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Geometry or algebra? The Cambridge approach

Michael Atiyah
Mathematician

Views | Duration | ||
---|---|---|---|

11. Early experiences with physics | 1941 | 01:55 | |

12. Sent to Trinity College Cambridge | 1443 | 00:57 | |

13. Gap year spent in the army | 1128 | 06:04 | |

14. First year at Cambridge | 1670 | 03:39 | |

15. Geometry or algebra? The Cambridge approach | 2329 | 01:19 | |

16. Top in the Tripos | 2080 | 02:24 | |

17. My chosen geometry supervisor | 1636 | 01:57 | |

18. Background to differential geometry | 1958 | 00:54 | |

19. Starting to understand harmonic integrals | 1595 | 01:32 | |

20. Vector bundles | 1674 | 03:23 |

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The traditional geometry approach at Cambridge was the synthetic approach, which concentrated on the geometrical pictures and the interactions, and that's really what appealed to people who liked geometry; the beauty of the patterns and the interrelationships. The algebraic side was brought in by people like Todd and others out of a sense of conscience; you had to justify some of the arguments and therefore you brought it in, you know, you knew you had to sort of play around with this stuff to be respectable; nobody liked it. He didn't like it. He would bring it…and sometimes of course the algebra would be helpful and useful in some formulas, but nobody took it as more than just, sort of, what you had to do to justify the arguments. And some didn't bother with it at all. Babbage and White and the older school, they never had any algebra in their stuff. So Todd had the algebra in it, but he wasn't really enamoured of the algebra; it was just there as I say to make respectability and clear his conscience, and he never got involved with the more abstract algebraic variety of stuff. I got that a bit from Hodge later on, with Hodge and Pedoe. And what appealed to me certainly was the geometry side; the algebra I didn't like either… but we had to do it.

Eminent British mathematician Sir Michael Atiyah (1929-2019) broke new ground in geometry and topology with his proof of the Atiyah-Singer Index Theorem in the 1960s. This proof led to new branches of mathematics being developed, including those needed to understand emerging theories like supergravity and string theory.

**Title: **Geometry or algebra? The Cambridge approach

**Listeners:**
Nigel Hitchin

Professor Nigel Hitchin, FRS, is the Rouse Ball Professor of Mathematics and Fellow of Gonville and Caius College, Cambridge, since 1994, and was appointed to the Savilian Professorship of Geometry in October 1997. He was made a Fellow of the Royal Society in 1991 and from 1994 until 1996 was President of the London Mathematical Society.

His research interests are in differential and algebraic geometry and its relationship with the equations of mathematical physics. He is particularly known for his work on instantons, magnetic monopoles, and integrable systems. In addition to numerous articles in academic journals, he has published "Monopoles, Minimal Surfaces and Algebraic Curves" (Presses de l'Universite de Montreal, 1987) and "The Geometry and Dynamics of Magnetic Monopoles" (Princeton University Press, 1988, with Michael Atiyah).

**Tags:**
Cambridge, John Todd

**Duration:**
1 minute, 19 seconds

**Date story recorded:**
March 1997

**Date story went live:**
24 January 2008