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Topic: [HM] Quotations from Godel
Replies: 21   Last Post: May 5, 2005 5:23 PM

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James A Landau

Posts: 217
Registered: 12/3/04
Re: [HM] "Pure Mathematics" Quote
Posted: Oct 7, 2004 5:25 PM
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In a message dated Tue, 5 Oct 2004 16:48:14 -0400 (EDT), Fred Shapiro
<> asks:
> Can anyone help me find the earliest evidence of the following quotation:
> Pure mathematics, may it never be of any use to anyone.
> Henry John Stephen Smith, quoted in Howard Eves, Mathematical
> Circles Squared (1972)

I haven't found the exact quote, but I've found similar sayings attributed to

Paul Hoffman _The Man Who Loved Only Numbers_ New York: Hyperion, 1998, ISBN
0-7868-6362-5, page 162
<begin quote>
many of the brightest minds in mathematics have prided themselves on doing
math that has no applications. Math for math's sake was the rallying cry. They
feared real world relevance might distract from the pristine order and beauty
that mathematics laid bare. When Euclid was investigating prime numbers, he
was proud that they contributed nothing practical to Greek life. G. H. Hardy,
too, reveled in his uselessness. "I have never done anything 'useful,'"he
once said, not as an apology,but in defiance. "No discovery of mine has made,
or is likely to make, directly or indirectly, for good or ill, the least
difference to the amenity of the world." Hardy was a committed pacifist, who
proudly claimed that his area of expertise, number theory, would never be used by
the military.
<end quote>

Benjamin H. Yandell _The Honors Class: Hilbert's Problems and Their Solvers_
Natick, Massachusetts: A. K. Peters, 2002, ISNB 1-56881-141-1, page 167
<begin quote>
Utility is never the goal and rarely the result. Hardy defended all of
mathematics on that ground and believed that freed mathematics from the
horrible association with war that he saw in science. Unfortunately, writing in
1940, he honored Einstein and Dirac as mathematicians and gave relativity and
quantum mechanics as examples of useless mathematics: "Almost as uyseless as
number theory. [Hardy p. 131]"
<end quote?
Unfortunately the bibliography has two different books by Hardy that could be
the source of this quote:
_A Mathematician's Apology_ Cambridge: Cambridge University Press, 1969
_Ramanujan: Twelve Lectures on Subjects Suggested by his Life and Word_ New
York: Chelsea, 1959.

Another quote by Hardy, also in Yandell, page 213:
"Archimedes will be remembered when Aeschylus is forgotten, because languages
die and mathematical ideas do not."

- James A. Landau

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