Another Five Numbers

Synopsis

A series of 15-minute programmes in which Simon Singh investigates the history of some of the most special numbers in mathematics - 4, 7, the largest prime, Kepler’s conjecture, and game theory

Language

English

Country

Great Britain

Year of release

2005

Year of production

2003

Notes

Broadcast on Radio 4 in 5 weekly parts from 22 April 2003.
Additional numbers are explored in the the original series FIVE NUMBERS and FIVE FURTHER NUMBERS

Subjects

Mathematics

Keywords

game theory; history of mathematics; Kepler, Johannes; mathematical concepts; prime numbers

Online availability

URI

http://www.bbc.co.uk/radio4/science/another5.shtml

Price

free

Delivery

Streamed

Sections

Title

Number Four, The

Synopsis

This first programme in the second series looks at the number 4. The question of whether any map can be coloured with just 4 colours so that no two neighbouring countries have the same colour has been puzzling mathematicians for many years. This programme looks at the research that led to the discovery of a proof. Includes contributions from Robin Wilson (mathematician and author), Marcus du Sautoy (University of Oxford) and Ken Appel (one of the mathematicians who proved the four colour theorum).

Duration

15 mins

Title

Number Seven, The

Synopsis

This edition looks at the number 7. The number seven is an important number in luck, or probability theory as it is known to mathematicians. It looks at Persi Diaconis and David Bayer’s discovery that it is necessary to riffle shuffle a deck of cards seven times in order to make it random again. Includes contributions from: Thomas Bass (author), Persi Diaconis (mathematician and gambler) and David Bayer (mathematician).

Duration

15 mins

Title

Largest Prime, The

Synopsis

This edition looks at prime numbers and the search for the largest one. A prime number is one that cannot be divided by any number except one and itself. They are important because any number can be expressed as two prime numbers multiplied together. The programme also looks at Mersenne primes and how they are used in encryption and the Great Internet Mersenne Prime Search (GIMPS). Recently Michael Cameron found the world’s largest prime number using GIMPS. Includes contributions from Adam Spencer (DJ and mathematician), Scott Kurowski (mathematician), Marcus du Sautoy (author and mathematician) and Ian Stewart (University of Warwick).

Duration

15 mins

Title

Kepler’s Conjecture

Synopsis

This edition looks at the problem of the most efficient way to utilise space when stacking oranges. In 1606, this problem was presented to German astronomer, Johannes Kepler, who concluded that the face-centred cubic lattice was the most efficient was to pack spheres - creating a packing efficiency of 74 per cent. However, no one was able to prove that there wasn’t some other way of packing that would lead to a higher percentage efficiency, until in 1998 Professor Thomas Hales and Samuel P. Ferguson devised an equation that confirmed it was impossible to achieve greater packing efficiency than 74 per cent and proved the Kepler conjecture. Includes contributions from Adam Spencer (DJ and mathematician), Ian Stewart (University of Warwick), Sam Ferguson (mathematician) and Professor Thomas Hales (mathematician).

Duration

15 mins

Title

Game Theory

Synopsis

This edition considers game theory. Game theory deals with player’s tactics. In any given game, a participant develops a strategy that incorporates their own strengths and goals, and those perceived in their opponent(s). Incomplete information and "bluff" can make things more complicated, and the balance shifts from a purely mathematical approach to one involving greater psychology. In the 1950s, mathematicians such as John Nash started to use these principles to study the economy. Nash focussed on ‘non-zero sum’ games. These occur when all sides can win or lose, unlike traditional ‘zero-sum’ games like poker, where one person’s victory simultaneously heralds the opponent’s defeat. The ‘Nash equilibrium’ occurs when competing strategies achieve a win-win compromise.

In 2000, the UK government received a windfall of around £23 billion from its auction of third generation (3G) mobile phone licences. This astronomical sum wasn’t the result of corporate bidders "losing their heads", but a careful strategy designed by Ken Binmore of University College London to maximise proceeds for the Treasury and bring new blood into the industry. He devised an auction with game rules engineered to achieve the government’s objectives, but which would also generate a ‘Nash equilibrium’ or win-win for all. Critics have argued that the phone companies paid over the odds but Binmore argues that they paid what they knew they could recoup from future profits.

Duration

15 mins

Production Company

Name

BBC Radio 4

Web

http://www.bbc.co.uk/radio4 External site opens in new window