A History of Mathematics

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That night we slept no more. " His reply to Huxley is interesting reading and bears strongly on the qualities of mental activity involved in mathematical research. In 1859 he gave lectures on partitions, not published until 1897. He wrote on partitions again in Baltimore. In 1S64 followed his famous proof of Newton's rule. A certain fundamental theorem in invariants which had formed the basis of an important section of A. Cayley's work, but had resisted proof for a quarter of a century was demo...n- strated by Sylvester in Baltimore. Noteworthy are his memoirs on Chebichev's method concerning the totality of prime numbers within certain limits, and his latent roots of matrices. His researches on invariants, theory of equations, multiple algebra, theory of numbers, linkages, probability, constitute important contributions to mathe- matics. His final studies, entered upon after his return to Oxford, were on reciprocants or functions of differential coefficients whose form is unaltered by certain linear transformations of the variables, and a generahzation of the theory of concomitants.

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