## Primes and Equations

One of the oldest subjects in mathematics is the study of Diophantine equations, i.e., the study of whole number (or fractional) solutions to polynomial equations. It remains one of the most active areas of mathematics today. Perhaps the most basic tool is the simple idea of "congruences," particularly congruences modulo a prime number. In this talk, Richard Taylor, Professor in the School of Mathematics, introduces prime numbers and congruences and illustrates their connection to Diophantine equations. He also describes recent progress in this area, an application, and reciprocity laws, which lie at the heart of much recent progress on Diophantine equations, including Wiles's proof of Fermat's last theorem.

Primes and Equations |

Related Links |

The Music of the PrimesThis will discuss the mystery of prime numbers, the history behind the Riemann hypothesis and the ongoing quest to solve it. |

Fermat's Last TheoremA story about a mathematician, Andrew Wiles, who struggled to prove the Fermat's Last Theorem and at last succeeded in proving it. |

The Story of MathsThis is a BBC documentary series written and presented by Professor Marcus du Sautoy, outlining aspects of the history of mathematics. |

The CodeThis is a BBC documentary series presented by Professor Marcus du Sautoy, revealing a hidden numerical code that underpins all nature. |