Bernhard Riemann, a German mathematician, submits his habilitation thesis Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe ("About the representability of a function by a trigonometric series"), in which he describes the Riemann integral. It is published by Richard Dedekind in 1867.
Medicine
April–May – Dr John Snow traces the source of one outbreak of cholera in London (which kills 500) to a single water pump, validating his theory that cholera is water-borne, and forming the starting point for epidemiology.
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