A Brilliant Failure

Early in the twentieth century, a group of mathematicians led by Bertrand Russell and Alfred North Whitehead set out to do something amazing; they wanted to build a complete formalization of mathematics. They started with nothing but the most basic axioms of set theory and then tried to build up the complete edifice of mathematics as one system, published as the Principia Mathematica. The system described in Principia would have been the ultimate perfect mathematics! In this system, every possible statement would be either true or false: every true statement would be provably true, and every false statement would be provably false.

This should give you a sense of just how complex the Principia system was: it took Whitehead ...

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