1. History

The history of harmonic analysis and harmonic series is, in itself, a condensed history of mathematics, since it has involved most of the great mathematicians since the eighteenth century, and gradually forced them to define precisely what were for them intuitive elements, such as functions, continuity, numbers, etc. In addition, it touches on extremely delicate points, but proved crucial when they were highlighted, such as uniform continuity, infinity and integration. In addition, it touches on points that are extremely delicate, but proved crucial when they were highlighted, such as uniform continuity, infinity and integration. Numerous debates have arisen from different points of view on these subjects. To a modern mathematician, living in a world entirely defined by the "refounding" work of the turn of the century, these quarrels may seem a little strange, but it was they that gave rise...