"Certain cubic and biquadratic problems" the Royal Academy of Sciences of Berlin awarded him the Steiner prize. In February, 1882, Smith was surprised to see in the Comptes rendus that the subject proposed by the Paris Academy of Science for the Grand prix des sciences mathématiques was the theory of the decomposition of integer numbers into a sum of five squares; and that the attention of competitors was directed to the results announced without demonstration by Eisenstein, whereas nothing was said about his papers dealing with the same subject in the Proceedings of the Royal Society. He wrote to M. Hermite calling his attention to what he had published; in reply he was assured that the members of the commission did not know of the existence of his papers, and he was advised to complete his demonstrations and submit the memoir according to the rules of the competition. According to the rules each manuscript bears a motto, and the corresponding envelope containing the name of the successful author is opened. There were still three months before the closing of the concours (1 June 1882) and Smith set to work, prepared the memoir and despatched it in time. Two months after Smith's death, the Paris Academy made their award. Two of the three memoirs sent in were judged worthy of the prize. When the envelopes were opened, the authors were found to be Smith and Minkowski, a young mathematician of Königsberg, Prussia. No notice was taken of Smith's previous publication on the subject, and M. Hermite on being written to, said that he forgot to bring the matter to the notice of the commission. Work on the Riemann integral In 1875 Smith published the important paper on the integrability of discontinuous functions in Riemann's sense. In this work, while giving a rigorous definition of the Riemann integral as well as explicit rigorous proofs of many of the results published by Riemann, he also gave an example of a meagre set which is not negligible in the sense of measure theory, since its measure is not zero: a function which is everywhere continuous except on this set is not Riemann integrable. Smith's example shows that the proof of sufficient condition for the Riemann integrability of a discontinuous function given earlier by Hermann Hankel was incorrect and the result does not hold: however, his result remained unnoticed until much later, having no influence