Bewildering discontinuity

Breaking with the search for regularity in scientific phenomena, the interest in discontinuous functions suddenly appeared at the beginning of the 19th century with the study of Fourier series. Greater rigor was then imposed to define the concepts of function, continuity, differentiability. Riemann, Lebesgue, Darboux and others proposed examples of monstrous functions to justify the interest in the theories they had developed, opening the field to new approaches in physics and even economics.

Georg Cantor and his set theory shook the foundations of mathematics by highlighting circular reasoning, that is to say, self-referential. At the turn of the 20th century, his paradoxes emerged under the pen of Burali-Forti, Russell and Richard, throwing Frege into dismay. Kurt Gödel showed that certain assertions cannot be proved or disproved within a given axiomatic framework, bringing a negative answer to a famous problem posed by Hilbert. Self-reference is also found in literature, painting, sculpture and… in the press where, intentional or not, it makes us smile.