Exploring Randomness

Notices of the AMS 48 (9):992-6 (2001)
Abstract
In the early twentieth century two extremely influential research programs aimed to establish solid foundations for mathematics with the help of new formal logic. The logicism of Gottlob Frege and Bertrand Russell claimed that all mathematics can be shown to be reducible to logic. David Hilbert and his school in turn intended to demonstrate, using logical formalization, that the use of infinistic, set-theoretical methods in mathematics—viewed with suspicion by many—can never lead to finitistically meaningful but false statements and is thus safe. This came to be known as Hilbert’s program.
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