Home > David Hilbert
2 Miscellaneous talks, essays, and contributions
Hilbert presented the paradox of the Grand Hotel, a musing about strange properties of the infinite.
He put forth an influential list of 23 unsolved problems in the Paris conference of the International Congress of Mathematicians in 1900.
Additionally, Hilbert is responsible for assisting several advances in the mathematics of quantum mechanics. These include his integral calculations of Hilbert spaces and proving the mathematical equivalency of Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation.
2.1 Hilbert's program
In 1920 he proposed explicitly a program (in metamathematics, as it was then termed) that became known as Hilbert's program. He wanted mathematics be formulated on a solid and complete logical foundation by showing that:
- all of mathematics follows from a finite system of axioms; and
- that that axiom system is consistent.
There seem to have been both technical and psychological reasons why he came out with this proposal. It affirmed his dislike of what had become known as the ignorabimus, still an active issue in his time in German thought, and traced back in that formulation to Emil du Bois-Reymond.
This program is still recognisable in the most popular philosophy of mathematics, amongst working mathematicians that is, usually called formalism. For example, the Bourbaki group adopted a milk-and-water version of it as adequate to the requirements of the twin projects of (a) writing encyclopedic foundational works, and (b) supporting the axiomatic method as a research tool.
Gödel's incompleteness theorem showed, however, in 1931 that Hilbert's grand plan was impossible, as stated. The point 2 cannot in any reasonable way be combined with the point 1.
3 Further reading
4 External links
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Hilbert, David
Hilbert, David
Hilbert, David
Hilbert, David
Hilbert, David
