Lately I've been thinking about number theory, Hilbert's program, and arithmetic. And I've been wondering if the axioms of arithmetic constitute a mathematical description of the cognitive processes underlying arithmetic. Hilbert's program was simply (although it wasn't simple) an effort to formalize mathematics in axiomatic form and to show the consistency of the system. Godel threw a bomb into the effort with his Incompleteness theorem.
A more thorough and better description of Hilbert's program is available at The Stanford Encyclopedia of Philosophy - Hilbert's Program.
Today's tags: math, mathcog