Abstract
THE award of the great Mathematical Prize of the French Academy to the late Prof. H. J. S. Smith may have the effect of drawing the attention of mathematicians to the wonderful extent and value of his researches on the Theory of Numbers. Probaly no more important or remarkable mathematical investigations have ever appeared in this country than his memoirs on systems of linear indeterminate equations and congruences and on the orders and genera of ternary quadratic forms and of quadratic forms containing more than three indeterminates, which were published in the Philosophical Transactions for 1861 and 1867 and the Proceedings of the Royal Society for 1864 and 1867. The results contained in these papers are by far the greatest additions that have been made to the Theory of Numbers since it was placed on its present foundation by Gauss in the “Disquisitiones Arithmeticæ” The subject for which the prize was awarded to Prof. Smith was that of the theory of the representation of a number as a sum of five squares, and of this question as well as that of the corresponding one for seven squares he had given the complete solution in the Proceedings of the Royal Society for 1867 (vol. xvi. p. 207). The words with which Prof. Smith introduced his statement of the solution of these important questions are as follows:—
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PROFESSOR H. J. S. SMITH AND THE REPRESENTATION OF A NUMBER AS A SUM OF SQUARES . Nature 27, 564 (1883). https://doi.org/10.1038/027564a0
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DOI: https://doi.org/10.1038/027564a0