ignoramus et ignorabimus

The Latin maxim ignoramus et ignorabimus, meaning "we do not know and will not know", stood for a position on the limits of scientific knowledge, in the thought of the nineteenth century. It was given credibility by Emil du Bois-Reymond, a German physiologist, in his Über die Grenzen des Naturerkennens ("On the limits of our understanding of nature") of 1872.

On the 8th of September 1930, the mathematician David Hilbert pronounced his disagreement in a celebrated address to the Society of German Scientists and Physicians, in Königsberg:

We must not believe those, who today, with philosophical bearing and deliberative tone, prophesy the fall of culture and accept the ignorabimus. For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: Wir müssen wissen — wir werden wissen! ('We must know — we will know!')

Hilbert worked with other formalists to establish concrete foundations for mathematics in the early 20th century. However, Gödel's incompleteness theorems showed in 1931 that no finite system of axioms, if complex enough to express our usual arithmetic, could ever fulfill the goals of Hilbert's program, demonstrating many of Hilbert's aims impossible, and establishing limits on mathematical knowledge.