Why math and society?
- What is the role of mathematics in society?
- What is my role as a mathematician in society?
- What is my role as a human being in society?
Abstract of the talk
This is a survey without much technical details. If you know what a subgraph is, then you will understand everything. If you don't, you can still get a lot from most of it!
(Disclaimer: This talk involves a Singaporean commenting on the politics of the United States, by speaking in Canada! I do not claim to be very familiar with the political intricacies, but by sharing what I know, I hope to spark a discussion on some very important questions.)
Where to learn more?
The Metric Geometry and Gerrymandering Group (MGGG), founded by Prof. Duchin, has a lot of resources relating to the math behind gerrymandering, including fun interactive web applets to let you explore the concepts involved.
On the research side, the theory of counting spanning trees on lattices has surprising connections to the physics of crystals; as a result, many of the asymptotic counting formulas were derived by physicists. Unfortunately I do not have a good reference at hand to explain this connection. Please tell me if you find one so I an actually understand this stuff!
- Moon Duchin. Political Geometry: The Mathematics of Redistricting. Talk at the Radcliffe Institute (2018).
- Daryl DeFord, Moon Duchin, Justin Solomon. Recombination: A family of Markov Chains for redistricting. (2019)
- Moon Duchin. Political Geometry: Voting Districts, ''Compactness," and Ideas About Fairness. Talk at the Joint Mathematics Meetings (2018).
- MGGG, Welcome to Gridlandia! An interactive introduction to the math of redistricting.
- Glasser, M. L., and F. Y. Wu. On the entropy of spanning trees on a large triangular lattice. The Ramanujan Journal 10.2 (2005): 205-214.
- MGGG, The Mathematicians' Brief in Rucho v. Common Cause. (2019)
- Supreme Court of the United States. Rucho v. Common Cause, No. 18-422, 588 U.S. ___ (2019)
I'd also like to highlight the great work of the Metric Geometry and Gerrymandering Group (MGGG), founded by Prof. Duchin, for their excellent work not only in the mathematical theory of gerrymandering, but also in bringing together mathematicians, political scientists, researchers in law and so on to collaborate. I think the complex social issues of our time need to be understood from both the technical and humanistic viewpoints, so scientists need to learn from their counterparts in the humanities, and vice versa, in order to craft solutions that are technically sound and that can also handle the uncertainties and irrationalities of society.