The power of mathematical thinking

By: Jordan Ellenberg

Published: 2014

Read: 2017

Summary:

About the application of mathematical reasoning in research, social sciences and everyday life. Mixing the history of a number of fundamental mathematical discoveries (such as probability theory, axiomatic reasoning, the law of large numbers, regression to the mean, utility theory) with examples of modern day applications.

Covers anything from basketball hot streaks, fund performance, big data (over)analysis, drug research, data compression, causation vs correlation, to elections.

Worth Reading:

While there isn’t a ton of structure to the book, and I would have preferred more math and less anecdotes and examples, there are some very good sections on issues like causation vs. correlation, or the various ways in which supposedly statistically meaningful studies can be meaningless or misleading. These sections provide satisfying mathematical explanations for typical pitfalls and common mistakes.

The book confirms how easy it is to get misled by scientific headlines (or documentaries), p-hacking, etc. For instance, headlines of the type: “The risk of X doubled”. This doesn’t say anything about how high the risk of X was to begin with (if the risk for X went up from 1 in a million to 2 in a million, it doubled, but the risk is still extremely low.)