"à l'infini et au-delà"

This is the last episode of the documentary entitled “The Story of Maths”. This episode considers the great unsolved problems that confronted mathematicians in the 20th century and tells the stories of those mathematicians who would try to crack them. Mathematicians like Georg Cantor, Henri Poincaré, and Kurt Gödel. Prof du Sautoy looked at the startling discoveries of the American mathematician Paul Cohen, examined the work of André Weil, and also reflects on the contributions of Alexander Grothendieck.

Georg Cantor investigated a subject that many of the finest mathematical minds had avoided, that is infinity. He discovered that there were different kinds of infinity, and some of them were bigger than the others.

Henri Poincaré was trying to solve one mathematical problem when he accidentally stumbled on chaos theory. This has led to a range of ‘smart’ technologies, including the machines which control the regularity of heart beats. But in the middle of the twentieth century, mathematics itself was thrown into chaos.

Kurt Gödel was an active member of the famous 'Vienna Circle’ of philosophers. He detonated a 'logic bomb’ under 3,000 years of mathematics when he showed that it was impossible for mathematics to prove its own consistency, and that the unknowable is itself an integral part of mathematics.

The American mathematician Paul Cohen was the one who established that there were several different sorts of mathematics in which conflicting answers to the same question were possible.

André Weil and his colleagues developed the algebraic geometry. It is a field of study which helped to solve many of mathematics' toughest equations, that includes Fermat’s Last Theorem.

Alexander Grothendieck’s ideas have had a major influence on the current mathematical thinking about the hidden structures behind all mathematics.

Prof Marcus du Sautoy concluded his journey by considering the great unsolved problems of mathematics today, which includes the Riemann Hypothesis. It is a conjecture about the distribution of prime numbers, which are the atoms of the mathematical universe. Now, there is a $1 million prize and a place in the history books for anyone who can prove Riemann’s theorem. Prof Marcus du Sautoy also concluded 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 looked at how mathematics was itself thrown into chaos by the discoveries of Kurt Godel, who showed that the unknowable is an integral part of mathematics, and Paul Cohen, who established that there were several different sorts of mathematics in which conflicting answers to the same question were possible.