Geodesic
The Complexity Of Nowhere Differentiable Continuous Functions
Canadian journal of mathematics, Tome 41 (1989) no. 1, pp. 83-105

Voir la notice de l'article provenant de la source Cambridge University Press

It was not always clear that there could exist a continuous function which was differentiable at no point. (Such functions are now known as nowhere differentiable continuous functions. By “differentiable” we mean having a finite derivative.) In fact in 1806 M. Ampere [2] even tried to show that no such function could exist but his reasonings were later discovered to be fallacious. Of the early attempts at constructing a nowhere differentiable continuous function mention must be made of B. Bolzano. In a manuscript dated around 1830, (see [21]) he constructed a continuous function on an interval and showed that it was not differentiable on a dense set of points. (It was later shown by K. Rychlik [21] that this function was in fact nowhere differentiable.) 
Ramsamujh, T. I. The Complexity Of Nowhere Differentiable Continuous Functions. Canadian journal of mathematics, Tome 41 (1989) no. 1, pp. 83-105. doi: 10.4153/CJM-1989-004-9
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