The Probabilistic Method

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Kaldor and Eddish came up with the probabilistic method to solve problems in graph theory. They found that if it's difficult to design a problem, don't design it - just choose your network entirely at random. This is very counterintuitive because you might think that if almost everything works, then surely you can just sit down and write down something that will work. But unfortunately, the set of things that you can actually describe is a very small set. So once you have this idea that perhaps you could just try choosing a random object and seeing if that almost always works, they become suddenly much easier. You start seeing this phenomenon all over the place.

Paul Erdős (1913 – 1996) is one of the most celebrated mathematicians of the 20th century. During his long career, he made a number of impressive advances in our understanding of maths and developed whole new fields in the subject.

He was born into a Jewish family in Hungary just before the outbreak of World War I, and his life was shaped by the rise of fascism in Europe, anti-Semitism and the Cold War. His reputation for mathematical problem solving is unrivalled and he was extraordinarily prolific. He produced more than 1,500 papers and collaborated with around 500 other academics.

He also had an unconventional lifestyle. Instead of having a long-term post at one university, he spent much of his life travelling around visiting other mathematicians, often staying for just a few days.

With

Colva Roney-Dougal Professor of Pure Mathematics at the University of St Andrews

Timothy Gowers Professor of Mathematics at the College de France in Paris and Fellow of Trinity College, Cambridge

and

Andrew Treglown Associate Professor in Mathematics at the University of Birmingham

The image above shows a graph occurring in Ramsey Theory. It was created by Dr Katherine Staden, lecturer in the School of Mathematics at the Open University.