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I have been able to find several counterexample books in some math areas. For example:

$\bullet$ Counterexamples in Analysis, Bernard R. Gelbaum, John M. H. Olmsted

$\bullet$ Counterexamples in Topology, Lynn Arthur Steen, J. Arthur Seebach Jr.

$\bullet$ Counterexamples in Probability and Statistics, Joseph P. Romano, A.F. Siegel

$\bullet$ Counterexamples in Probability and Real Analysis, Gary L. Wise and Eric B. Hall

$\bullet$ Counterexamples in Probability, Jordan M. Stoyanov

Why are there no other examples of books in other math topics (number theory, numerical analysis, DEQs, PDEs, Dynamical Systems, Discrete Math...)?

Is it that it is just not a rich enough area, examples are too trivial, the book wouldn't warrant publishing (low sales), someone just hasn't written one, I missed it or something else?

Regards

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    $\begingroup$ Your list is not complete. $\endgroup$ Jan 15, 2013 at 16:16
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    $\begingroup$ Nice question! Maybe, community wiki fits it? $\endgroup$
    – SBF
    Jan 15, 2013 at 16:16

4 Answers 4

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The following list of titles, all of which can be found on Amazon, may help to answer the question:

  • Counterexamples in Optimal Control Theory

  • Lectures on Counterexamples in Several Complex Variables

  • Counterexamples in Topological Vector Spaces

  • Theorems and Counterexamples in Mathematics

  • Counterexamples in Calculus

  • Convex Functions: Constructions, Characterizations and Counterexamples

  • Surprises and Counterexamples in Real Function Theory

  • Examples and Counterexamples in Graph Theory

  • Counter-Examples In Differential Equations And Related Topics

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    $\begingroup$ @michealGreinecker these books are very much addictive. It is a different kind of fun to read them. Please add a few more $\endgroup$ Oct 15, 2017 at 11:56
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There is a new book on counterexamples in measure theory:

"Counterexamples in Measure and Integration" by René L. Schilling, Franziska Kühn. Cambridge University Press, 2021.

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No idea if it's any good, but here's a new one:

Counterexamples in Operator Theory - Mohammed Hichem Mortad

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    $\begingroup$ Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Jun 1, 2022 at 2:49
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An interest on counterexamples in mathematics was recently revived on Twitter: Examples of books on counterexamples (*). With additional contributions, a list of such books is provided in a frequently updated pdf (as of May 2023): Examples of mathematical books on counterexamples. A snapshot of the list on May, 27th 2023 follows: Examples of mathematical books on counterexamples, May, 27th 2023. See pdf link for updates.

(*) Partly triggered by the following cartoon by Shen Comix, with Borwein-Borwein integrals leading to counterintuitive sinc series.

Shen Comix: finding papers in mathematics

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