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In computer science it's often noted, said or agreed on that algorithms are the poetry of computer science. What is considered the poetry of mathematics? Is it statistics? If there is something agreed on of course, like from a famous quote of a mathematician or so.

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closed as primarily opinion-based by pjs36, Simon S, hardmath, anomaly, Asaf Karagila May 29 '15 at 20:50

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Mathematics is beautiful in itself and needs no sub-class of especial beauty. Statistics if anything is the dubious step-child. $\endgroup$ – Simon S May 29 '15 at 20:41
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    $\begingroup$ Mathematics is the poetry of mathematics. $\endgroup$ – Gregory Grant May 29 '15 at 20:41
  • $\begingroup$ Beauty is in the eye of the beholder, but I'd say usually (abstract) algebra. $\endgroup$ – Omnomnomnom May 29 '15 at 20:42
  • $\begingroup$ @SimonS I'm not a native speaker. What do you mean by dubious step-child? $\endgroup$ – Jack Twain May 29 '15 at 20:44
  • $\begingroup$ I mean we (mathematicians) admit that statistics is a close relative. But it isn't strictly of our lineage and often doesn't reflect our best traits. Anyway, see Bertrand Russell quote below. $\endgroup$ – Simon S May 29 '15 at 20:50
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Proofs are the poetry of mathematics. Even the most simple proofs are beautiful.

Proof: $0a = 0$ $$0a = (1-1)a = a - a = 0$$

Proof: The number of primes is infinite.

Assume that the number is finite. Suppose that $p_1=2 < p_2 = 3 < ... < p_r$ are all of the primes. Let $P = p_1p_2...p_r+1$ and let p be a prime dividing P; then p can not be any of $p_1, p_2, ..., p_r$, otherwise p would divide the difference $P-p_1p_2...p_r=1$, which is impossible. So this prime p is still another prime, and $p_1, p_2, ..., p_r$ would not be all of the primes.

Proofs are beautiful. Based on a few axioms, we can describe wonders.

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  • $\begingroup$ I'm pretty sure $P_n+1$ has $2$ as a factor $\endgroup$ – Alessandro Codenotti May 29 '15 at 20:56
  • $\begingroup$ "$P_n+1$ has no prime factors"... unless $P_n=2$, we must have $2\mid P_n+1$... $\endgroup$ – abiessu May 29 '15 at 20:56
  • $\begingroup$ Totally agree with this $\endgroup$ – Jack Twain May 29 '15 at 21:01
  • $\begingroup$ @Alessandro I edited the proof. $\endgroup$ – Jimmy360 May 29 '15 at 21:02
  • $\begingroup$ @abiessu I edited the proof $\endgroup$ – Jimmy360 May 29 '15 at 21:02
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Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

-- Bertrand Russell, "The Study of Mathematics" (1919)

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    $\begingroup$ I was about to look up this quote in response to this question. I think some of the best statements about the beauty of mathematics comes from mathematicians of the early 20th century such as Russell, Hardy, Hilbert, and others. $\endgroup$ – Joel May 29 '15 at 21:04

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