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I recently stumbled over the "Happy Ending Problem" (cf e.g. http://en.wikipedia.org/wiki/Happy_Ending_problem), which made we wonder, if there are other conjectures, theorems or problems, whose names do not give any indication to what they are about or, to which person it is related;
the "kissing number" would not qualify here, because it is a definition, but neither a problem nor a theorem.

Besides the "Happy Ending Theorem", I also found

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    $\begingroup$ I thought Happy Ending referred to something completely different. $\endgroup$
    – Will Jagy
    Commented Oct 22, 2014 at 4:35
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    $\begingroup$ voted to close because it's nowhere near research level. I'm not sure whether or not this is on-topic at math.SE because I don't know enough about that site. $\endgroup$
    – Peter McNamara
    Commented Oct 22, 2014 at 7:42
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    $\begingroup$ @WillJagy: See also the Going Down Theorem. $\endgroup$
    – Nate Eldredge
    Commented Oct 22, 2014 at 18:38
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    $\begingroup$ Yes, I believe that's known as Yemon's Observation. $\endgroup$
    – Gerry Myerson
    Commented Oct 22, 2014 at 22:05
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    $\begingroup$ I propose Myerson's Observation: "If we are going to add theorems named after the wrong people then we will be here all day." $\endgroup$
    – JRN
    Commented Oct 23, 2014 at 5:16

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I'm not sure if all these give "no clue", but they are somewhat obscure clues:

The Law of the Unconscious Statistician.

The Chinese Postman Problem

The Googol Game (aka the Secretary Problem)

The Butterfly Lemma and The Snake Lemma

The Art Gallery Theorem (or Problem)

and for those who know some Latin:

Theorema Egregium and Pons Asinorum

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  • $\begingroup$ as this is a soft question, all of these are acceptable to me $\endgroup$
    – Manfred Weis
    Commented Oct 22, 2014 at 5:12
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    $\begingroup$ The Tomato Can principle. $\endgroup$
    – Robert Israel
    Commented Oct 22, 2014 at 7:03
  • $\begingroup$ @RobertIsrael: Gauß has a theorema aureum, too. André Weil even wrote once something like, "he [the Princeps Mathematicorum] was very fond of this type of names"... $\endgroup$
    – José Hdz. Stgo.
    Commented Oct 23, 2014 at 0:18
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The Ham Sandwich Theorem.

The Hungarian Method.

The Hairy Ball Theorem.

The Konigsberg Bridge Problem.

The St. Petersburg Paradox.

The Futurama Theorem.

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The Ten Martini Problem was a conjecture posed by Kac and Simon and answered by Avila and Jitomirskaya.

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The Killing-Hopf theorem (yes, Hopf is already dead).

The ugly duckling theorem.

The no free lunch theorem.

The Cox-Zucker machine.

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  • $\begingroup$ For a layman hearing ‘Cox-Zucker’ for the first time, it might take on a whole different meaning. $\endgroup$
    – Transcendental
    Commented Oct 22, 2014 at 19:41
  • $\begingroup$ "problems, whose names do not give any indication to what they are about or, to which person it is related...." Do Killing-Hopf and Cox-Zucker qualify? $\endgroup$
    – Gerry Myerson
    Commented Oct 22, 2014 at 22:07
  • $\begingroup$ In the strict sense: no, but let's be generous $\endgroup$
    – Manfred Weis
    Commented Oct 23, 2014 at 0:17
  • $\begingroup$ Similar to the Killing-Hopf theorem, the Italian name for the Gaussian elimination method sounds like someone is debating on the best way to kill poor C.F. Gauss. $\endgroup$
    – Federico Poloni
    Commented Nov 15, 2014 at 10:02
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The Busy Beaver Problem.

The Beer Glass Theorem.

The Garden of Eden Theorem.

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    $\begingroup$ After posting this, I tried to StartPage "beer glass theorem" and couldn't find anything, so maybe it's not so well known by that name. Too bad, it would be a nice accompaniment to the Ham Sandwich Theorem. $\endgroup$
    – bof
    Commented Oct 22, 2014 at 6:42
  • $\begingroup$ The Beer Glass Theorem says that, if three congruent circles in the plane intersect at one point, then the circle determined by the other three intersections is congruent to the original circle. Is there another name for this theorem? $\endgroup$
    – bof
    Commented Oct 23, 2014 at 3:47
  • $\begingroup$ I mentioned the Byzantine Generals in an earlier comment on the original post. $\endgroup$
    – Gerry Myerson
    Commented Oct 23, 2014 at 4:42
  • $\begingroup$ @GerryMyerson Dagnabbit! I searched the page for "Byzantine" but I forgot to click on "show more comments". I will delete the generals from my answer. $\endgroup$
    – bof
    Commented Oct 23, 2014 at 4:52
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Pigeonhole (or Box) Principle. (Note that "rational box problem" is very different from "Box principle".)

Jugendtraum (as with Dirichlet for the Pigeonhole Principle, the name of Kronecker is sometimes omitted).

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Hauptvermutung

Technically this is a conjecture, but there are results about whether it is true or not under various circumstances.

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  • $\begingroup$ That meets the kriterion of obscurity and not being a definition (if the conjecture were proven, it would be a theorem). $\endgroup$
    – Manfred Weis
    Commented Oct 22, 2014 at 7:14
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Tropical geometry

Margulis napkin problem

Traveling salesman problem

Canadian traveller problem

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  • $\begingroup$ Speaking of tropical geometry: the Aztec diamond and the arctic circle theorem ( en.wikipedia.org/wiki/Aztec_diamond ). $\endgroup$
    – darij grinberg
    Commented Oct 22, 2014 at 21:13
  • $\begingroup$ And speaking of Aztec diamond, Cairo pentagonal tilings. $\endgroup$
    – Yoav Kallus
    Commented Oct 22, 2014 at 21:26
  • $\begingroup$ "problems, whose names do not give any indication to what they are about or, to which person it is related...." Does the Margulis napkin problem qualify? $\endgroup$
    – Gerry Myerson
    Commented Oct 22, 2014 at 22:06
  • $\begingroup$ @GerryMyerson : Maybe I should use the Wikipedia name, "napkin folding problem." But then maybe the objection is that "folding" is a clue to what it is about. $\endgroup$
    – Timothy Chow
    Commented Oct 23, 2014 at 17:40
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The master theorem. ${}{}{}{}{}{}{}{}{}$

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For a theorem whose name is actually misleading about its actual content, check out the case of the Diversity trumps ability theorem, as described by Abigail Thompson in a recent Notices: http://www.ams.org/notices/201409/index.html

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The Hauptsatz (due to Gentzen).

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The Stable marriage problem. $ $

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  • $\begingroup$ The Stable Marriage problem (or theorem) is about the stability of marriage, isn't it? $\endgroup$
    – bof
    Commented Oct 23, 2014 at 3:42
  • $\begingroup$ I guess, though that sort of objection applies to lots of other answers here too (e.g., the Traveling Salesman problem is about a traveling salesman). $\endgroup$
    – dfan
    Commented Oct 23, 2014 at 12:37

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