Marek Jarnicki and Petter Pug, Continuous nowhere differentiable functions. The monsters of analysis, Springer Monographs in Mathematics, Springer - Cham, Heidelberg, New York, Dordrecht, London, 2015, xii+299 p., ISBN 978-3-319-12669-2/hbk; 978-3-319-126

Abstract

After Newton put the basis of the differential calculus and applied it to the study the physical world, there was a general belief between mathematicians that a continuous function must be differentiable excepting a finite number of points. The famous mathematician and physicist A.-M. Ampere even published a proof of this result (based on some intuitively justified geometric reasonings on the behavior of curves) which was generally accepted by the mathematical community and included in almost every calculus book of that time.