They hire better-qualified teachers, and more of them, offering higher salaries to lure those with qualifications in difficult subjects such as physics, mathematics and foreign languages, and now have twice as many teachers per pupil as state schools do.

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To teach cleaners and nightwatchmen advanced mathematics (such as adding up without a calculator) seemed pretty wasteful, and apt to breed discontent.

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Dr Irwing told The Times the differences "may go some way to explaining the greater numbers of men achieving distinctions of various kinds, such as chess grandmasters, Fields medallists for mathematics, Nobel prize-winners and the like".

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Those with experience and education particularly in fields such as science, technology, engineering, and mathematics have the edge because they can work across disciplines and see the big picture.

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Formal proof is a notion developed in the early part of the 20th century by logicians such as Bertrand Russell and Gottlob Frege, along with mathematicians such as David Hilbert (who can fairly be described as the father of modern mathematics) and Nicolas Bourbaki, the pseudonym of a group of French mathematicians who sought to place all of mathematics on a rigorous footing.

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The report said that for more selective universities, such as those in the Russell Group who tend to ask for higher A-level grades, mathematics requirements can be a useful filtering tool.

BBC: Universities 'dumbing down on maths' to fill places

While India is producing huge numbers of mathematics, physics and chemistry graduates British numbers are falling, being replaced with soft subjects such as media studies.

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