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Math Trek

How to (really) trust a mathematical proof

Mathematicians develop computer proof-checking systems in order to realize century-old dreams of fully precise, accurate mathematics.

3:32pm, November 14, 2008

The one source of truth is mathematics. Every statement is a pure logical deduction from foundational axioms, resulting in absolute certainty. Since Andrew Wiles proved Fermat’s Last Theorem, you’d be safe betting your life on it.

Well … in theory. The reality, though, is that mathematicians make mistakes. And as mathematics has advanced, some proofs have gotten immensely long and complex, often drawing on expertise from far-flung areas of math. Errors can easily creep in. Furthermore, some proofs now rely on computer code, and it’s hard to be certain that no bug lurks within, messing up the result.

Bet your life on Wiles’ proof of Fermat? Many mathematicians might decline.

Still, the notion that mathematical statements can be deduced from axioms isn’t hooey. It’s just that mathematicians don’t spell out every little step. There’s a reason for that: When Bertrand Russell and Alfred North Whitehead tried

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