What are the Ten Equations?

Maths is often seen as hard.

Not ‘hard’ as in ‘difficult’ (it can be that too, of course) but ‘hard’ as in delivering hard truths, undeniable facts and fool-proof reasoning.

For me, maths isn’t like that. My 20 years of experience as an applied mathematician — modelling everything from gambling and football to racial segregation and epidemics — has taught me that maths has a softer side.

Maths can be used to think about whether you should give up (or stick with) a romantic relationship. It helps you deal with feelings of insecurity that arise when you compare yourself to others. It provides ways of coping with the vast flood of information from social media and to decide how long your kids should be allowed to spend on their phones. It can even help you binge on Netflix series without a fear of missing out on something better.

One of the situations I describe in The Ten Equations that Rule the World: And How You Can Use Them Too concerns Jess, who is unsure if she should quit her job at a human-rights organisation. Her boss is horrible, but the job is for a worthwhile cause. Jess starts using a star-based system, similar to that used on Tripadvisor, to rank each day with between 0 and 5 stars. After a few months, she uses the third equation of the Ten, the confidence equation, to decide whether or not her 2.1 (± 0.1) star job is worth the hassle.

Jess’s situation is fictional, but her story illustrates how easy it is to use an equation (in this case the confidence interval) to make life changing decisions. No advanced mathematical expertise required.

While writing The Ten Equations I discovered that this soft form of thinking is not widely appreciated outside of mathematical circles (and not even fully understood within these circles). I describe the inner workings of a secret society, which I call TEN, that is not unlike the Priory of Sion in Dan Brown’s book The Da Vinci Code. The society of TEN was first grounded by Abraham De Moivre, nearly 300 years ago, when he explained confidence intervals — the same ones now used by Jess — to a small group of businessmen, gamblers and scientists (including Sir Isaac Newton).

The society has since discovered nine other key equations. These include the learning equation, applied by three engineers in California to increase the time viewers spend watching YouTube by 2000%. There is also the betting equation, the influencer equation, the market equation and the correlation equation which have reshaped, respectively, betting, technology, finance and advertising. All these equations generate billions of dollars of profits for a small number of the society’s members.

They have revolutionised the world. And they can, if you learn them, revolutionise your life.

The hard side of maths — the one used to bludgeon each other with numbers or accuse each other of lacking logical reason — takes a back seat in the Ten Equations. Instead, I lift out this softer side. The side that allows us to forgive each other, to judge each other fairly, and to grow more confident in ourselves.

The book was written before the current crisis. A crisis in which numbers have played an important role.

For me, the spread Covid-19 and the changes it has brought to society has reinforced the power of the Ten Equations. The equations can be used to navigate new challenges as they come up. You can use the judgement equation to assess your personal risk from the Corona virus or use the influencer equation to understand why viruses spread so fast. Maths can model an epidemic but, as I find when I look at the morality of mathematics with help of the universal equation, I also find that maths can’t be used to put a numerical value on any person’s life.

Maths is about learning the right way to solve new problems as they come up, rather than about having all the correct answers ready in advance. The book presents equations in a way that is accessible and easy to relate to. Its scope stretches from history and philosophy to the mundane and the every day. It is about approaching life carefully and considerately. It takes a soft approach.

The Ten Equations shows you how you can adopt that approach in your own life. I hope you find it useful.

Professor of Applied Mathematics. Books: The Ten Equations (2020); Outnumbered (2018); Soccermatics (2016) and Collective Animal Behavior (2010).

More from David Sumpter

Professor of Applied Mathematics. Books: The Ten Equations (2020); Outnumbered (2018); Soccermatics (2016) and Collective Animal Behavior (2010).