Book review - Jordan Ellenberg's "How not to be wrong"

Why is Math interesting? Jordan Ellenberg starts out with the critical student question "When am I going to use this?" and has written this inspiring defense of thinking as an answer to that question. In the very first page he notes that the usual answers to this question are not satisfying to anyone. His short good answer (in the first page or so - I'm not giving anything anywhere) is something like this (My words not his) "mathematics classes are training for your brain to amplify your common sense. Just like in sport you would never do drills during a game, when you use math you won't be doing drills but solving problems, but you have to do the drills to get good. And just like in sports the fun and fitness are useful even if you aren't a world star math professional." from there the student/reader asks to go beyond the practical and for some specific examples, which leads into the Book proper and the first example of Abraham Wald and amplifying the un-intuitive common sense of missing bullet holes to better armor war planes in WW2.

I think the book fails in that mission as it drifts to a larger one of defending thinking and mathematical thinking in general - the last chapter is a particularly strong and literate defense, but unfortunately all of the students I know asking that question will not find the connection to their math classes. Still the larger question - a defense of thinking and intellectualism in general is far more important, and probably a greater work.

Usefully Ellenberg is also a fan of literature a writing which in an alternate universe would have been his career. This leads to extremely good writing with many literary references, as he plys his way through a grab bag of mathematical stories aiming for stories that are profound and simple - although perhaps a little  too much emphasis on some fascinating stories from the lottery. The stories are very well told, and when it is meandering it is well worth the read, but for my purposes - to understand what a well educated person in the 21st century should know about math it feels like the simplification for the general audience - staying with the simple and the profound, but not allowing some introduction to the intermediate levels of complexity and the laundry list of things (I wonder if some of the chapters could be in a different order without changing the book at all) make this book less than it could be. Perhaps it is interesting to contrast this book to Risk Savvy by Gerd Gigerenzer where the simpler mission and more straight forward and precise writing leads to a directly successful but slightly less emotionally satisfying book.

Still I highly recommend reading this one, despite it not being what I am looking for this great defense of thinking is needed in todays political world of deliberate no-nothingism, and attack on "experts" as a dirty word as seen in the UK Brexit. It is very well written, and very engaging to read, very much worth your time. 

Find it at the Houston Library , amazon, or borrow my copy if your in town.