MATH PAPERS/ARTICLES



The positive false discovery rate: a Bayesian interpretation and the q-value by J.D. Storey

This is one of my favorite statistics papers. A simple idea that connects two very different sides of statistics (frequentist vs Bayesian measures in testing) with beautifully clear and concise explanations.

Cauchy-Schwarz Inequality: Yet Another Proof by T. Andreescu, B. Enescu and J.M. Steele

This proof clearly shows how Cauchy-Schwarz is just in disguise.

A Proof of Liouville's Theorem by E. Nelson

This is what mathematics at its purest looks like.

Paintings, Plane Tilings, and Proofs by R. Nelsen

Proofs of classic identities using art. I especially like the proof of the Cauchy-Schwarz inequality at the end.

Mafia: A theoretical study of players and coalitions in a partial information environment by M. Braverman, O. Etesami and E. Mossel

Diana and I first learned of this paper after proposing to play Mafia with Elchanan Mossel. He replied (paraphrasing): "Oh, I can't play that game anymore... I solved it in a paper."



MATH BOOKS



Convergence of Probability Measures by P. Billingsley

This book is the gold standard for how to write about a highly technical topic in an efficient way. My favorite research-level math book.

Linear Algebra Done Right by S. Axler

This is my favorite college-level math textbook. A master of explaining highly abstract concepts in plain English.

The Cauchy-Schwarz Masterclass by J.M. Steele

This is a really interesting book. On the one hand, inequalities are simple objects which are easily understood by anyone. On the other hand though, they reflect deep truths and are rich enough that one can gain a lot of insight into how professional mathematicians think through them.



NOT MATH



How to Do Nothing: Resisting the Attention Economy by Jenny Odell

Reading through, I felt all of the incoherent ramblings I've had for the past 10 years come into incandescent focus. It takes all the half-baked ideas of the "quit social media" canon to their logical conclusion. And for me, it traces a line all the way back to high school: I was assigned Walden in English class fully expecting a snoozefest, but instead I came out delighted. I never really understood why until now.

Siddhartha by Hermann Hesse

No book has had a deeper influence on me than Siddhartha. I believe that it's a book that eventually speaks to everyone because its theme is universal and inevitable. If it doesn't resonate now, it will later.