Beautiful Math

Der Guardian hat einen sehr schönen Artikel über die Schönheit der Mathematik (uh!) und über genau das, was ich damals auch so anziehend an Mathe fand: Irreelle Zahlen. Die Wurzel aus -1. Das Konzept der Unendlichkeit. Bei sowas werd' ich wach.

Hardy writing about being a mathematician: "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." Later he writes: "The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics."

For Hardy, mathematics seemed to be a subject with a sense of aesthetics. His book contained two proofs. Like playing a delicate mathematical minuet, he explained the ancient Greeks' discovery that there are infinitely many primes. It was a revelation that one could prove with such a simple piece of logical reasoning that these indivisible numbers with no discernible pattern spiral off to infinity. That our finite minds could master the infinite was inspiring. Here was the power of analytical thinking to get you to new places, new discoveries, new knowledge.

The other proof he explained was the discovery that the square root of 2 cannot be written as a fraction, another proof for which the ancient Greeks were responsible. It led to the creation of a whole new sort of number called irrational numbers. Mathematics is full of these extraordinary moments of creativity and discovery, breakthroughs that have had an impact on understanding the world we live in.

The creation of a number whose square is -1 seems a moment of absurdity, but led to the maths that allows us to formulate quantum physics.

The secret life of numbers (via Digg)