>Since posting my query, I have done a little research and found evidence >that casts some doubt on the idea that Smith originated this saying: > >"Carried to an extreme, the eulogy of such men and their work is expressed >in the toast of the Mathematical society of England: 'Pure mathematics; >may it never be of use to any man!" > Science, 10 Dec. 1886, p. 543 > >It is possible that the Mathematical Society got its toast from Smith, but >in the absence of further evidence this is speculative. > >Fred Shapiro
I think this can be disregarded. It seems to be either a misunderstanding or a deliberate exaggeration by the speaker (who is a physician arguing for emphasis on the practical applications of science).
Here are the reasons for this conclusion.
There is (and was) no English organization called just the "Mathematical society"; what must be meant is the London Mathematical Society, which first met in 1865. Smith was one of those who joined in that first year; but so was James Clerk Maxwell, mainly (in modern terms) a physicist. Similarly, Smith was president of the LMS in 1874-76; but he was immediately succeeded by Lord Rayleigh, whom everyone would call a physicist (in 1904, he was co-winner of the Nobel Prize in Physics for the discovery of argon). Thus applied mathematics was part of the LMS from the beginning, and so it is very unlikely that the LMS as a body would have adopted such a slogan.