kottke.org

...is a weblog about the liberal arts 2.0 edited by Jason Kottke since March 1998 (archives). You can read about me and kottke.org here. If you've got questions, concerns, or interesting links, send them along.

Basic rules of arithmetic may be broken

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?

By Jason Kottke    Aug 18, 2010 at 02:46 pm    mathematics

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