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Later, Fresnel independently worked out his own wave theory of light and presented it to the Académie des Sciences in 1817. Siméon Denis Poisson added to Fresnel's mathematical work to produce a convincing argument in favor of the wave theory, helping to overturn Newton's corpuscular theory. By the year 1821, Fresnel was able to show via mathematical methods that polarization could be explained by the wave theory of light if and only if light was entirely transverse, with no longitudinal vibration whatsoever.[citation needed]