Book Review — Shape by Jordan Ellenberg

Thursday 01, June 2023

Shape discusses the geometry of everyday life: it’s role in games, spreading pandemics, how we define the land we live in, family ties, and holes in straws. Jordan Ellenberg touches on some interesting fields in math including topology and algebraic geometry without going too in depth. I really enjoyed the topic on Markov Chains and their continued appearance throughout the book.

Ellenberg is a math professor at my alma mater, the University of Wisconsin Madison. Regrettably, I never had the chance to take a course with him. All the same, he is a well respected mathematician, and a generally cool person who happens to be an adept writer as well and is particularly good at public math education.

The nature of the book is very…contemporary. There’s a fun discussion on AI models that helps to explain some of the statistical magic that runs them. I personally found it as a good reminder that at the end of the day it really is just stats and data that make these things tick—especially with the current talks in the news and in social circles about the absolute disrupting power of AI.

The book was clearly written in 2020/2021 as the covid-19 pandemic was reaching new heights in both infections and its politicization. While the math behind the spread and explanation of certain predictive models was interesting, I found the discussion to be very tiring. But maybe that’s just a personal qualm having lived through that whole news cycle and another 2 years more from the book’s publication date. At any rate, it did clear up some questions about how some predictions were so bad and why the disease could have spread the way it did.

What I particularly enjoyed in the book aside from the “real content” was the candidness about the life of a mathematician. How different it is to do math from what most people get out of high school and maybe 2 years of calc in college. The discovery and experimentation that goes into things, the long histories of fields being built piece by piece, missed connections between people working on the same problem, and better yet, serendipitous encounters that result in huge outcomes. Interestingly enough, the discussion on AI made me realize a different way of representing some data in a knitting programming project, and ultimately led to a better way of processing that data than how I was originally doing it.

Overall I thought the book was a rather interesting read, and one that I would do again in a decade’s time.