Finite simple groups are the building blocks of finite symmetry.
The effort to classify them precipitated the discovery of new examples, including the monster, and six pariah groups which do not belong to any of the natural families, and are not involved in the monster.
"Composers took Bach as their bedrock," he says, "whether it's Beethoven, Mozart, Schumann or Chopin."I don't think there was a day when Chopin wasn't playing Bach.
When Schumann went into depression, he wrote fugues, and he always told his wife, Clara, to study Bach.
The defiant figure in Pariah wears an indigenous amulet and has wavy black hair that suggests African ancestry.
Dimas depicted his monumental figure using a range of paintings styles associated with abstract art that flourished in New York during and after the 1950s.
You can use a certain amount of pedalling - not overdone - because that's part of the piano."And the sense of direction is important even in Bach. That's what fascinates me about music." The Big Short, the film adaptation of Michael Lewis' book of the same name about the causes of the financial crisis, opens in UK cinemas this weekend.
How will the story stack up against the greatest films about business?
As we approach a vote on the UK's membership of the European Union, we look at what 50 writers, actors, historians, artists and comedians have said about Europe and its nations.It was an important part of their musical make-up."Perahia's teenage studies at Mannes College of Music in New York gave him a firm foundation for the way he approached Bach, forging a link with the great Austrian theorist Heinrich Schenker, who died in 1935."All his former students were teaching there, having escaped the Nazis," Perahia says, "and I'm very much influenced by his thinking.When I was away from the concert platform, I was reading his books, and I felt that I was in touch with something deeper about what music is about.What do you do when fate delivers a nasty blow and there is the grim prospect of never being able to play again?This is the situation that Murray Perahia had to face in the Nineties, when an inexplicable and agonising swelling in his right thumb compelled him to put on hold an illustrious career that had been blossoming ever since he won the Leeds Piano Competition in 1972.