... conjecture¹

The Goldbach conjecture says that every even number greater than 3 is the sum of two prime numbers: 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 5 + 5, 12 = 5 + 7, etc.

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... revolution²

For a good debate as to whether revolutions are possible in mathematics read [#!Gil92!#].

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... sets³

The number 0 can be defined as the empty set . 1 is a set with a single element and in general . In this system all the sets are built up from the empty set using more and more brackets, but this is enough to do arithmetic.

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... magic⁴

One who appeared to believe in such magic powers was Hegel: in 1800 he argued, on the basis of philosophy alone, that the number of planets could not be other than seven. It was simply bad luck that in the following year the eighth planet, Ceres, was discovered.

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