Street-Fighting Mathematics by Sanjoy Mahajan is probably the least intimidating math book I’ve ever read.

That’s meant to be a compliment, by the way.

The subtitle to this book is *The Art of Educated Guessing and Opportunistic Problem Solving* and Mahajan sums up his philosophy in the very first paragraph of his preface:

*Too much mathematical rigor teaches rigor mortis: the fear of making an unjustified leap even when it lands on a correct result. Instead of paralysis, have courage—shoot first and ask questions later. Although unwise as public policy, it is a valuable problem-solving philosophy, and it is the theme of this book: how to guess answers without a proof or an exact calculation.*

This book weighs in at a scant 135 pages including the index. The title comes from a short course of the same name taught by Mahajan at MIT. The makeup of the class ranged from first-years to grad students in a wide variety of academic programs. The course was designed to focus on techniques for using math to solve real-world problems.

This may seem odd at first because we already use math every day to solve real-world problems.

Don’t we?

Well, yes. But, as pointed out above, there is a time and place for mathematical rigor (as taught in traditional classes) and at other times you need to be able to *feel* the answer. It’s kind of hard to explain but Chapter 4 (“Pictorial proofs*”*) suggests what the author is trying to achieve:

*Seeing *an idea conveys to us a depth of understanding that a symbolic description of it cannot easily match.

Make no mistake. This is not a book simply listing short-cuts or “cheat codes” that we can use to *avoid* math. This is instead a different approach to mathematics by way of mapping math to our life experience and giving us a way to internalize it, giving us a sort of sixth sense.

Let me give an example. A bookshelf that is out of alignment and unstable can be described by a series of geometric expressions, involving lengths, widths, angles and so forth. However, an experienced carpenter can tell if a bookshelf is out of alignment and unstable by looking at it and touching it. Now the carpenter certainly knows the mathematical properties of a well made bookshelf but she has internalized the math so that now she can ‘sense’ when something is wrong. It doesn’t add up, so to speak.

The book covers a wide range of topics, from economics and Newtonian mechanics to geometry, trigonometry and calculus. Yet it’s very reader-friendly, written in a clear, engaging style with plenty of examples and even some sample problems. There are only six chapters and you can dip into the material in almost any order. The book has been published under a Creative Commons license so there is a PDF version that is freely available for download. If you’re like me, however, you’ll also spring for the paperback edition.

*Street-Fighting Mathematics* is a unique book that will reward you with hours of thought-provoking (and practical) reading.

References

Mahajan, S. (2010). *Street-fighting mathematics: The art of educated guessing and opportunistic problem solving*. Cambridge, MA: MIT Press.