In
mathematics,
Hilbert's program, formulated by
German mathematician
David Hilbert, was a proposed solution to the
foundational crisis of mathematics, when early attempts to clarify the
foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of
axioms, and provide a proof that these axioms were
consistent. Hilbert proposed that the consistency of more complicated systems, such as
real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic
arithmetic.