Mathematical mysteries: The gentlemen from Basle and the Petersburg Paradox

Just over 220 years have passed since the death of one of the most distinguished mathematicians in history: Daniel Bernoulli, who died on March 17th, 1782. The name of Bernoulli asks for precision since the family from Basle produced no fewer than eight outstanding mathematicians within three generations.

More or LessA new series of More or Less, BBC Radio 4's series devoted to all things numerical, starts on November 12th. Presenter Andrew Dilnot tells Plus about the motivation behind the programme.
Mathematical mysteries: Transcendental meditation

Nineteenth-century German mathematician Leopold Kronecker once said

God created the integers, all the rest is the work of man.

Beyond reasonable doubtIn 1999 solicitor Sally Clark was found guilty of murdering her two baby sons. Highly flawed statistical arguments may have been crucial in securing her conviction. As her second appeal approaches, Plus looks at the case and finds out how courts deal with statistics.
Blast it like Beckham?What tactics should a soccer player use when taking a penalty kick? And what can the goalkeeper do to foil his plans? John Haigh uses Game Theory to find the answers, and looks at his World Cup predictions from last issue.
Safety in numbersToday's digital world with its free flow of information, would not exist without cryptography to guarantee our privacy. Plus meets mathematician, author and broadcaster Simon Singh to find out about the science of secrecy.
Tying it all upTheoretical physicists are searching for a 'Theory of Everything' to reconcile quantum mechanics and relativity - the two great physical theories of the twentieth century. String theory is a current hot favourite, and some of the world's most eminent physicists tell us why.
Mathematical mysteries: The Barber's Paradox

Suppose you walk past a barber's shop one day, and see a sign that says

"Do you shave yourself? If not, come in and I'll shave you! I shave anyone who does not shave himself, and noone else."
This seems fair enough, and fairly simple, until, a little later, the following question occurs to you - does the barber shave himself?

Games, Life and the Game of LifeWhen we finally meet the Martians, John Conway believes they are going to want to talk mathematics. He talks to Plus about his Life game, artificial life and what we will have in common with extraterrestrials.
On the ballIf your team scores first in a football match, how likely is it to win? And when is it worth committing a professional foul? John Haigh shows us how to use probability to answer these and other questions, and explains the implications for the rules of the game.
Going with the flowFluid mechanics is the study of flows in both liquids and gases, and is therefore enormously important in understanding many natural phenomena, as well as in industrial applications. Geophysicist Herbert Huppert tells us what happens when two fluids of different densities meet, for example when volcanos erupt and hot ash-laden air is poured out into the atmosphere.
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

  • The BloodCounts! project is gearing up towards one of the largest-scale applications yet of machine learning in medicine and healthcare.

  • What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.

  • Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!

  • How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?

  • Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.