From cell biology to tessellations
Raymond Goldstein blurs the line between mathematics and biology in the 2026 Simons Lectures
If you stepped foot into room 2-190 between April 27–29, you would find yourself in the middle of an immersive discussion that jumped between disciplines, taking you from swimming microorganisms to tessellations. At the front of the lecture hall stood the second speaker of the Simons Lectures, Professor Raymond Goldstein ’83 of the University of Cambridge, bridging the gap between pure math, biology, and physics.
Goldstein gave three lectures in total: “Stirring Tails of Evolution,” “The Geometry of Multicellular Life,” and “Decision-Making Without a Brain.” The topics of these lectures were interdisciplinary. On one slide, he showed attendees videos of spherical cells moving and inverting themselves; on the next, he pointed to a model of a phase oscillator — an oscillating system, much like the classic spring on a mass — and its associated differential equations. Further into the lectures, he explained how tessellations in pure math play a role in the geometry of how cells distributed themselves.
When asked about why the intersection of biology, applied math, and physics interests him, Goldstein pointed to the relatively unstudied nature of biology compared to mathematics.
“In mathematics, there are plenty of people who will have as their life’s work proving things that others have conjectured,” he said. On the other hand, biology is “so open compared to so many of the areas in physics that formulating the questions is the most difficult and challenging thing.”
The Simons Lectures Series, financially supported by MIT alumnus, mathematician, and investor Jim Simons ’58, is held every spring at the Institute, featuring one week of lectures in pure mathematics and one week in applied mathematics. Past topics in pure math include sphere packing and graph theory, while past topics in applied math include quantum complexity theory and the mathematics of private data analysis. Goldstein, who graduated from MIT with a double major in chemistry and physics in 1983, is the first lecturer since 2006 to cover biological systems.
He’s particularly interested in problems related to non-linear systems and complexity. One such example concerns flagella, micrometers-long lash-like appendages that help organisms swim. When green algae swim, their flagella undergo a phenomenon in which they synchronize and desynchronize.
Although miniscule in size, these appendages have more than just miniscule effects. In fact, the spinning direction of a different type of appendage, the hair-like cilia, is what causes the placement of the heart on the left side of the body for most humans and other vertebrates. Goldstein said that researchers confirmed this by taking developing mice embryos and manually swirling the fluid in the other direction, and voilà — the mice developed with their hearts on the right sides of their body.
Researchers noticed the appendages synchronized most of the time, like a swimmer’s arms during breaststroke. However, around 10% of the time, there would be durations — called phase slips — where the flagella briefly fell into an asynchronous swimming pattern, and then resynchronized. Even more rarely, around 5% of the time, the flagella could oscillate at different frequencies altogether, before going back into their synchronous swimming style. Goldstein’s goal is to solve the mystery of why the flagella behave this way.
The behavior of the flagella involves fluid dynamics and complex systems — systems that are composed of many interacting components and are hard to predict based on individual pieces. Goldstein approaches this complex problem with a mix of a theoretical and an experimental approach. He combines a physicist’s reductionist perspective of looking for the simplest physical or mathematical realization of the system — a lesson that was ingrained in him in his undergraduate studies at MIT — with a biologist’s experiments and observations.
“It’s a matter, partly, of doing experiments, sometimes without a clear hypothesis, but just saying, let me see for myself what’s going on,” Goldstein said. “There’s no substitute for staring through the microscope at something.”
Goldstein compared balancing theory and experimentation to painting. “If you make a painting, you may have a sketch of where things are roughly on the canvas,” he explained. “And as you put material down, you end up refining it and fiddling with things and going back over things.”
“So, it’s this kind of back and forth between theory and experiment, which is the scientific method,” Goldstein said. “That’s what we use.”
This approach was very evident in Goldstein’s research on flagella synchronization. First, he connected the swimming motion of the flagella to a model of two waving sheets synchronized in a fluid, originally conceived by British physicist G.I. Taylor in the 1950s to describe the swimming of microorganisms. By analyzing models where the sheets had separation distances from one another, Goldstein's team deduced that energy dissipation was minimized when the sheets were waving in phase — in other words, the synchronizing of the flagella could be nature’s way of minimizing energy loss in the fluid.
Next, Goldstein conducted his own experiments using a high-speed camera to film the beating of the flagella in both the original organism and a mutant organism that displayed antiphase synchronization; instead of the flagella moving in a breaststroke motion, they moved in a freestyle motion. These experiments, combined with analysis of another physical model, showed that the synchronization was affected by another factor: the internal structure of the flagella. The wild type organism had its two flagella essentially connected on the inside of the organism — as Goldstein put it, elastically coupled — while the mutant type did not.
Goldstein’s lecture not only gave attendees valuable insight into the intersection of the world of math, physics, and biology, but also connected the research of his lab in Cambridge, England, to the attendees in Cambridge, Massachusetts halfway across the world.
In academia, it can often feel like there are rigid barriers between different fields, where the “Department of Mathematics” lives not only in name but also physically apart from the “Department of Biology.” Goldstein’s research, however, is a reminder that sometimes, the most interesting results come from deliberately blurring these lines.