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I have recently been reading about serendipitous discoveries in science and I found them quite inspiring. Most of those discoveries are in Chemistry. I'm looking for examples of these kinds of discoveries in Mathematics and Computer Science.

Examples of serendipitous discoveries include the discoveries of penicillin, saccharine and superglue.

Poincare's accidental discovery of Chaos Theory qualifies.

I am looking for the element of surprise and accident. A wonderful proof which consists of an extremely enlightened step does not qualify because the person was still searching for a proof. But, if a person was working in area X and suddenly realized that it's a way of solving Y, then that discovery would qualify.

Note : There is a question on this already on the site. My question is different for two reasons. Firstly, I'm not asking for important discoveries. Secondly, I'm not asking for recency either. Any discovery in the history of Mathematics qualifies.

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    $\begingroup$ Does Gauss' Theorm Egregium count? en.m.wikipedia.org/wiki/Theorema_Egregium $\endgroup$ – Peter Diehr Jun 6 '16 at 12:54
  • $\begingroup$ @PeterDiehr Can you tell me what the serendipity is here ? I don't know enough about differential geometry to follow ... Was it discovered by accident ? $\endgroup$ – user230452 Jun 6 '16 at 13:05
  • $\begingroup$ No, but the result was surprising. For a surprising application see wired.com/2014/09/curvature-and-strength-empzeal $\endgroup$ – Peter Diehr Jun 6 '16 at 13:10
  • $\begingroup$ @PeterDiehr This was informative and you could post an answer if you'd like. But, I'm looking for accidental results, more than surprising or counter-intuitive ones. Nevertheless, I'm glad to have learnt something new. $\endgroup$ – user230452 Jun 6 '16 at 13:48
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    $\begingroup$ This 500+ page paper, available to read online for free, given extensive detail of serendipitous discoveries in maths : jstor.org/stable/2322795?seq=1#page_scan_tab_contents $\endgroup$ – Nick R Jun 7 '16 at 23:35
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I can think of two major examples offhand.

For Computer Science, John McCarthy's original Lisp paper was meant to be a foray into using computers to represent knowledge for artificial intelligence. Instead, he ended up accidentally inventing both functional programming and garbage collection.

In mathematics, Eilenberg and Mac Lane were studying algebraic topology, and ended up discovering category theory, which had huge effects, from simplifying Cayley's theorem as the Yoneda lemma, to modelling programming languages, to quantum physics.

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