and Oslo, an Associate of the Institute of France, and a Member of the Pontifical Academy of Sciences, Nazionale dei Lincei, Madrid, Naples, Boston. He was awarded the title of Baron by King Albert 1 of the Belgians in 1928. In 1961, de la Vallée Poussin fractured his shoulder, and this accident and its complications led to his death in Watermael-Boitsfort, near Brussels, Belgium, a few months later. A student of his, Georges Lemaître, was the first to propose the Big Bang theory of the formation of the Universe. Work Although his first mathematical interests were in analysis, he became suddenly famous as he proved the prime number theorem independently of his coeval Jacques Hadamard in 1896. Afterwards, he found interest in approximation theory. He defined, for any continuous function f on the standard interval , the sums , where and are the vectors of the dual basis with respect to the basis of Chebyshev polynomials (defined as Note that the formula is also valid with being the Fourier sum of a -periodic function such that Finally, the de la Vallée Poussin sums can be evaluated in terms of the so-called Fejér sums (say ) The kernel is bounded () and obeys the property , if Later, he worked on potential theory and complex analysis. He also published a counterexample to Alfred Kempe's false proof of the four color theorem. The Poussin graph, the graph he used for this counterexample, is named after him. Cours d’analyse The textbooks of his mathematical analysis course have been a reference for a long time and had some international influence. The second edition (1909-1912) is remarkable for its introduction of the Lebesgue integral. It was in 1912, "the only textbook on analysis containing both Lebesgue integral and its application to Fourier series, and a general theory of approximation of functions by polynomials". The third edition (1914) introduced the now classical definition of differentiabilily due to Otto Stolz. The second volume of this third edition was burnt in the fire of Louvain during the German invasion. The further editions were much more conservative, returning essentially to the first edition. Starting from the eight edition, Fernand Simonart took over the revision and the publication of the Cours d’analyse. Selected publications Œuvres, vol. 1 (Biography and number theory), 2000 (eds. Mawhin, Butzer, Vetro), vols. 2 to 4 planned Cours d´Analyse, 2 vols., 1903, 1906 (7th edition 1938),