Henry John Stephen Smith: Proposal

“We must confine ourselves to what we may term the great highways of the science; and… we must wholly pass by many outlying researches of great interest and importance, as we propose rather to exhibit in a clear light the most fundamental and indispensable theories, than to embarrass the treatment of a subject, already sufficiently complex, with a multitude of details, which, however important in themselves, are not essential to the comprehension of the whole.”

Henry John Stephen Smith

Report on the Theory of Numbers (1859) Part I, p. 39.
The Collected Mathematical Papers of Henry John Stephen Smith (1894) Vol. 1

Light , Science

“So intimate is the union between Mathematics and Physics that probably by far the larger part of the accessions to our mathematical knowledge have been obtained by the efforts of mathematicians to solve the problems set to them by experiment, and to create for each successive class phenomena a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature. Sometimes the mathematician has been before the physicist, and it has happened that when some great and new question has occurred to the experimentalist or the observer, he has found in the armory of the mathematician the weapons which he needed ready made to his hand. But much oftener, the questions proposed by the physicist have transcended the utmost powers of the mathematics of the time, and a fresh mathematical creation has been needed to supply the logical instrument requisite to interpret the new enigma.”

Henry John Stephen Smith

As quoted in The Century: A Popular Quarterly (1874) ed. Richard Watson Gilder, Vol. 7, pp. 508-509, https://books.google.com/books?id=ceYGAQAAIAAJ&pg=PA508 "Relations of Mathematics to Physics". Earlier quote without citation in Nature, Volume 8 (1873), page 450.
Also quoted partially in Michael Grossman and Robert Katz, Calculus http://babel.hathitrust.org/cgi/mb?a=listis;c=216746186|Non-Newtonian (1972) p. iv. ISBN 0912938013.

Mathematics , Question , Nature , Knowledge

“The problem of the direct determination of the primitive roots of a prime number is one of the 'cruces' of the Theory of Numbers. Euler, who first observed the peculiarity of these numbers, has yet left us no rigorous proof of their existence; though assuming their existence, he succeeded in accurately determining their number. The defect in his demonstration was first supplied by Gauss, who has also proposed an indirect method for finding a primitive root.”

Henry John Stephen Smith

Report on the Theory of Numbers (1859) Part I, p. 49.
The Collected Mathematical Papers of Henry John Stephen Smith (1894) Vol. 1

Problem