I picked up an audiobook copy of “How not to be Wrong” for the drive to and from Boston this weekend. I’m about half way through it at this point and have really enjoyed it. It is a great book if you are interested in getting a look at the world through the eyes of a mathematician.

Among his achievements, Ellenberg was one of the top students in math competitions the year I graduated from high school and was also one of the top students in the Putnam exam during his time at Harvard. Our senior year of college, his Harvard team beat my MIT team in a way similar to how a #1 seed beats a #16 seed in the NCAA basketball tournament. He’s gone on to have a really interesting career in academic math, writing, and probably 20 other things that I don’t really know anything about 🙂

So far the book offers fascinating insights into math education, scientific and political proclamations about probability, and an interesting range of more mathy topics such as Zhang’s breakthrough on prime numbers from last year, and a great discussion on the group of MIT students that figured out how to win one of the Massachusetts lottery games.

Several more comprehensive reviews of the book by Cathy O’neil and Evelyn Lamb are here:

http://mathbabe.org/2014/05/29/how-not-to-be-wrong-by-jordan-ellenberg/

and here:

http://blogs.scientificamerican.com/roots-of-unity/2014/05/31/how-not-to-be-wrong-book-review/

Some of the fun takeaways for me so far include:

(1) His take on the math education wars explains my own position better than I could have myself.

(2) I wish that I would have seen his discussion of Zhang’s prime number breakthrough before I did this little talk with my kids last week:

https://mikesmathpage.wordpress.com/2014/05/31/prime-gaps-and-a-james-tanton-problem/

Ellenberg’s explanation of the problem, Zhang’s solution, and why the problem is interesting to begin with is as clear and understandable as I’ve seen. Also, his back of the envelope explanation of logs is really great.

(3) The part about the Massachusetts lottery and why the MIT team filled out their forms by hand is really incredible. I’m actually still in the middle of that one, but having heard the story from a few other people loosely connected to the group that figured out this hole in the lottery game, Ellenberg’s telling of the tale ties a lot of loose ends together for me.

(4) He talks through a proof of the Buffon needle problem that I’d never seen before. I’d previously know that problem to be only a neat high school calculus example, but this other proof makes a clever geometry / probability argument and is remarkably similar to this problem that Guass solved:

https://mikesmathpage.wordpress.com/2014/03/23/a-really-neat-problem-that-gauss-solved

(5) Finally, probably the most interesting bit to me personally was the section on how humans guess numbers in a way that is totally non-random. In the two big billion dollar games that I’ve been involved in – Pepsi’s “Play for a Billion” in 2003 and 2004, and the Quicken Billion dollar bracket game in 2014 – reviewing the guesses by the contestants after the game was over (1000 numbers from 000000 to 999999 for the Pepsi game, and NCAA brackets for the Quicken game) it was almost shocking how the guesses of the contestants clustered.

I’m sure I’ll have many more fun takeaways from the book once I finish it. Even half way through it, though, I’d recommend this book without any hesitation to anyone looking for a fun book about how math comes into play in all sorts of different situations. While that topic may seem like a pretty heavy one, Ellenberg is a gifted writer and the book is a really enjoyable read. In a way I’d put it on par with Roger Lowenstein’s “When Genius Failed” or Bethany McLean’s “Smartest Guys in the Room” and “All the Devils are Here” – potentially difficult topics turned into relatively easy and informative reads (and basically must reads) by great writers.

Go pick up your copy today!