In Our Time Folgen

Melvyn Bragg and guests discuss an iconic piece of 20th century maths - Gödel’s Incompleteness Theorems. In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox. Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so Gödel changed the way we understand what mathematics is and the implications of his work in physics and philosophy take us to the very edge of what we can know.With Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.

Melvyn Bragg and guests discuss one of the greatest intellectual projects in history - the mass translation of Greek ideas into Arabic from the 9th century onwards.One night in Baghdad, the 9th century Caliph Al-Mamun was visited by a dream. The philosopher Aristotle appeared to him, saying that the reason of the Greeks and the revelation of Islam were not opposed. On waking, the Caliph demanded that all of Aristotle’s works be translated into Arabic. And they were. And it wasn’t just Aristotle. Over the next 200 years Greek philosophy, medicine, engineering and maths were all poured and sometimes squeezed into Arabic. Centred on Baghdad, this translation movement introduced the Islamic world to the philosophy of Aristotle, the geometry of Euclid and the Medicine of Galen. It caused an intellectual ferment that demanded the creation of new words to explain new concepts and house new arguments. Over 600 years before the European renaissance the intellectual legacy of Greece was woven into the tapestry of Arabic thought and it was only through the Arabic versions that Europe go its hands on many Greek ideas. With Peter Adamson, Reader in Philosophy at King’s College London; Amira Bennison, Senior Lecturer in Middle Eastern and Islamic Studies at the University of Cambridge; and Peter Pormann, Wellcome Trust Assistant Professor in Classics and Ancient History at the University of Warwick

Melvyn Bragg and guests discuss the parting of the Red Sea, the feeding of the five thousand and the general subject of miracles. Miracles have been part of human culture for thousands of years. From St Augustine in the 4th century through the medieval cult of saints to David Hume in the 18th, miracles have captured the imaginations of believers and sceptics alike. The way they have been celebrated, interpreted, dissected and refuted is a whole history of arguments between philosophy, science and religion. They have also been used by the corrupt and the powerful to gain their perverse ends. Miracles have been derided and proved to be fraudulent and yet, for many, the miraculous maintain a grip on our imagination, our language and our belief to this day. With Martin Palmer, Director of the International Consultancy on Religion, Education and Culture;Janet Soskice, Reader in Philosophical Theology at Cambridge University; Justin Champion, Professor of the History of Early Modern Ideas at Royal Holloway, University of London.