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This question is quite unimportant, so feel free to close if you think it is inappropriate.

I've been thinking about how mathematicians come up with names for the ideas/objects they study, and how that differs from the practices of people in other fields.

It seems that almost always we do one of two things: 1) we pick a name that describes some feature of the object (sometimes not very well, e.g. flat modules, sets of second category), or 2) we name it after a person (who may or may not have studied that object).

Very rarely we name something after a place. (This is much more common in other fields.) I can think of only 3 examples:

*Japanese rings

*Polish spaces

*Tropical geometry

Does anyone know of any other examples in mathematics?

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closed as no longer relevant by Daniel Litt, Oliver, Dan Petersen, Franz Lemmermeyer, Ben Webster May 12 '11 at 18:30

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Yet another empty question... –  SNd May 11 '11 at 15:01
+1, I think this is at least a little amusing. I must admit, I don't understand why this question has been received poorly (as indicated by the number of votes on SNd's comment, and the number of upvotes on the question itself) when other "empty questions," such as the one about jokes, get over 30 positive votes. What am I missing? –  Eric Naslund May 11 '11 at 19:54
A matter of timing, I suspect. The crowd is just not in the mood. –  Tom Goodwillie May 11 '11 at 21:05
-1. I voted this down because I don't see the value in the question being open (just go to Emmanuel's blog post if you're interested in this). The question is just taking up valuable real estate on the front page as it gets continually bumped by what are generally low quality answers. (and even the OP claims the question is unimportant!) –  Peter McNamara May 12 '11 at 5:01

44 Answers 44

The Aarhus integral of rational homology 3-spheres

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Swiss cheese (one type in complex analysis, another in cosmology)

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Don't forget the Swiss cheese operad. –  Todd Trimble May 12 '11 at 1:20

Two amusing examples from distributed computing are:

The Bysentian generals problem. The problem asks for an algorithm that allows a large number of processors to reach a consensus on something (say a bit value) when some of the processors behave in a malicious way. The original paper motivated the problem with a fictional account of Byzantine generals trying to coordinate a joint attack. There's also a related "Chinese Generals Problem".

Paxos algorithms. This is a family of algorithms that also allow a number of participants to reach a consensus. These were introduced by Leslie Lamport in paper written as a story about the downfall of an ancient Parliament on the (fictional) island of Paxos. The story ends when the parliament inadvertently restricts membership to dead sailors which, of course, can then not be corrected. As you can read about here, the novel exposition of the paper led to a very delayed publication of what has since been recognized as an important result (and is reportedly used in Google, Microsoft and IBM products).

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K. Barré-Sirieix, G. Diaz, F. Gramain and G. Philibert proved the Mahler–Manin conjecture in St-Étienne, so the result is now called the "Theorem of St-Étienne" (see Hida's book Hilbert modular forms and Iwasawa theory, p. 62). The theorem states that the Tate parameter of an elliptic curve $E_{/\overline{\mathbf{Q}}}$ with split, multiplicative reduction is transcendental (over $\mathbf{Q}$).

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The semi-symmetric Ljubljana graph, from algebraic graph theory.

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Black Cow Factor in Optimal Cloning of Pure States by R.F. Werner (arXiv:quant-ph/9804001). He writes,

"The reason for this terminology is that it plays an important role in discussions of the cloning problem started by Chiara Machiavello and Artur Ekert at the Black Cow Café in Croton-on-Hudson, NY, and further clarified in collaboration with Dagmar Bruß [BEM]. I learned about this line of argument from a set of “Black Cow Notes” by Nicolas Gisin and Sandu Popescu."

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In computer science, the Vienna Definition Language, or the related Vienna Development Method. (A tool for definining program semantics).

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Italian Algebraic Algebraic Geometry

One that is not but I used to think so: Catalan number :)

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What if named after a person who derives his name from a place?

e.g. Hamburger expansion

How about moonshine? If moon is allowed, why not Stone (as in Stone-Weierstrass)? And then Stein manifold, Einstein metric, Eisenstein criterion?

There are also buildings and chambers and apartments of Jacques Tits. (BTW, is the last word of previous sentence a place?)

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Why focus on Stone? Surely Weierstrass got his name from the Weierstrasse, on which one of his ancestors happened to live. But I am afraid this new twist opens up a potential avalanche of responses, and I would rather discourage pursuing it. –  Michael Renardy May 12 '11 at 17:24

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