The Ten Equations you need to know…


Portrait of David Sumpter

David Sumpter, professor of Applied Mathematics at Department of Information Technology and author of the new book The Ten Equations that Rule the World: And How You Can Use Them Too.

COLUMN. Maths is often seen in terms of a lonely genius trying to answer a difficult obscure riddle. For me, maths has never been like that. In my research at Uppsala University I have used maths to model everything – from ant trails and fish schools, to racial segregation in schools and epidemics in sub-Saharan Africa, to football and gambling.

These studies have taught me that maths has a softer side. It is about working together with biologists and social scientists. It is about seeing biology, society and sports in a different, deeper way. It is about cooperation and teamwork.

It is also very much about describing things which are everyday and part of all our lives.

I decided to take some of the techniques I have used at work and think about how you might apply them in your life. The answer comes in the form of The Ten Equations that I believe everyone needs to know about.

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 deciding 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.

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 coronavirus 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 the 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. Maths when used properly is about approaching life carefully and considerately. It is a soft approach.

This is the approach I take in my research, in my teaching and in my writing. It is also an approach I try to take in living my own life.


David Sumpter, Professor at Department of Information Technology and author of the new book The Ten Equations that Rule the World: And How You Can Use Them Too, Allen Lane, 2020

1 October 2020

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Last modified: 2022-12-22