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Bunyakovsky published over 150 works on mathematics and mechanics. He is best known for his discovery of the Schwarz inequality, published in a monograph in 1859, 25 years before Schwarz.
His work in number theory was important and he gave a new proof of Gauss's law of quadratic reciprocity. Dickson, in his book on the history of number theory, gives 40 references to papers of Bunyakovsky.
Bunyakovsky also worked on geometry, applied mechanics and hydrostatistics. In 1853 he examined Euclid's fifth postulate, giving a critical account of previous attempts to prove it. He then attempted his own proof, unaware that Lobachevsky had invented non-euclidean geometry 25 years before and, although it was published, it had been rejected by Ostrogradski when it had been submitted for publication in the St Petersburg Academy of Sciences.
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