BBC
In the last programme in the series, Marcus du Sautoy looks at some of the great unsolved problems that confronts mathematics in the twentieth century and tells the stories of the mathematicians who would try to crack them. Mathematicians like Georg Cantor, who investigated a subject that many of the finest mathematical minds had avoided – infinity.
Cantor discovered that there were different kinds of infinity - and that some were bigger than others. Henri Poincaré was trying to solve one mathematical problem when he accidentally stumbled on chaos theory, which has led to a range of ‘smart’ technologies, including machines which control the regularity of heart beats. But in the middle of the twentieth century, mathematics was itself thrown into chaos.
Kurt Gödel, an active member of the famous 'Vienna Circle’ of philosophers, 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.
In this programme, Marcus looks at the startling discoveries of the American mathematician Paul Cohen, who established that there were several different sorts of mathematics in which conflicting answers to the same question were possible. He also examines the work of André Weil and his colleagues, who developed algebraic geometry, a field of study which helped to solve many of mathematics' toughest equations, including Fermat’s Last Theorem.
He also reflects on the contributions of Alexander Grothendieck, whose ideas have had a major influence on current mathematical thinking about the hidden structures behind all mathematics. Marcus concludes his journey by considering the great unsolved problems of mathematics today, including the Riemann Hypothesis - a conjecture about the distribution of prime numbers – which are the atoms of the mathematical universe. There is now $1 million prize and a place in the history books for anyone who can prove Riemann’s theorem.
First broadcast: Monday 13 Oct 2008 on BBC Four. For further broadcast details, and to watch online where available, visit bbc.co.uk.
The Story of Maths series guide:
OU on the BBC: The Story of Maths - About the series
Production team
Marcus DuSautoy takes a journey through the heart of the universe - find out more about the series. Read more : OU on the BBC: The Story of Maths - About the series
OU on the BBC: The Story of Maths - The Frontiers of Space
BBC
By the seventeenth century Europe had taken over from the Middle East as the world’s power house of mathematical ideas, the beginning of the Golden... Read more : OU on the BBC: The Story of Maths - The Frontiers of Space
OU on the BBC: The Story of Maths - The Genius of the East
Production team
When ancient Greece fell into decline, mathematical progress became the preserve of the genius of the East. Read more : OU on the BBC: The Story of Maths - The Genius of the East
OU on the BBC: The Story of Maths - The Language of the Universe
OU
It's numbers, not words, which make up the language of the universe. Read more : OU on the BBC: The Story of Maths - The Language of the Universe
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Since the dawn of civilisation, humans have used everyday materials to create mathematical models of the world around them. This album explores the ancient Greeks'... Read more : Mathematical models: from sundials to number engines
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Comments on: " To infinity and beyond"
Rossmore has started a thread discussing To infinity and beyond.
I hope you would also make a biography programme about the lives of our great mathematicians so that even those so called layman would be able to relate in personal level on mathematics.
Great programme,I'm from the Philippines which is not known for its mathematical and scientific interest,I just want you to know that even from this obscure nation, someone appreciates your work. I hope there would be more of these kind of programmes in the future.
great programme. wish i'd seen them all. would like to learn more. not likely to do an OU course. *might* get round to reading the 800-page history of maths recommended in your 'taking it further' section, but wonder if i might just satisfy my curiosity by reading a transcript of the programme? i hoped i might find one here. perhaps you could publish it?
To the person above. If you would like to read more about specifically Riemn Hypothesis, I recommend a book called Euclids Window.
I myself have a maths degree, and find the subject fascinating, but the book is accessible to people with limited experience, and number theory(the main branch of maths which deals with the Riemann conjecture) is the greatest for the non mathematician as it contains the base of mathematics, accessible to all who have and inquiring mind, and a few hours to spare!
Re: Comments on: " To infinity and beyond"
Dear Peoplesdavid
So few intelligent people can be bothered to take the time out of their lives to properly patronise those of us who struggle with the difference between two and too
I thoroughly enjoyed the whole series but these last too programmes were particularly engaging. They have encouraged me to find out more and take this further.