how information can be efficiently spread through these networks. The other major project involved looking at the complex patterns that emerge when multiple robots move randomly along these network tracks without crashing into each other.
His newly earned NSF research grant, The Computational Algebra of Representations of Categories, focuses on making certain mathematical theories computationally amenable. The importance of this notion comes from the existential nature of most results in abstract math. Ramos explains that “making a theory ‘computationally amenable’ means finding ways to actually compute those objects. That shift from ‘it exists’ to ‘here’s how to find it’ makes the theory more useful, especially for applied fields like physics or robotics.”
One project he will be working on under this grant centers on the categorical Graph Minor Theorem, which Ramos considers one of the greatest achievements in combinatorics. Alongside the 20-year-long monumental effort of 20 papers to prove the theorem, he explains that it has significant mathematical implications. “A graph is a set of vertices (dots) connected by edges (lines). The Graph Minor Theorem says that in any infinite collection of graphs, one graph will always be ‘contained’ within another. That’s remarkable because you’d expect infinite graphs to grow infinitely complex and unique. But the theorem shows that no matter how different you try to make them, there’s always some overlap — one fits within another.”
Ever active, Ramos also plans to host an interdisciplinary conference to further work on the aforementioned robot traversal problem. Focusing on motion planning and topological robotics, he says this will “connect robotics, mechanical engineering, and mathematics, especially topology, which studies the properties of space. Understanding the topology can help design better movement algorithms.” On November 17, he presented research on one of the many conjectures of famous mathematician Paul Erdos to Stevens’ Algebra and Cryptography Center. This project used an Artificial Intelligence (AI) enhanced approach to attempt to find counterexamples to a proposed property of trees, a specific type of graph.
With more than a decade of experience teaching mathematics at both the undergraduate and graduate levels, Ramos is committed to improving access to mathematical education. His work on the Erdos conjecture was done with a student he mentored as part of the NYC Discrete Math REU, a summer research program for undergraduate students. He also has and plans to continue using his own grant funding to help students in summer research. “I realized that the old belief that ‘real mathematicians don’t care about money’ excludes talented students from less privileged backgrounds. So now I always budget for paid student research positions. Access matters. Students shouldn’t have to choose between pursuing math and earning an income.”
He gives one final message: “I want to show students that while not everyone will be a great mathematician, a great mathematician can come from anywhere.”
