Smith's two earliest mathematical papers were on geometrical subjects, but the third concerned the theory of numbers. Following the example of Gauss, he wrote his first paper on the theory of numbers in Latin: "De compositione numerorum primorum formæ ex duobus quadratis." In it he proves in an original manner the theorem of Fermat---"That every prime number of the form ( being an integer) is the sum of two square numbers." In his second paper he gives an introduction to the theory of numbers.
Smith's two earliest mathematical papers were on geometrical subjects but the third concerned the theory of numbers. Following the example of Gauss, he wrote his first paper on the theory of numbers in Latin: "De compositione numerorum primorum formæ ex duobus quadratis." In it he proves in an original manner the theorem of Fermat---"That every prime number of the form ( being an integer) is the sum of two square numbers." In his second paper he gives an introduction to the theory of numbers.