Eric Ramos Awarded NSF Grant to Advance Combinatorial and Computational Algebra at Stevens

Eric Ramos, an assistant professor in the Department of Mathematical Sciences at Stevens Institute of Technology, says he wasn’t always drawn to mathematics. But a TV show he watched in high school helped change that. The show, “Numb3rs,” was a typical police procedural with a twist: “the main detective’s brother was a math genius who used mathematical reasoning to solve crimes,” he explained.

That early spark, which Ramos calls his “supervillain origin story,” led to a deeper curiosity about abstract mathematics and set him on a lifelong path toward a career in mathematics and, most recently, a grant award from the National Science Foundation (NSF).

The NSF-supported research grant, “The Computational Algebra of Representations of Categories,” explores how to make certain mathematical theories computationally amenable. Ramos explained that many results in abstract math are existential. “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,” he said.

Advancing combinatorial and computational algebra through collaboration

With this NSF-supported project, Ramos aims to enhance the state of the art in combinatorial and computational algebra and its applications through several key research projects. One project centers on the categorical Graph Minor Theorem, which he considers one of the greatest achievements in combinatorics.

“There are two ways to look at it. First, from a human perspective — the sheer time and effort. The theorem was proven in over 20 papers published across 20 years. That kind of sustained collaboration and precision is rare,” he said.

The second reason is mathematical, he explained. “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. That insight has huge implications across mathematics and computer science.”

“I want to show students that while not everyone will be a great mathematician, a great mathematician can come from anywhere.”

In advancing combinatorial and computational algebra, Ramos emphasizes the importance of collaboration and highlights a growing trend in mathematics: the application of machine learning to mathematical problems. He explains that this trend is not about studying the math of machine learning but using AI tools to explore math itself.

Enter the Stevens Institute for Artificial Intelligence (SIAI).

“Over the summer, I used SIAI’s lab space and GPU resources for computations required in the project. The new Laboratory for Mathematics Education and AI is also partnering with Nebius, which provides more computational power. These resources are essential — modern mathematical computations require massive processing power,” Ramos explained. 

As part of his NSF-supported research, Ramos also plans to host an interdisciplinary conference on motion planning and topological robotics. “The motion planning problem involves figuring out how robots can move through a space — say, a factory — without colliding and while being efficient. This connects robotics, mechanical engineering, and mathematics, especially topology, which studies the properties of space. Understanding the topology can help design better movement algorithms.”

Broadening student access and sparking an interest in mathematics

Ramos, who has more than a decade of experience teaching mathematics at both the undergraduate and graduate levels, is also committed to improving access to mathematical education.

“Before Stevens, I used grant funding to support 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 said.

In a previous role, he also started a seminar to broaden participation in math, featuring speakers from diverse backgrounds and career paths. “The idea was to break down the myth that mathematicians are all child prodigies.” As part of this NSF research project, Ramos hopes to do similar outreach at Stevens. “I want to show students that while not everyone will be a great mathematician, a great mathematician can come from anywhere.”

Ramos said his role as a teacher is to help students find that spark and to show them that being ‘bad at math’ doesn’t mean they can’t become mathematicians. 

“I wasn’t naturally gifted at math. I struggled and felt anxious about it for years. What changed for me was finding that spark — something that made me curious enough to keep trying despite mistakes,” he said, adding that “mathematics is hard, even for professionals, and the key is to view mistakes as part of the process, not as failures.”

A serendipitous connection through mathematics

When Ramos decided to attend graduate school, his goal was to work with Jordan Ellenberg, a professor at the University of Wisconsin and author of “How Not to Be Wrong: The Power of Mathematical Thinking,” as well as a number theorist. Number theory is the mathematical study of integers. 

“Like many math students, I started in number theory because it’s the oldest field and theoretically rich,” he said. “Over time, I moved toward combinatorics — the mathematics of counting. It might sound simple, but there are still deep questions about counting.” 

Ellenberg would eventually become his advisor. Ramos later found that Ellenberg was also the math consultant for the inaugural season of “Numb3rs.”

“Total serendipity,” Ramos said.