# The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love

The subtitle explains more clearly what the book is about: *How a mathematical approach to life adds up to health, wealth, and love*. It is thus one of these books showing to the layperson how mathematics *can* be used in everyday life (not necessarily how it *is* used in practice). Therefore the mathematics are really elementary. Unlike similar books, written with the same purpose, here the health, wealth and love take up some serious part of the pages, and give only little mathematics in return.

Let's start with the health. That subject has two chapters: one on the calories you take in and burn and one about the composition of your diet. What you get to digest for mathematics is a weighted linear sum of components such as your age, weight, and height that are influencing your metabolic rate, your calorie burning, or your cholesterol ratio. A simple quadratic defines your maximal heart rate as a function of age, and the expected years of life loss as a function of waist to height ratio.

The second part has the promising title *A mathematician's guide to manage your money*. This also has two chapters. One is about managing your budget and the second about financial transactions like saving and investing. The mathematics we learn here is that taxes are computed in a linear way but only within certain intervals, so that it is actually a piecewise linear function. Also we learn what a compound interest rate is (or inflation rate in this case) and this leads to Euler's constant e and consequently also to the logarithm. A glimpse at the financial markets is the occasion to introduce some statistical concepts like average and standard deviation.

The 'love' part introduces a formula to compute the number of possible dating candidates, and the well known 37 percent rule which states that if you need to select the best one (for example partner among the candidates) in a sequence, then you should first register the best candidate among the first 37% of the sequence and then take the first one that is better than that one. It also describes the Gale-Shapley algorithm to solve the stable matching problem. The last chapter is mathematically the most involved one of the book and analyses the relation between two persons as a dynamical system described by two simple differential equations. Also the Nash bargaining problem is discussed in which the optimalization of the quadratic Nash product has to be found when the couple has to come to a joint decision.

Most of the mathematical derivations and computations are removed from the text and are summarized in appendices and if you want to apply it to your own life, you don't even need a pocket calculator because the publisher's web page has a link to online apps that will evaluate the formulas for you when you introduce your data. Each chapter also ends with a summary of the mathematical and nonmathematical takeaways. If you are interested in one of the topics, further reading is provided. Indeed, all the equations and methods described here are abstractions and usually drastic simplifications of reality. Therefore I would also like to refer to a don't-try-this-at-home type of warning that Fernandez provides in the introduction: if you want to implement major changes in your life based on the methods presented in this book, be sure there is an expert (like for example your medical doctor) to assist you and give good advise.

I doubt that the noble hope of the author, which is that by reading this book the reader will adopt a mathematical approach to life, shall be fulfilled. The mathematics are really precalculus, while the problems like composing a diet, financial investment, and finding a partner for life, do not seem like the problems one is facing at the age one is brought in contact with the required precalculus. Somehow I think that the level of the applications and the level of the mathematics do not match well. There are however still wise lessons to learn from the book which anybody (certainly journalists and politicians) should know. For example one should have the numeracy to know that doubling the price of a sandwich over 10 years, does not mean that the inflation is 10% per year. Also the mathematical techniques shown here do not only apply to the three main topics enumerated above, but they are also applicable in many other situations, like an optimal selection of a secretary or the best way to subdivide a pizza among a number of hungry children.

I believe it would take a student already interested in mathematics to be sincerely attracted to reading the book. On the other hand, teachers may find inspiration in some of the examples to use these as illustrations in their teaching. Or perhaps the mathematics that are used in the book may be an inspiration for them to apply it in perhaps similar applications that are more adapted to their particular set of students.

**Submitted by Adhemar Bultheel |

**20 / Apr / 2017