David Hilbert (1862-1943), a mathematician from the University of Goettingen, launched his program during an address to the International Congress of Mathematicians in the summer of 1900. Hilbert contended that all mathematical principles, or axioms, should be derived from first-order statements, with the logic of deduction and reasoning leading to final conclusions regarding the problem at hand. Using this methodology, the foundations of mathematics could be developed exactly and with certainty; these fundamental axioms would form the basis for all other research into the varied branches of mathematics. In his address, Hilbert famously outlined 23 "unsolved problems" that he characterized as both interesting and important for further study in the coming century. Hilbert hoped that his "program" of formalism would be applied to each.

Hilbert's program, as his initiative as come to be called, was a call to the mathematics community to formalize the basic tenets of the...