Miscellaneous

The instrument that brings about mediation between theory and practice, between thought and observation, is mathematics; it builds the connecting bridge and makes it ever more capable of bearing weight. Hence our entire present-day culture, insofar as it rests upon the intellectual understanding of nature and the harnessing of its powers, finds its foundation in mathematics.

Galileo already says: Only those who have learned its language and the signs through which it speaks to us can understand nature; this language, however, is mathematics, and its signs are mathematical figures. 

Kant made the statement: “I maintain that in every particular natural science, only as much genuine science can be found as there is mathematics contained in it.” Indeed: we do not master a theory of natural science until we have extracted its mathematical core and fully laid it bare.

Without mathematics, present-day astronomy and physics are impossible; these sciences, in their theoretical parts, resolve themselves into mathematics.
It is to these, as well as to its numerous other applications, that mathematics owes its esteem, insofar as it enjoys such esteem among the wider public.

Nevertheless, all mathematicians have refused to let applications count as a measure of value for mathematics. Gauss speaks of the enchanting appeal that has made number theory the favorite science of the foremost mathematicians, not to mention its inexhaustible richness, in which it so far surpasses all other parts of mathematics.

Kronecker compares number theorists to the Lotus Eaters, who, once they have partaken of this food, can never again leave it alone. The great mathematician Poincaré once turns with striking sharpness against Tolstoy, who had declared that the call for “science for science’s sake” was foolish.

The achievements of industry, for example, would never have seen the light of day if practitioners alone had existed and if these achievements had not been advanced by disinterested fools. The glory of the human mind, so said the celebrated Königsberg mathematician Jacobi, is the sole purpose of all science.

We must not believe those who today, with a philosophical air and a tone of superiority, prophesy the downfall of culture and take satisfaction in the Ignorabimus. For us there is no Ignorabimus, and in my opinion none for natural science at all. In place of the foolish Ignorabimus, let our motto, on the contrary, be:

We must know,
We will know.

I believe this motto still holds today.

The above is an english translation of the German transcript from https://smith-at-sfsu.net/Documents/HilbertRadio/HilbertRadio.pdf.