SPIRITUAL AI

Hilbert, Gödel, and Turing In the 1920s, David Hilbert (left) wanted to put mathematics on firmer foundations. Kurt Gödel (center) and Alan Turing later showed that Hilbert’s dream was impossible.  The impact of Gödel's and Turing's breakthroughs in the 1930s is best understood against the background of the mathematical ambitions definitively expressed by David Hilbert in the 1920s (though foreshadowed in a famous address that he gave in 1900). Hilbert – founder of the "formalist" approach in Philosophy of Mathematics – advocated in 1921 that researchers' primary aim should be to establish mathematics on a solid and provably consistent foundation of axioms, from which, in principle, all mathematical truths could be deduced (by the standard methods of first order or "predicate" logic). Then in 1928 he formulated his Entscheidungsproblem or "decision problem": could an effective procedure be devised which would demonstrate – in a fini