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The future of proof

The use of computers means that modern mathematical proofs can run to millions of pages. Such proofs can never be fully verified by humans alone. Does this mean, as some argue, the death of proof?

By Ian Stewart   March 2007

The year: 1611. The person: Johannes Kepler, mathematician and astrologer. The problem: Kepler wanted to give his sponsor, John Matthew Wacker, a new year’s present, but was short of cash. The solution: he wrote a book and dedicated it to Wacker. The work was Strena Seu de Nive Sexangula (“On the Six-Cornered Snowflake”); it discussed the puzzling tendency of snowflakes to form beautiful tree-like shapes with approximate sixfold symmetry.

We now know that these shapes—and many others that snowflakes can take—are the result of crystal growth in the presence of varying temperature and humidity, up above in the storm clouds.…

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