How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg is a schizophrenic book. On the one hand it is an attempt to fulfill the promise of its main title and on the other it is a paean to mathematical life celebrating the subtitle – sort of – “This is the smart way to think about a situation and it is so cool.”
These types of books need to appear every few years. They bring the issues of quantitative literacy back into the public eye however briefly and sometimes provide a more modern approach or at least explanation for math-in-the-world problems.
Dr. Ellenberg makes some good choices. He includes equations. He uses hand-drawn graphs of appealing simplicity. He has a knack for a turn of phrase. But who is he writing for? The non-technically inclined individual who is interested in how to think about medical diagnoses and treatments, finances, elections and polling, and secure internet communication – those interested in “math as common sense?” Or the dreamer type interested in logic and the consistency of arithmetic and deep mathematical structures? Or maybe his mathematical friends? It isn’t clear.
There are footnotes – generally asides that complete or elaborate a statement that a knowledgeable math trained person might question and there are end notes with references and sometimes further elaboration. Exactly who is the reader that needs footnotes but not the end notes? Another example. There is a quote in Italian followed by its translation. What is that doing there? Does the intended audience know Italian? Does Dr. Ellenberg know Italian and did he translate the passage himself (I didn’t read the end note)? What was the intention? Items like this give the book an odd tone. I had the feeling I was being talked down to, of not belonging to a select society, of looking outside in at a bunch of mathematicians enjoying their special jokes.
One last thing. Dr. Ellenberg seems to have lived (I really don’t know) a pain-free existence. He likes (at least twice) to use metaphors of aversion that involve physical pain like driving a fork into one’s hand. I have a mildly crippled left hand and found myself cringing.