The Accidental Mathematician?: Professor Michael Lindsey

Professor Michael Lindsey in his office (Photo by Johnny Gan Chong)

September 3, 2024

Avi Rosenzweig

Stanford alumnus (Honors BS ’15) Michael Lindsey chose UC Berkeley for his PhD program largely because he wasn’t sure what areas of mathematics he was interested in pursuing – the Berkeley department encompasses a very broad range of theoretical and applied topics, and therefore afforded him a lot of flexibility. Lindsey wasn’t certain about a lot of things, actually. Most Stanford STEM majors assumed they would end up as engineers in Silicon Valley, him included. He grew up in Washington, DC with a professional policy wonk dad and pediatrician mom with no physical science leanings, but was fortunate to be offered linear algebra in high school. That course was like a fork in the road for him, and he took it. The challenge of taking on a difficult topic was exciting.

Skip ahead to 2024, and Michael Lindsey is an assistant professor in the Mathematics Department here at UC Berkeley, listed in the directory right after his PhD-advisor-now-colleague Lin Lin. It still surprises him that choosing a topic because it was challenging has turned into an academic career. He works on computational methods driven by numerical linear algebra, optimization, and randomization, with a special focus on high-dimensional scientific computing problems. These include quantum many-body problems arising in chemistry and condensed matter physics, as well as various problems in applied probability. His approaches draw on a wide variety of techniques, including semidefinite relaxation, Monte Carlo sampling, and optimization over parametric function classes such as tensor networks and neural networks. High-dimensional problems require unmanageably large amounts of computation by current methods. Professor Lindsey’s work may yield efficiencies that bring many-body problems back down to earth.

(Photo by Johnny Gan Chong)

The way physics was covered at Stanford seemed inscrutable to Lindsey in the 2010s, perhaps because he lacked “physical intuition”, and the math required to comprehend quantum mechanics was very challenging. But that was its appeal for Lindsey. In his junior year he decided he wanted to go to graduate school. He spent a post-graduation year studying quantum field theory without really taking it in, but his reaction was “Challenge Accepted” rather than looking for something easier. Lin Lin had recently joined the faculty here at UC Berkeley, and he organized a 290 seminar on Quantum Many-Body Problems. It was then that Lindsey started to approach the physics literature from his own applied math perspective, always trying to understand physical theory in terms of computational methods. What he learned studying with Lin then helped him to communicate with investigators in other fields and to expand his own understanding of the physical sciences. There have been productive collaborations. The applied parts of his work reconnect Lindsey with chemistry and physics and are inching quantum mechanics forward.

As a young professor, Lindsey also connects well with students in both introductory and advanced courses. Leading an intro course “reminds you what it was like to not know” and compels you to reassess your apparent certainties. Covering an applied math class with limited meeting hours forces you to trim away the less important material so you can emphasize “what really matters”. This teaching experience pushed approximation theory to the top of his mind and led him in new directions. In turn, this helped Lindsey pick up some new tricks that fed back into the teaching of the course the next year. He especially enjoys seeing students understand something important for their first time, like subspace iteration for the computation of multiple eigenvectors. What a kick!

Professor Lindsey insists that he holds “an unromantic view” of mathematics. The aesthetic appeal of certain solutions, like systematic frameworks for computation, doesn’t hurt but what really draws him in is their capacity to compute difficult problems faster. He is trying out various methods, like Monte Carlo sampling, in search of better ways of getting results, not because he has some faith or investment in a tool. He approaches the work without prejudice. He welcomes “serendipitous” or unforeseen connections that arise from those collaborations with chemists and physicists. He also exudes a calm comfort with ignorance—sitting with doubt because his confidence about rising to a challenge is secure. Curiosity-driven research is enough to keep him going, since our “universally shared” experience as scientists is that most of our attempts fail most of the time. His temperament manages to hold seemingly contradictory attitudes: an open, untroubled vision of how things are, and a dogged determination to puzzle those things out. This is how understanding grows.

(Photo by Johnny Gan Chong)