Mathematicians develop computer proof-checking systems in order to realize century-old dreams of fully precise, accurate mathematics.
Julie Rehmeyer in Science News:
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 to do so for just the most elementary parts of mathematics, they produced a 2,500-page tome. The result was so difficult to understand that Russell admitted to a friend, “I imagine no human being will ever read through it.”
Where humans falter, computers can sometimes prevail. A group of mathematicians and computer scientists believe that with new proof-validation programs, the dream of a fully spelled-out, rigorous mathematics, with every deduction explicit and correct, can be realized.