TRANSLATION OF AN ADDRESS GIVEN BY DAVID HILBERT IN KONIGSBERG, FALL
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
ADDRESS BY DAVID HILBERT
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".