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Results tagged with big-list
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user 6794
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
-3
votes
Suggestions for good notation
I like the notation $f:A\cong\subseteq B$ for "$f$ is an embedding of $A$ into $B$." The idea is that the relation of embeddability is obtained by composing the relations "isomorphic to" and "substru …
30
votes
Theorems first published in textbooks?
Long ago, I proved that every derivation from $C^{k+1}$ functions to $C^k$ functions is given by a $C^k$ vector field. (The same fact with $\infty$ in place of $k$ and $k+1$ is, of course, classical. …
21
votes
Nonequivalent definitions in Mathematics
An extension of a group $A$ by a group $B$ can be either a group $G$ with a normal subgroup isomorphic to $B$ with $G/B$ isomorphic to $A$ or a group $G$ with a normal subgroup isomorphic to $A$ with …
21
votes
Never appeared forthcoming papers
Dana Scott and Robert Solovay, "Boolean-valued models of set theory"
9
votes
German mathematical terms like "Nullstellensatz"
"Urelement" is used in set theory as a fancy name for an atom, i.e., something that can be a member of a set but is not itself a set.
252
votes
What are some examples of colorful language in serious mathematics papers?
Does merely transposing two words count? "It is also hard not to show that ..." [Arnold W. Miller, "Some Properties of measure and category," Trans. A.M.S. 266, 1981, p. 106]
7
votes
Which math paper maximizes the ratio (importance)/(length)?
Lawvere's paper "Quantifiers and sheaves" (1970 International Congress of Mathematicians at Nice, vol. 1, pp. 329--334) was the first publication of his work with Tierney on elementary topoi. It cont …
6
votes
Dimension leaps
The free modular lattice on $n$ generators is finite for $n=1,2,3$, but for $n=4$ not only is it infinite but its word problem is recursively unsolvable.
13
votes
Pseudonyms of famous mathematicians
I'm not sure whether to count as pseudonyms the altered names that people took (often to avoid antisemitic prejudice) as replacements for their real names. For example, Alfred Tarski's last name was …
10
votes
Important results with one or more than one proof
The first example that occurs to me is Hindman's theorem: If the set of positive integers is partitioned into finitely many pieces, then there is an infinite set $H$ such that all sums of finitely man …
10
votes
Examples of $G_\delta$ sets
In the space of all subsets of $\mathbb{N}$ (identified via characteristic functions with $2^{\mathbb{N}}$ and topologized as the product of copies of the discrete 2-point space), the set of infinite …
- 73.2k
22
votes
Examples of theorems with proofs that have dramatically improved over time
I described an example, Hindman's theorem, at https://mathoverflow.net/questions/94546 . The short version is that Hindman's original proof was unpleasantly complicated, whereas a later proof by Galv …
3
votes
How should the Math Subject Classification (MSC) be revised or improved?
My experience has been that the editors of Math Reviews pay attention to suggestions about revisions of the classification system. I'm not saying that they implement all the suggestions (especially b …
9
votes
Mathematical ideas named after places
anarboricity of graphs (named in honor of the city of Ann Arbor by Frank Harary, but also having something to do with non-trees (http://mathworld.wolfram.com/Anarboricity.html)
1
vote
Mathematical ideas named after places
The Conway-Paterson-Moscow theorem