Being as dumb as I am, learning math can be frustrating. Therefore I have a deep appreciation for those special papers and books which, through their elegance and beauty, motivate me to keep exploring. Here are a couple of my favorites.



PAPERS/ARTICLES



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.

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.

A Proof of Liouville's Theorem by E. Nelson

This is what mathematics at its purest looks like.

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

I found out about this paper as Diana and I were walking down a street in Philly with Elchanan Mossel. Somehow Mafia came up and he said (paraphrasing) "Oh, I can't play that game anymore... I solved it in a paper."



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 accessible yet efficient way. My favorite research-level math book.

Linear Algebra Done Right by S. Axler

This is my favorite college-level math textbook. An important subject, too.

Visual Complex Analysis by T. Needham

It explains complex analysis using pictures. That alone is amazing. Also comes with a nice set of exercises.

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 are so fundamental and ubiquitous that one can gain a lot of insight into how professional mathematicians think through them. Definitely recommended.