The following is a translation of an address given by David Hilbert at the meeting of the Society of German Scientists and Physicians in Konigsberg in fall 1930, on the occasion of presentation to Hilbert (upon his retirement) of an honorary citizenship of the town. Reidemeister and Szego made arrangements for Hilbert to repeat the last part of his speech over the local radio station; a record of this talk pronounced at the broadcasting studio exists and was recently acquired by Victor Katsnelson. He kindly supplied his colleague Victor Vinnikov with the transcript of Hilbert's address, which was then diligently translated to English by Amelia and Joe Ball.

For more details on Hilbert's address and surrounding circumstances, see Constance Reid's book "Hilbert", Chapter 22. For the German original of the address, please contact Victor Vinnikov


The tool implementing the mediation between theory and practice, between thought and observation, is mathematics. Mathematics builds the connecting bridges and is constantly enhancing their capabilities. Therefore it happens that our entire contemporary culture, in so far as it rests on intellectual penetration and utilization of nature, finds its foundations in mathematics.

Already some time ago Galileo said "Only one who has learned the language and signs in which nature speaks to us can understand nature."

This language however is mathematics, and these signs are the figures of mathematics.

Kant remarked "I maintain that, in any particular natural science, genuine scientific content can be found only in so far as mathematics is contained therein."

In fact we do not have command of a scientific theory until we have peeled away and fully revealed the mathematical kernel. Without mathematics, modern astronomy and physics would be impossible. The theoretical parts of these sciences almost dissolve into branches of mathematics. Mathematics owes its prestige, to the extent that it has any among the general public, to these sciences along with their numerous broader applications. Although all mathematicians have denied it, the applications serve as the measure of worth of mathematics.

Gauss speaks of the magical attraction which made number theory the favorite science of the first mathematician---not to mention the inexhaustible richness of number theory which far surpasses that of any other field of mathematics.

Kronecker compares number theorists with the lotus eaters, who, once they started eating this food, could not let go of it.

The great mathematician Poincare once sharply disagreed with Tolstoy's declaration that the proposition "science for the sake of science" would be silly.

The achievements of industry for example would not have seen the light of the world if only applied people had existed and if uninterested fools had failed to promote these achievements.

The honor of the human spirit, so said the famous Konigsburg mathematician Jacobi, is the only goal of all science. We ought not believe those who today, with a philosophical air and reflective tone, prophesy the decline of culture, and are pleased with themselves in their own ignorance. For us there is no ignorance, especially not, in my opinion, for the natural sciences.

Instead of this silly ignorance, on the contrary let our fate be: "We must know, we will know".