Abstract
In this contribution, we give a historical survey of Hilbert's interpretation of a space-filling Peano curve which Hilbert presented at the Gesellschaft Deutscher Naturforscher und Ärzte session in Bremen in 1890. Since Hilbert was systematically working in the field of number theory in that period, we try to explain the reason for his sudden interest and immediate reaction to Peano's surprising result from the same year which proved the possibility of continuous mapping from a line onto a part of plane.
We argue that by means of his address, he was trying to express his positive view of Cantor's set theory, an affinity which was also present in his selection of the continuum hypothesis as the first problem on his list of mathematical problems for the 20th century and which also led his thinking long afterwards in the 1920s while working on Hilbert's programme in logic.