In the ‘America of science,’ diversity yields inspiring opportunities for mathematicians
In her own words, Carina Curto considers herself a mathematician; but, perhaps surprisingly, her research is driven by questions in neuroscience.
“The kinds of questions that I’m interested in are about how neurons encode information about the world and how neural networks are set up in order to enable this storing and retrieving of memories— these kinds of things,” she explained.
Using a variety of approaches—from computational methods and data analysis techniques to modelling and more-theoretical work—Curto attempts to answer these questions in ways that, at first glance, do not seem like the work of your typical mathematician or even your typical neuroscientist; but—
“These are actually pretty standard approaches in the theoretical neuroscience community,” she said. “Mathematics provides another way of trying to understand how neural networks may be working, and of generating hypotheses.”
Most of Curto’s current research is part of what’s likely the largest and most complex effort of its kind ever undertaken—the NIH-funded BRAIN Initiative.
“We’re trying to gain insight into the structure of connectivity between neurons in different parts of the brain,” she said. “It’s a very big project.”
I would describe what I do as developing theory,” she continued. “Many people are doing this—trying to develop a theory of how the brain works, theories of how neural networks work, how the brain encodes information, how memories are stored and retrieved. There are so many aspects to the brain. It’s really a whole universe in and of itself.”
In this light, it seems rather tting that the BRAIN Initiative would require a multitude and diversity of minds to accomplish its mission.
“I think mathematicians and physicists and computer scientists are all needed in this problem, which at its source is a biological problem,” said Curto. “But like any rich and deep problem, it’s something that can be tackled from a variety of perspectives.”
“One of the things that’s really cool about neuroscience is that it’s a land of immigrants—it’s like the America of science, in a way, because as a field it’s very young and the people who laid its foundation have come from psychology, biology, biochemistry, physics, math, computer science, and statistics. Philosophers work on neuroscience. Engineers work on neuroscience. You see more social scientists getting involved. There’s neural economics now, where people try to connect neuroscience with the science of decision-making. It’s really a land of opportunity, in a way, where people come from really diverse backgrounds, and that’s what makes it so interesting and exciting,” she said.
Although Curto works primarily on problems in neuroscience, she still, because of her background and the tools she uses, defines herself as a mathematician—”or a physicist,” she added. Labels notwithstanding, she is emblematic of the rich diversity of skills and approaches that are necessarily marshalled by the field of modern neuroscience toward illuminating the nooks and crannies of our gray matter.
“It’s really cool to be able to talk to people who have such different scientific languages and such different scientific cultures,” she said. “And to learn how they think about things and what they think are interesting questions—I think that’s one of the selling points of this field. It’s also really cool to see how different areas of mathematics that you wouldn’t necessarily expect to be applied here can be useful. In my own work, I’ve used ideas and techniques from algebra, topology, geometry—all kinds of areas of math that aren’t necessarily associated with applications. There are so many questions in neuroscience that lend themselves to different kinds of analyses that it’s really a fruitful playground for using mathematics in interesting ways. Like physics in the 20th century, neuroscience—and, more generally, biology—is becoming an increasing source of inspiration for mathematics.”
Carina Curto is an associate professor of mathematics at Penn State