Nineteenth-century German mathematician Leopold Kronecker once said

God created the integers, all the rest is the work of man.

What tactics should a soccer player use when taking a penalty kick? And what can the goalkeeper do to foil his plans? John Haigh uses Game Theory to find the answers, and looks at his World Cup predictions from last issue.
When we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.
Clearly the modern electronic computer couldn't have been built before electronics existed, but it's not clear why computers powered by steam or clockwork weren't invented earlier. Tom Körner speculates on the historical reasons why computers were invented when they were.
Nobel Prizewinning Physicist Professor Gerardus 't Hooft has always been fascinated by the mathematical mysteries of nature. He tells Plus about his early life, and what our Universe might really be like.

The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.

What happens when one black hole meets another? Professor Kip Thorne shows us how to eavesdrop on these cosmic events by watching for telltale gravitational waves.
Neuropsychologist Brian Butterworth tells us about research showing that even newborn babies have a basic understanding of number. It seems we are all mathematicians!