“I’m always thinking about how the end result can help people live healthier, more enjoyable lives in harmony with their environment”
When starting my postdoc in the mathematics department at the University of Michigan, I didn’t expect to find myself three years later working as a cloud developer, building data engineering pipelines based on cutting-edge mathematical biology. At the time, I was pursuing a career as a pure mathematician working in the closely intertwined fields of algebraic geometry and commutative algebra. Algebraic geometry and mathematical biology are, by and large, very far from one another in terms of goals, outlooks on mathematics, and applicability to the real world. So what changed?
Firstly, I became more constructivist in my philosophy of math. It’s common in pure math to prove that solutions to problems exist while having absolutely no way to construct examples of such solutions. Computationally it can be impossible to even approximate such solutions because they live in spaces that have infinitely many dimensions, built out of “simple” pieces with uncountably many points (tl;dr hugely infinite). If the objects studied in math are the characters in a TV show, an “existential proof” solution is like a show where you know there are characters because of certain plot points, but it’s impossible to give any details on those characters. “We know there must be carpenters because there are always more houses… but has anyone ever seen them?” The thrill I felt as a younger person in being able to understand such abstract proofs wore off, and started to feel pretty formal and dry. I wanted more action in my mathematics!
The second change, related to the first, is that I felt a calling to work on problems with tangible benefits, something I could point to and say “I built that” when telling friends and neighbors what I do all day. Plenty of tangible good has come out of pure mathematics— e.g. elliptic curves are used to secure communications and repair data damaged in transit; persistent homology is used to understand massive data sets, leading to better better treatments through new medicines— but my thesis work was sufficiently esoteric that it’s challenging to explain the ideas to other mathematicians!
Landing at Arcascope allowed me to continue solving hard problems while bringing our ideas to life through tech. Some days I’m building Linux containers to respond intelligently to data uploads. Other days I’m simulating ODE systems or ruminating on the symplectic geometry of cotangent bundles. But I’m always thinking about how the end result can help people live healthier, more enjoyable lives in harmony with their environment.