Basic rules of arithmetic may be broken AUG 18 2010
And not just broken but unrepairable without the addition of uncertainty. Gödel's incompleteness theorems aren't even the half of it.
With Friedman's work, it seems Gödel's delayed triumph has arrived: the final proof that if there is a universal grammar of numbers in which all facets of their behaviour can be expressed, it lies beyond our ken.
But don't worry..."the most severe implications are philosophical". Phew?