The NSF-Simons National Institute for Theory and Mathematics in Biology is composed of investigators at the forefront of innovative research at the interface of mathematics and biology. Each member of the NSF-Simons NITMB brings a unique perspective that is vital for achieving the NITMB’s mission to develop new mathematics and inspire biological discovery. In order to highlight the diversity of expertise present, and the valuable contributions of NITMB members, the NITMB will be sharing insight into one of our members every month.
Shmuel Weinberger, Andrew MacLeish Distinguished Service Professor of Mathematics, University of Chicago
Shmuel Weinberger is the Andrew MacLeish Distinguished Service Professor of Mathematics at the University of Chicago. Weinberger is also a member of the NITMB, where he is a collaborator on the NITMB supported research project ‘Topological Analysis of Biological Data.’
We spoke with Professor Weinberger to learn more about his work and his hopes for questions the NITMB will explore.
Can you share with us a big question you’ve been asking throughout your research?
“How can you tell if two things that look similar to each other are different -- or, in reverse, if things that are presented to you in different ways, and seem to be different, are actually the same thing? Partly this involves understanding how much of some resource is necessary to deform one (low complexity) "state" of an object to another.”
What disciplines does your research integrate?
“Within mathematics, geometry, topology, analysis, and algebra. It connects to probability and statistics and from there to other sciences.”
Where do you find inspiration?
“Other people! There are lots of smart hard-working people out there, each working on different problems. On the other hand, lots of time the key difficulties are the same or analogous, so if you're open-minded and looking at these, you might be able to adapt progress in one direction in another. (Or learn something when you see that it doesn't transfer.)”
What aspects of the central question you’ve been working on could be interesting to mathematicians or applied to biology?
“First of all, much biological data are about configurations of objects that have shape, so the tools of geometry/topology should be relevant. Changes in topology require mechanisms -- so topology can be a tool for inferring existence of important mechanisms. Secondly, the high dimensional data collected by biologists (might) have a geometric structure that can help in their analysis.”
What about the mission of the NITMB do you find exciting?
“Most prosaically, the field of topological data analysis cannot develop without coming to terms with and learning the idiosyncrasies of different types of data -- and biological data is really different than the data I've studied. More abstractly, the geometry of genotypical and phenotyical spaces are quite different, which should be responsible (at least after evolutionary processes) for features of the map from genotype to phenotype. Finally, biological processes take place in time, and have a type of stability that is completely different than the kinds of stability ordinarily studied in dynamical systems theory; this is but one example of the need for developing new mathematics inspired by biology and which hopefully will return the favor and give new biological insights.”
What career achievement are you most proud of?
“Whatever I did yesterday.”
Outside of your research, what other interests do you have?
“Jewish law and philosophy. Economics and the stories it tells; evolutionary biology and its stories. Chick lit and thrillers. Random music.”
What are you hoping to work on in the future?
“I wish I knew! The project I've been working on for the past 30 years is not one that I had known in advance is something I'd be interested in. Being a theorist means being able to change directions (relatively) easily in response to the surprises that seem to keep on being discovered.”
The NITMB is excited to explore how Shmuel Weinberger’s expertise in topology and other mathematical disciplines will result in meaningful contributions to NITMB research projects such as the ‘Topological Analysis of Biological Data’ project.