prize as diffraction. One of the participants, civil engineer and opticist Augustin-Jean Fresnel submitted a thesis explaining diffraction derived from analysis of both the Huygens–Fresnel principle and Young's double slit experiment. Poisson studied Fresnel's theory in detail and looked for a way to prove it wrong. Poisson thought that he had found a flaw when he demonstrated that Fresnel's theory predicts an on-axis bright spot in the shadow of a circular obstacle blocking a point source of light, where the particle-theory of light predicts complete darkness. Poisson argued this was absurd and Fresnel's model was wrong. (Such a spot is not easily observed in everyday situations, because most everyday sources of light are not good point sources.) The head of the committee, Dominique-François-Jean Arago, performed the experiment. He molded a 2 mm metallic disk to a glass plate with wax. To everyone's surprise he observed the predicted bright spot, which vindicated the wave model. Fresnel won the competition. After that, the corpuscular theory of light was dead, but was revived in the twentieth century in a different form, wave-particle duality. Arago later noted that the diffraction bright spot (which later became known as both the Arago spot and the Poisson spot) had already been observed by Joseph-Nicolas Delisle and Giacomo F. Maraldi a century earlier. Pure mathematics and statistics In pure mathematics, Poisson's most important works were his series of memoirs on definite integrals and his discussion of Fourier series, the latter paving the way for the classic researches of Peter Gustav Lejeune Dirichlet and Bernhard Riemann on the same subject; these are to be found in the Journal of the École Polytechnique from 1813 to 1823, and in the Memoirs de l'Académie for 1823. He also studied Fourier integrals. Poisson wrote an essay on the calculus of variations (Mem. de l'acad., 1833), and memoirs on the probability of the mean results of observations (Connaiss. d. temps, 1827, &c). The Poisson distribution in probability theory is named after him. In 1820 Poisson studied integrations along paths in the complex plane, becoming the first person to do so. In 1829, Poisson published a paper on elastic bodies that contained a statement and proof of a special case of what became known as the divergence theorem. Mechanics Analytical mechanics and the calculus of variations Founded mainly by Leonhard Euler and Joseph-Louis Lagrange in the eighteenth century, the calculus of variations saw further