Melvyn Bragg and guests discuss 25 pivotal concepts, theorists and developments that have advanced the science of mathematics.

In Our Time is a Radio 4 phenomenon, a knowledge juggernaut that has informed and entertained over 2 million listeners each week since its first broadcast in 1998. In its 25 years on air, it has covered an astonishing array of topics, from the Second Law of Thermodynamics to the Sistine Chapel.

Beginning with three introductory episodes, this specially curated collection explores 25 of the most important individuals, ideas and discoveries that have transformed our understanding of mathematics over the past 5,000 years. We learn how Indian mathematics provided the foundations for much of our modern thinking, discover why Euclid's Elements is the most influential textbook ever written and hear of the epic feud between Sir Isaac Newton and Gottfried Leibniz over who invented calculus.

Plus, we are introduced to influential mathematicians including Pythagoras, Blaise Pascal, Emmy Noether and Alan Turing, as well as key concepts, problems and puzzles such as negative numbers, infinity, Fermat's Last Theorem, the Poincaré conjecture and P v NP.

Enlightening, thought-provoking and inspiring, these wide-ranging discussions make abstruse ideas accessible and demystify mathematics, showing how it shaped our world and made us who we are.

Production credits

Presented by Melvyn Bragg

Produced by Simon Tillotson, Thomas Morris and Natalia Fernandez

First broadcast on BBC Radio 4 on the following dates:

Part I: Context

Mathematics 6 May 1999

Mathematics and Platonism 11 January 2001

Mathematics' Unintended Consequences 11 February 2010

Part II: History of Mathematics

Indian Mathematics 14 December 2006

Euclid's Elements 28 April 2016

Maths in the Early Islamic World 16 February 2017

Renaissance Maths 2 June 2005

Calculus 24 September 2009

Part III: Influential Mathematicians

Pythagoras 10 December 2009

Archimedes 25 January 2007

Blaise Pascal 19 September 2013

Emilie du Châtelet 4 February 2021

Carl Friedrich Gauss 30 November 2017

Ada Lovelace 6 March 2008

Emmy Noether 24 January 2019

Alan Turing 15 October 2020

Part IV: Key Concepts

Zero 13 May 2004

Prime Numbers 12 January 2006

Negative Numbers 9 March 2006

e 25 September 2014

Pi 2 September 2004

Imaginary Numbers 23 September 2010

Infinity 23 October 2003

Part V: Problems and Puzzles

Zeno's Paradoxes 22 September 2016

Fermat's Last Theorem 25 October 2012

The Poincaré Conjecture 2 November 2006

Gödel's Incompleteness Theorems 9 October 2008

P v NP 5 November 2015