Vision: Mathematics is an almost unreasonably powerful language to describe and dissect natural phenomena. Wigner's article poetically conveys the sense of awe that many of us feel as mathematical scientists. However, it is remarkable, by and large, how ineffectively mathematics has been leveraged in furthering our understanding of Life. Mathematics isn't just a convenient language to communicate models of how some little corner of Life works, at its most powerful it provides a general framework that organizes and illuminates a vast diversity of phenomena. Mathematics, and mathematical scientists, achieve this through abstraction. And it is through abstraction that general and simplifying principles can be distilled -- As with Picasso's Bulls. What new abstractions must we seek out to deepen our understanding of Life?
What we do: Our group pursues lines of inquiry where we attempt to develop novel mathematical abstractions that provide insights into biological phenomena and data. Precisely by virtue of our pursuit of discovering general mathematical abstractions, we are compelled to work on a diversity of biological phenomena that have been classified by the community into distinct and unrelated categories. These include organismal development, cellular physiology and structure, and ecological dynamics.
How we do it: These mathematical abstractions are pursued working closely with modern biological data. And, thus, data-driven and AI approaches are a large part of the algorithms we use and develop. Pairing these approaches with the aesthetics and sensibilities of mathematics and theoretical physics is the middle ground we strive to inhabit. All our work is conducted within the context of long-term collaborations with experimental biology groups.
Our scientific vision is a corollary to a human vision of helping young scientists enjoy the pursuit of mathematics and science, developing their talents and tastes.
What is "new mathematics"? Just as a beautiful novel doesn't necessarily involve new words, a scientific study where old mathematics has been used in new ways is rewarding and contributes to the community. In this sense, pushing the boundaries of the class of phenomena that can be spoken about with the elegance and rigor of mathematics is our goal. Were they to inspire purer mathematicians (as we did in this instance) it would provide an additional sense of awe at the nature of mathematics and how it interacts with studying the world.