Talk:A Mathematician's Apology

Linking to copyrighted works
I'm not sure, but I believe that Wikipedia's WP:COPY policy wouldn't support the link at the bottom of the article. "If you know that an external Web site is carrying a work in violation of the creator's copyright, please don't link to that copy of the work. Knowingly and intentionally directing others to a site that violates copyright has been considered a form of contributory infringement in the United States (Intellectual Reserve v. Utah Lighthouse Ministry)." I believe the general policy is to act in compliance with the laws of Florida, where Wikipedia's servers are stored, so even though the site is in public domain in Canada, America's bazillion year long copyright laws are still in effect, so this linking might be a form of contributory infringement. I won't do anything about it, because I'm ignorant of these matters. I just thought I'd bring it up. Geuiwogbil 20:13, 20 December 2006 (UTC)

Writing not very good
The article was interesting, but to be brutally honest, the writing is pretty horrendous, not graceful or elegant which it should be given the subject.

Might I add that "Firstly" is not a word and should be removed? —Preceding unsigned comment added by 124.190.42.33 (talk) 23:41, 5 November 2007 (UTC)


 * It's a perfectly legitimate word. Not well used here, but it is a word. - DavidWBrooks 01:44, 6 November 2007 (UTC)

How does the theory of relativity lead to atomic weapons? —Preceding unsigned comment added by 91.3.197.53 (talk) 23:20, 16 January 2008 (UTC)
 * E%3Dmc2 98.203.237.75 (talk) 03:50, 1 June 2008 (UTC)


 * The problem here isn't exactly the writing, I guess, it is much more what's written. Is it reasonable to describe the ones like Euler and Galois as "pure mathematicians", while they lived in a time when there really wasn't made a distinction, between pure and applied mathematics? Back then, there was only mathematics, and nothing else.


 * Similarly, this sentence:
 * Hardy expounds by commenting about a phrase attributed to Carl Friedrich Gauss that "Mathematics is the queen of the sciences and number theory is the queen of mathematics". Some people believe that it is the extreme non-applicability of number theory that led Gauss to the above statement about number theory;


 * C. F. Gauß, as a matter of fact, was not only a mathematician, but at the same time an astronomer and a physicist, as well. Now, astronomy and physics obviously aren't pure mathematics, but mathematics in pure application. So, this doesn't mean Gauß was an applied mathematician, yet by no means was he (solely) what Hardy evidently considers a pure mathematician. Maybe that's the difference between someone like Gauß and someone like Hardy, as Gauß was big enough to simply do both: He could have his cake and eat it too! Meanwhile Hardy's kind of black-and-white/ugly-beautiful/applied-pure view on mathematics seems pretty cheap and absurd.


 * "There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world." ..even Lobachevsky knew of that simple truth in his time. Zero Thrust (talk) 01:42, 3 January 2010 (UTC)

Being translated into German
Just wanted to let people know. --OberMegaTrans (talk) 17:23, 28 October 2010 (UTC)

„Hardy's more prominent examples of elegant mathematical discoveries with no use (proofs of the infinity of primes and the irrationality of the square root of two) still hold up.“
Huh? That are very, very basic results, used anywhere… --Chricho ∀ (talk) 13:14, 5 November 2011 (UTC)


 * The statement is not about how basic the results are, it is about the practical utility of the results. These are beautiful mathematical results, but there is no real world problem that I can think of that uses the results in a meaningful way. --Bill Cherowitzo (talk) 19:06, 28 January 2019 (UTC)

The Irrationality of Root-two
The proof of the irrationality of root two does have at least one practical application. In 3D computer graphics, it demonstrates the impossibility of designing finite-precision algorithms for drawing polygons on finite resolution displays without cracks and/or overlaps when the vertex of only polygon lies on the edge of another. SteveBaker 19:27, 7 June 2006 (UTC)

I think this comment understates the case! The fact that numbers like sqrt(2) are irrational is fundamental to the design decisions used in the design of the representation of real numbers for any computational application, not just computer graphics. Thanks to this theorem, anyone designing floating point formats knows immediately not to even try for an exact representation. We take this fact so much for granted that we fail to notice how important this result is. —Preceding unsigned comment added by 208.72.12.12 (talk) 18:15, 21 July 2010 (UTC)

And things like elliptic curve cryptography wouldn't be possible if someone hadn't shown the irrationality of "most" integer roots as these things lead on to the idea of polynomials and the like. Mathematics is very connected. I think this statement should be removed as it is misleading and wrong.

To add to the above paragraphs, I think the infinitude of the primes is essential to the long-term use of public key cryptography, which is even mentioned in the preceding sentence. I just removed this statement. Even if one could argue these theorems are useless, it's certainly not established fact that their uselessness "holds up." Bunzobunzo (talk) 03:59, 28 January 2019


 * These are pretty bogus concerns. From a practical point of view every use of the square root of two involves a rational approximation and if you assume that the error of approximation is on the order of Planck's constant, any of these theoretical results can be established. Elliptic curve cryptography is done mostly over finite fields and there is no concept of rationality in that setting. For all practical purposes, the infinitude of the primes can be replaced by "a really large number of primes" (like Skewes number, or other unimaginably large numbers). I replaced the sentence, as it still holds up. --Bill Cherowitzo (talk) 19:35, 28 January 2019 (UTC)

closing paragraph
"Prosiness"? That strikes me as an unnecessary and confusing word, and I'm not quite sure what it's supposed to convey. Hunting through the text, I can't find any good synonym for prosiness applied to applied math. He never says applied math is unimaginative or dull. - DavidWBrooks (talk) 14:22, 3 February 2019 (UTC)
 * I also can not find anything resembling "prosiness" in the text, but it might be trying to be a succinct way (perhaps too succint) of describing the contrast between how pure mathematicians can say things in clear and precise ways, while applied mathematicians must deal with the "physical reality" thus forcing them to deal with some vagueness inherent in that arena (section 23). I think Hardy would approve, but the term is more likely to have come from some commentator. He does say that at least some areas of applied mathematics (such as ballistics and aerodynamics) are "repulsively ugly and intolerably dull" (section 28). These are, however, areas with wartime applications and I don't think the condemnation holds for all of applied mathematics. --Bill Cherowitzo (talk) 04:54, 4 February 2019 (UTC)


 * Perhaps this is a cultural difference compared to Britons but I bet 95% of Americans have no idea what "prosiness" even means. It's not good to have such an obscure word in an encyclopedia article. But I'm not quite sure what to replace it with. - DavidWBrooks (talk) 13:20, 4 February 2019 (UTC)