Berry's Paradox
"The smallest number that cannot be described in fewer than twelve words." That description is eleven words long.
1906 (published by Russell, crediting Berry); communicated c. 190419 min read
Algorithmic information theory
Gregory Chaitin
1947
Argentine-American mathematician and computer scientist, one of the independent founders of algorithmic information theory alongside Kolmogorov and Solomonoff. His 1974 incompleteness theorem turns Berry's paradox into a precise limit: no consistent formal system can prove that any specific string has complexity much greater than the system's own description.