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It seems like in most textbooks, there are a few especially important theorems that are given names and there are numerous others that are merely assigned numbers specific to the textbook being perused (e.g. theorem 4.1).

These numbered theorems are, by consequence of them only being numbered, harder to find additional information on, harder to cite, and harder to keep organized in my head owing to their lack of distinct keywords.

Presumably, whomever comes up with these theorems would have bothered to name them given the prestige involved and the fact many of these theorems are foundational to various genres of mathematics.

So: is my presumption that these numbered theories are in fact named correct? And if so, how can I go about finding the names of these theorems?

William Muenzinger
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    No, most theorems are not named. – Michael Albanese Jan 08 '14 at 14:57
  • tagging of theorems depend on an axiomatic choice and author taste, and believe: that is pretty dynamic! – janmarqz Jan 08 '14 at 15:02
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    I would go farther than to say that most are unnamed and say that most which are named are named after the fact, especially if they involve a person's name. However, to name one of your own theorems after yourself wouldn't involve prestige as you say, but would probably be seen as incredibly pretentious. – Chris Bonnell Jan 08 '14 at 15:12

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Most theorems are not named.

However, sometimes authors give a name to a previously unnamed theorem in order to facilitate future ease of reference.

This happens, for example, in Davey & Priestley's Introduction to lattices and order, wherein they name the following theorem the Connecting Lemma.

Theorem. Let $L$ be a lattice and suppose $x,y \in L$. Then the following are equivalent.

  1. $x \leq y$

  2. $x \wedge y = x$

  3. $x \vee y = y$

The theorem is so named because it reveals the connection between the order relation and the meet and join operations in any lattice. If memory serves, the authors refer back to this theorem quite a few times, so giving it a name was definitely a good idea.

Of course, once an article or book has baptized a theorem with a name, it tends to stick, since names are useful.

goblin GONE
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  • If names are useful, why not start with them? – William Muenzinger Jan 08 '14 at 15:08
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    @Dargatz If bookmarks are useful, why not place a bookmark on every page? – Erick Wong Jan 08 '14 at 15:13
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    @Dargatz, because its hard to give them memorable names, and time is scarce. – goblin GONE Jan 08 '14 at 15:14
  • @Erick Wong Too much clutter. But naming things and forcing people to memorize every name are not mutually implicit propositions. – William Muenzinger Jan 08 '14 at 15:15
  • @user18921 Coming up with the best name could take a while. Producing a placeholder name, which people could later modify by some formal or informal process, is not. – William Muenzinger Jan 08 '14 at 15:18
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    @Dargatz That is a reasonable proposal and indeed some authors adopt such a style (Tao comes to mind). There is also the practical advantage of making it easier to remember the LaTeX name of each theorem. You might want to rephrase your original question, which seems to reject ad hoc naming specific to a paper (what does it mean to find "the name" of a theorem that appears under five placeholder names in five different places, with small but essential variations in each?) – Erick Wong Jan 08 '14 at 15:42
  • @Erick Wong The originator should produce the placeholder name. Per instance, you could use the name of the author followed by a number. So that per instance you would have: [author's name]1 for that author's first theorem. That theorem name could be used thereafter by everyone who felt it worth the bother to look up the name and cite it - until an alternative name was chosen. This is sort of default, lazy, but very practical and useful naming convention is similar to what is used in some sciences (eg biology and astronomy). – William Muenzinger Jan 08 '14 at 16:02
  • @Dargatz You are underestimating the difficulty of finding a good name, overestimating the compliance of the readers and overlooking the fact that different from animals and stars, theorems do not come in well-defined quantities. – Phira Jan 09 '14 at 10:24