**GA Math Book Club Continues**

My spring and summer reading has been dominated by Swedish noir and giant historical novels, most recently the incredible *A Place of Greater Safety* by Hilary Mantel. The French Revolution—Aaaaaaaaaaah! So brutal! However, I needed enough breaks from the guillotine to make it through two very worthwhile mathy volumes in the last few months: *Weapons of Math Destruction*, by Cathy O’Neil, and *Genius at Play: The Curious Mind of John Horton Conway*, by Siobhan Roberts. Neither of these books were what I expected, but I was pleased with both in their own ways.

*Weapons of Math Destruction* came out last year, and has been on my reading list since Evelyn Lamb reviewed it in the Scientific American blog. It hits some of my usually disconnected strong interests: interesting and unusual career paths in mathematics, the intersections of mathematics and social justice, and the ways in which acting with good or neutral intentions can lead to negative unforeseen and sometimes devastating consequences (I know, this is a weird interest, but where would all those depressing novels and plays be without this principle?). Cathy O’Neil has followed an unusual and interesting path, from academic life to Wall Street, data mining, and now her own company auditing algorithms. I enjoy reading O’Neil’s mathbabe blog. *Weapons of Math Destruction* was an important book for me to read, because my usual vision of mathematics and social justice involves the ways that mathematical tools can be used to fight for fairness or justice (for example, to identify gerrymandered congressional districts). However, O’Neil describes how the algorithms we design for efficiency and optimization, and even fairness, can treat people very unfairly and lead to systemic injustice. She does this well, though without any real technical discussion. This book is truly accessible to a general audience. This spring, I gave it to some of my students who were taking summer jobs in finance or considering careers in industry. This was not at all to discourage them from working in these areas, but to provide some context and some case studies. I want my students to love their careers, and I know that many of them have a strong sense of responsibility to the larger world. *Weapons of Math Destruction* is, among other things, a manual for those who feel this sense of responsibility, of things we should not overlook or sweep aside as we try to build the better, faster, more efficient algorithm for everything.

*Genius at Play* also interests me as the story of an unusual mathematical life. John Horton Conway has, in some ways, followed a very narrow path in math: from early talent to Cambridge student, then Cambridge professor, and then on to Princeton. However, his remarkable approach to mathematics and life, as well as his totally wacky charisma—captured in his own words whenever possible—make this a very different mathematical biography. Siobhan Roberts does us the service of allowing us to meet Conway through their relationship as biographer (or “amanuensis”, as Conway sometimes refers to her) and subject. I found the conversational and non-linear narrative style of *Genius at Play* uncomfortable at points, but I really liked it in the end. One reason I read this book was to get a bit of context on the history of cellular automata; I came away with much more than I bargained for. I also learned that, if I ever get the chance to meet Conway, I should probably not ask him about the Game of Life. Roberts walks a careful line to respect Conway’s privacy, but hints at some of his personal adventures. This has the possibly unintentional consequence of making the reader, used to tell-all type biographies, even more curious about what is left out. On the other hand, a significant amount of math is kept in the book, and Roberts/Conway do a remarkably deft job of explaining big picture topics and even elucidating full proofs, while never seeming to oversimplify or condescend to the reader. This book gave me a new sense of the explosion of mathematical creativity brought on by the rise of computers, and the sense that I had experienced the extraordinary personality of John Conway first hand.

**I hope that I can read a book about Richard Guy someday.**

This week I am blogging about books from a conference in Diophantine Approximation and Algebraic Curves at the Banff international Research Station (BIRS). This has been a great conference in several ways—seeing some of awesome math friends, meeting new people, very good talks, the chance to play exceedingly non-serious but very fun bridge. I had a really valuable math discussion in which someone explained a difficult idea to me in an intuitive way (thanks, Benjamin Maschke!). All this, plus BIRS is in a stunning natural setting in Banff National Park (in the Canadian Rockies). Finally, the conference was great because I got a chance to talk with Richard Guy.

Number theorist Richard Guy really deserves his own book. He did just get his own 100^{th} birthday conference, but that’s not going far enough. Richard Guy collaborated extensively with Conway, and was mentioned many times in the GaP; however, there is so much more to his life and career than this collaboration. A few highlights: Guy was born in 1916 in England. He excelled in mathematics, obtaining BA and MA degrees at Cambridge, then got a teaching certification from the University of Birmingham and became a mathematics teacher. He worked as a teacher in England for several years, though he was sent to Iceland and then Bermuda with the meteorological branch of the Royal Air Force for a period during World War II. In the 1950s, Guy moved to Singapore and then to India, teaching at the University of Malaya and the Indian Institute of Technology. In 1960, Guy met Paul Erdös in Singapore. Erdös encouraged Guy to pursue his interests in mathematics more seriously, and they began a mathematical collaboration that led to four joint papers. Guy and his family moved to Calgary, Alberta, in 1965, where he joined the mathematics department at the University of Calgary and is still an active emeritus Professor. He has written many books, including the classic *Unsolved Problems in Number Theory*. He is also a very accomplished mountaineer, and… well, I could go on for a long time. I am a great admirer, of both his mathematics and adventurous spirit. Sometimes it seemed that Richard Guy was essentially the star of the conference—the lecture room was full for his talk on the final afternoon, and all week people shared stories about their experiences with him and spoke with reverence about how he still proves theorems and walks up tall mountains. Just before his talk, Jennifer Park said, “I hope I still love math as much as he does when I’m 100.” Agreed.

Thursday afternoon I found him in the lounge chatting with Andrew Bremner about Wimbledon, so I took this opportunity to introduce myself. I asked Richard about mathematical life and I really loved his response.

**Me:** “What would you say to early career mathematicians about how to have a great life in math?”

**Richard Guy:** “Math is fun, and it is difficult, but you have to find your own level. When you’re a small child, you learn to count and add and subtract and such. There are lots of whiz kids at arithmetic, who then just kind of fold up when algebra, with all the x’s and such, comes along. And it happens again with trigonometry, calculus and so on. When you hit more and more abstraction as you go along, it’s easy to feel you’ve got beyond your depth. But you can find your own level of abstraction and work there, because there are plenty of things to work on at each level. The thing is not to get depressed when you don’t understand—and I mean sometimes I hardly understand—what people at conferences are talking about.”

Thoughts on the books? Hopes for your relationship with math at 100? Please share in the comments.

Excellent post. Very interesting. Thanks.

Cathy O’Neil’s book is fantastic. An Applied Math PhD candidate, I pounded through it in a day– I loved it. There are several issues and problems brought up that mathematicians (and hopeful future mathematicians!) need to understand when bridging the gap into data science; before this book, I had seen several of the issues before (risk of reaffirming recidivism, wild instability of code, etc), but from her book one actually sees and might be surprised by where these problems crop up.

(Sorry to note publicly, but her last name is “O’Neil,” not “O’Neill.”)

Thanks! I also could not put it down, and am quite interested to see how my undergrad students responded to the book.

Great advice by one of the masters regarding early career path!