3 books that changed my perception of math

A fortnight ago we talked about films, today we are talking about books!

In the last article of “Absolute Beginners”, we said how important it is to read a lot to write well, which applies to every language, not just English. I love reading a lot, and I usually alternate between novels and essays. I don’t think essays are boring. I think they are essential to keep up to date with recent discoveries and currents of thought to better understand what is going on and get new insights for our research and teaching.

How to navigate and choose which essays to read among the flood of new releases and literary cases is much more difficult. I usually rely on the suggestions given by some of the newspapers I typically read and other blogs and sites I follow.

So today, I wanted to recommend three essays that, even if they don’t talk directly about logistics, have been very useful for me to rethink both research and (above all) teaching. They are not books that have come out recently, so they are easy to find in bookshops, online platforms, and even libraries!

  • The Black Swan: The Impact of the Highly Improbable by Nassim Nicholas Taleb (2007)

A great classic that is an absolute must-read. Taleb not only had the brilliant idea of giving a beautiful name to unlikely events (a name that immediately evokes Swan Lake and, personally, the wonderful movie by Aronofsky), but he also develops a convincing theory. Taleb’s thesis is that we should not necessarily predict unlikely events but create a ‘robustness’ in our systems that allows them to withstand even extreme and improbable conditions.

Taleb also points out that the world’s most famous statistical distribution, the normal or Gaussian distribution, is not suitable for describing most of the world’s events and phenomena. Yet, it is the most widely used to describe them. In fact, I also ran into this problem. At the beginning of my PhD, I thought that the distribution of goods in a city centre followed a normal distribution. Still, as I proceeded with the data analysis and during my visiting period I discovered that each type of goods has its own particular distribution. Practically none of the urban freight distribution were normals (except for pharmaceutical deliveries).

Reading this book has undoubtedly helped me better understand risk analysis and how to think about these unlikely events and changed the way I view normal distribution!

Photo by grainfalls on Unsplash
  • Weapons of Math Destruction by Cathy O’Neil (2016)

Cathy O’Neil has an exciting career behind her that has made her one of the most authoritative voices on the subject she discusses in her book. Cathy O’Neil received her PhD in mathematics from Harvard in 1999, taught at MIT, and researched arithmetic algebraic geometry. She then left academia in 2007 and became an analyst for a significant edge fund. In 2007. Not exactly the best timing since she was able to see at first hand what improper use of financial instruments can lead to with the subprime mortgage crisis and the real estate bubble (to understand more, watch “The Big Short” by Micheal Lewis, highly recommended). O’Neil also left finance to become one of the “minds” of the Occupy Wall Street movement and became a writer and populariser. I have been following her blog (https://mathbabe.org/) for years, and it is always full of interesting insights. But what are the weapons of mathematical destruction that give the book its title? They are all the decision support algorithms that continue to perpetrate the same cultural and cognitive biases that humans do instead of optimising a choice process. More simply, O’Neil explains how the algorithms that are used to select the best high school teachers, to choose admissions to the most prestigious colleges, to determine which prisoners deserve house arrest, to decide who to give a mortgage to or who to hire in a company end up continuing to disadvantage the lower classes, blacks, women, members of LGBTQ+ communities and minorities in general. How can this happen? Shouldn’t an algorithm be more ‘objective’ than a human being? However, let’s not forget that algorithms are created by humans (who can make mistakes) and are often ‘trained’ with past data, thus containing all the biases of people. O’Neil succeeds in talking about such a technical subject with a fresh, funny, simple language that can be understood even by those who have only seen mathematics in high school.

Her book taught me to explain optimisation models in another way by focusing students’ attention not only on the correctness, effectiveness and efficiency of the models but also on a careful analysis of the outputs that must guarantee equal treatment. Suppose I have to choose a model to place an ambulance hub. In that case, the variables and parameters involved must maximise benefits and minimise costs and ensure that no one finds themselves risking their life more just because they live in the “wrong” place. Algorithms also have ethics that must be taken into account.

Photo by Lloyd Blunk on Unsplash
  • How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg (2014)

I recommended this book to everyone I knew. Jordan Ellenberg, child prodigy, mathematical genius, lecturer at the University of Wisconsin-Madison and researcher on issues related to arithmetic geometry (as was Cathy O’Neil). He is also the author of a very popular blog (https://quomodocumque.wordpress.com/). He gives us what, for me, is the mathematical divulgation book par excellence. In fact, this book explains many critical issues in mathematics such as linear regression, the null hypothesis, the binomial theorem, the “p-value”, the Bayesian Inference and much more with straightforward examples that stick in mind. Memorable are the explanations of the survivorship bias through the anecdote of Abraham Wald or the wrong statistical assumptions through the analysis of NBA statistics and the so-called “hot hand” phenomenon. In short, Ellenberg’s book gives us a better understanding of a number of mathematical topics that we have come across in our studies and in our everyday lives. It provides us with anecdotes and examples, thanks to which these topics will remain in our minds forever.

I really wish mathematics had been explained to me like this in high school!

I think it is essential that as researchers, we do not limit ourselves to our own areas of research but continue to explore, poke around and look for new ideas in the work of other researchers, even if they are far removed from our own subjects! I have told you how these three books changed my perception as a researcher and lecturer on specific topics. What are the essays that have helped you in your research and teaching? That made you see things from a different perspective?

Alexandra

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