There are many fields in mathematics, in which one wants to optimize a process, for example finding the shortest way in a graph etc. However I got curious and wondered, if there are also books or papers about the topic of how to maximize the effort or steps needed to reach a certain goal, for example an algorithm that works as slowly as possible but still ends after a finite number of steps.

One has to care about loopholes, for example one can easily extend the time one who wants to walk from A to B, if he just keeps moving forward and backwards, but never reaching his goal. I am sure, there are more things one has to worry, take care about to do serious mathematics.

Does anyone know one author who worked on those kinds of problems and if there is actually a good book for beginners to that topic etc.? (if not, if there is a book especially recommendable) My question isn't very specific yet, cause first I want to gain a better overview over that field/topic.

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    $\begingroup$ Welcome to the site! This site is dedicated to questions on teaching mathematics and mathematics education more generally. A site for mathematics questions is Mathematics. Your questions does not appear to be about mathematics education, and this would thus fit better on that other site. You can make the question more education oriented via an edit or you can reask it on Mathematics (or just let me know that you want it moved there and I will move it there). $\endgroup$ – quid Jan 19 '15 at 13:46
  • $\begingroup$ Thank you very much for your advice and welcoming me. I wasn't sure, where those kind of topics are best suited. I will reword my question though to make the question clearer. $\endgroup$ – Imago Jan 19 '15 at 13:56
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    $\begingroup$ You might be interested in pessimal algorithms---algorithms which work correctly, but as slowly as possible. See Broder, Andrei, and Jorge Stolfi. "Pessimal algorithms and simplexity analysis." ACM SIGACT News 16.3 (1984): 49-53. ACM link $\endgroup$ – Joseph O'Rourke Jan 19 '15 at 17:03
  • $\begingroup$ One of the first places I might look is algorithms that provide methods of quickly computing certain real numbers; I have in mind the BBP formula for $\pi$ versus, say, $$\pi = \sum_{k = 0}^{\infty}\frac{(-1)^k 4}{2k + 1}$$, which uses the series representation of $4\arctan(1)$. $\endgroup$ – Benjamin Dickman Jan 19 '15 at 17:42
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    $\begingroup$ seems like there is something to good Rube Goldberg which is not captured by mere optimization. I mean, the shortest or longest path is not the thing: somehow, we want an "interesting" path. How to quantify that? That is an interesting question. $\endgroup$ – James S. Cook Jan 22 '15 at 21:25

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