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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.
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Seven World Riddles
Emil du Bois-Reymond used ignoramus et ignorabimus in discussing what he called seven "world riddles", in a famous 1880 speech before the Berlin Academy of Sciences.
He outlined seven "world riddles", of which three, he declared, neither science nor philosophy could ever explain, because they are "transcendent". Of the riddles, he considered the following transcendental and declared of them ignoramus et ignorabimus: "1. the ultimate nature of matter and force, 2. the origin of motion, ... 5. the origin of simple sensations, a quite transcendent question."
Hilbert's reaction
David Hilbert suggested that such a conceptualization of human knowledge and ability is extremely pessimistic. We can find answers to many of these questions, and by considering them unsolvable, we limit our understanding.
In 1900, in an address to the International Congress of Mathematicians in Paris, Hilbert suggested that answers to the problems of mathematics are possible with human effort. He declared, "In mathematics there is no ignorabimus.", and he worked with other formalists to establish concrete foundations for mathematics in the early 20th century.
On 8 September 1930, Hilbert elaborated on his view in a celebrated address to the Society of German Scientists and Physicians, in Königsberg:
Answers to many of Hilbert's Program of 23 questions have been found in the following hundred years of the 20th century. Some have been shown to be impossible to answer with mathematical rigor. Some have been answered definitively, and a few remain yet open to be solved. For Hilbert's 23 questions, see Hilbert's problems.
Sociological responses
The sociologist Wolf Lepenies has discussed the ignorabimus with a view that du Bois-Reymond was not really retreating in his claims for science and its reach:
— it is in fact an incredibly self-confident support for scientific hubris masked as modesty —This is in a discussion of Friedrich Wolters, one of the members of the literary group "George-Kreis". Lepenies comments that Wolters misunderstood the degree of pessimism being expressed about science, but well understood the implication that scientists themselves could be trusted with self-criticism.