To Infinity and Beyond

Marcus du Sautoy concludes his investigation into the history of mathematics with a look at some of the great unsolved problems that confronted mathematicians in the 20th century.

After exploring Georg Cantor's work on infinity and Henri Poincare's work on chaos theory, he looks at how mathematics was itself thrown into chaos by the discoveries of Kurt Godel, who showed that the unknowable is an integral part of maths, and Paul Cohen, who established that there were several different sorts of mathematics in which conflicting answers to the same question were possible.

He concludes his journey by considering the great unsolved problems of mathematics today, including the Riemann Hypothesis, a conjecture about the distribution of prime numbers. A million-dollar prize and a place in the history books await anyone who can prove Riemann's theorem.