Mathematics of Life
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Vision: Mathematics is an 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 striking, 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 experiments and 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 where we aspire to inspire the next experiment.
Our scientific vision is a corollary to a human vision of working with young scientists to enjoy the pursuit of mathematics and science, developing their talents and tastes.
"Man’s mind cannot grasp the causes of events in their completeness, but the desire to find those causes is implanted in man’s soul. And without considering the multiplicity and complexity of the conditions any one of which taken separately may seem to be the cause, he snatches at the first approximation to a cause that seems to him intelligible and says: “This is the cause!” In historical events (where the actions of men are the subject of observation) the first and most primitive approximation to present itself was the will of the gods and, after that, the will of those who stood in the most prominent position—the heroes of history. But we need only penetrate to the essence of any historic event—which lies in the activity of the general mass of men who take part in it—to be convinced that the will of the historic hero does not control the actions of the mass but is itself continually controlled. It may seem to be a matter of indifference whether we understand the meaning of historical events this way or that; yet there is the same difference between a man who says that the people of the West moved on the East because Napoleon wished it and a man who says that this happened because it had to happen, as there is between those who declared that the earth was stationary and that the planets moved round it and those who admitted that they did not know what upheld the earth, but knew there were laws directing its movement and that of the other planets. There is, and can be, no cause of an historical event except the one cause of all causes. But there are laws directing events, and some of these laws are known to us while we are conscious of others we cannot comprehend. The discovery of these laws is only possible when we have quite abandoned the attempt to find the cause in the will of some one man, just as the discovery of the laws of the motion of the planets was possible only when men abandoned the conception of the fixity of the earth.” -- Tolstoy’s War and Peace, Book 13, 1812, Chapter 1
