This was disproved by Paul du Bois-Reymond, who showed in 1876 that there is a continuous function whose Fourier series diverges at one point.
Paul Du Bois (1859–1938) was a Belgian sculptor and medalist, born in Aywaille, and died in Uccle.
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Among his most famous monumental works, located in Brussels, are the monument to Frederic de Merode, and the tribute to Edith Cavell and fellow nurse Marie Depage (of the RMS Lusitania), the Four Elements group in the Botanical Garden of Brussels, and several sculptures in the City of Saint-Gilles.
His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere.
Under the influence of Weierstrass and Bernhard Riemann this concept and related questions were intensely studied at the end of the 19th century by Hermann Hankel, Paul du Bois-Reymond, Ulisse Dini, Cesare Arzelà and others.
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In 1883, Wytsman was a founding member of "Les XX", the famous avant-garde group in Brussels, inspired by the figure of Octave Maus, and founded by Frantz Charlet, Jean Delvin, Darío de Regoyos, Paul Du Bois, James Ensor, Willy Finch, Charles Goethals, Fernand Khnopff, Pericles Pantazis, Frans Simons, and Théodore Verstraete.