David Hilbert's Radio Broadcast

Königsberg, 8 September 1930

The tool that serves as intermediary between theory and practice, between thought and observation, is mathematics. She builds the linking bridges, and gives them ever more reliable forms. Thus, it has come about that our contemporary culture, inasmuch as it is based on intellectual elucidation and the practical exploitation of nature, has its foundations in mathematics.

Already Galileo declared: "To understand nature, we must learn the language and the signs through which nature speaks to us." But this language is mathematics, and these signs are mathematical figures!

Kant pronounced: "I assert that, in every particular natural science, one encounters intrinsically scientific substance only to the extent that mathematics is present." Indeed, we do not master a scientific theory until we have shelled and completely pried free its mathematical kernel. Without mathematics, the astronomy and physics of today would be impossible. These sciences, in their theoretical branches, virtually dissolve into mathematics. They, along with the many other applications, are responsible for whatever esteem mathematics enjoys with the general public.

Nevertheless, all mathematicians have refused to accept applications as valid measure of the worth of mathematics. Gauss speaks of the magical attraction that made number theory the darling discipline of the earliest mathematicians. Not to mention number theory's inexhaustible wealth, so far surpassing that of any other branch of mathematics. Kronecker likens number theorists to the lotus eaters, who, having once savored this delight, could never give it up.

To Tolstoy, who had declared the pursuit of 'Science for the sake of Science' to be 'foolish', the great mathematician Poincaré replied with unusual sharpness, noting that the triumphs of industry, for example, would never have seen the light of day, if only practical men had existed, and these triumphs had not been made possible by disinterested 'fools'.

The glory of human intelligence, so said the famous Königsberg mathematician Jacobi, is the one purpose of all science.

We should not believe those who today prophesy the decline of scientific culture. Adopting a philosophical tone and an air of superiority, they smugly accept the concept of the 'unknowable'. For us mathematicians, there is no 'unknowable', and, in my opinion, there is none whatsoever for the natural sciences. In place of this foolish 'unknowable' let our watchword on the contrary be: We must know --- we shall know!

Translation Notes:

  • The term 'unknowable' translates 'Ignorabimus' which is the Latin for 'we shall not know'. It had been discussed in the introduction to Hilbert's 23 problems of 1990. The notion was a theme of the Berlin physiologist Emile du Bois-Reymond (1818-1896). Hilbert was not refering to the newly discovered Heisenberg uncertainty principle in quantum physics, which Einstein was refusing to believe. Gödel's epoch-making incompleteness theorem was to be submitted for publication a few months after this radio address.
  • Hilbert's closing jab at the negativism of the 'Ignorabimus' theme seemed anachronistic to this translator in 1995. I was wrong; it is a theme that has been lurking; see for example the 1996 book "The End of Science, Facing the limits of Knowlege in the Twilight of the Scientific Age", John Horgan, Helix Books, Addison Wesley, 1996, reviewed by D. Hoffman in Notices AMS 45(Feb. 1998), 260--266. As proof that such views may dominate, consider the muted role of science during the 500 years of Roman hegemony.
  • The above fairly free translation evolved by successive approximations. A paraphrase of some corresponding parts of the longer address appeared in Constance Reid's 1969 book "Hilbert". In late 1995, remarking on the poetic quality of the German original, Victor Vinnikov <vinnikov@wisdom.weizmann.ac.il> posted, on the internal e-mail list of MSRI in Berkeley, a first translation by Amelia and Joe Ball <ball@calvin.math.vt.edu> along with a German transcription by V. Katznelson. One of the editors (L.S.) replied with a second translation shortly thereafter. But it was still was not quite right, and Otto Siebenmann <mdhors@inforamp.net> brought to light several remaining misunderstandings. The above is a hopefully a happy synthesis. -- L.S.

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