Problems and riddles: Hilbert and the du Bois-Reymonds (Q813416)

In Hilbert's celebrated list of problems set in 1900 there can be seen the influence of the two Prussian brothers du Bois-Reymond: Emil, who in a famous 1872 lecture (Ignorabimus, ``we shan't know'' was the common name for the debate it aroused) had argued that there are problems inherently insoluble by physics; and Paul, who in his book of 1882 argued that mathematicians would never resolve basic disagreements about the nature of the continuum. This paper traces connections between the brothers' skepticism and Hilbert's problems, both where the problems essentially call for replies to skeptical arguments, and where they draw limits acknowledging skeptical points.