Is there a reference containing standard mathematical notations? - MathOverflow

Is there a reference containing standard mathematical notations?

2010-07-23T23:35:59Z

Suppose you are writing a mathematical text (say an article) and you want to call an object (for example, a set) by a letter. It would be cool then to have some reference (optimally available on the internet) where you could find some standard letters and notations of mathematical objects and pick one that you like. Does such a "notation dictionary" exist?

ADDED. Thanks everybody for interesting answers! Maybe it is worth to add that I had in mind rather basic things. The question was trigged by my attempt to find a good letter to denote a subset of the segment $[0,1]$. Finally I decided to call it $T$ (in the course of the proof it turns out that $T$ is equal $[0,1]$ :) ).

Answer by Greg Kuperberg for Is there a reference containing standard mathematical notations?

2010-07-24T00:18:44Z

Really the closest that you can get is Wikipedia or the right kind of search in Google Scholar. The community needs tools to establish or recognize consensus, which of course is an open-ended problem. These tools, while they are certainly far from perfect, are the best tools that exist. If you did embark on a project to document standards, that could be a great thing to do, but it would probably eventually be co-opted by Wikipedia.

When I think about quantum algebra, a topic which is notorious for "notation sprawl", I use Wikipedia and Google Scholar. The more traditional method is follow a few respected papers and textbooks, and this is also still reasonable.

Answer by Greg Friedman for Is there a reference containing standard mathematical notations?

2010-07-24T00:19:22Z

I'm not sure this is quite what you have in mind, but there is a "comprehensive" LaTeX symbol list: http://www.ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf

Unfortunately, it doesn't make suggestions about what kinds of symbols should be used for what kinds of objects, but that's usually a moving target anyway.

Answer by Jim Humphreys for Is there a reference containing standard mathematical notations?

2010-07-24T14:21:26Z

The question presupposes the existence of some standard letters and notations of mathematical objects, which I'm doubtful about in many research areas. My experience with subjects that have a long history suggests that notation in mathematics evolves over time in less than logical ways. In some areas there simply isn't any "standard" notation, while in many others some influential sources have tended to establish a de facto standard. But quite a few mathematicians just make up their own symbols as they go along (I won't name any names), forcing readers to translate according to their own taste. It depends a lot on whose earlier work you most rely on. Even Chevalley, in volumes 2 and 3 of his abandoned series of books on the theory of Lie groups, made some really eccentric choices of fonts and letters.

On the other hand, there are some good lists of LaTeX symbols, as already pointed out. But such a list can only reflect overall usage, not tell you what is currently thought to be "standard" in a given subject area.

Answer by Pietro Majer for Is there a reference containing standard mathematical notations?

2010-07-24T21:35:49Z

Indeed, when in your research you happen to meet an interesting object, totally unknown to you, first you have to check whether it has already defined, as it's quite likely to be. How to find a reference then? One good thing in modern mathematics is that today we have reached a good level of standardization; very often names are given just following the most reasonable and obvious way, avoiding fancy or weird terms. Therefore, in this situation the first question one has to ask is simply: "how would I name this guy?" and then, just google it. So, yes, the dictionary does exist and is the whole Internet. In my experience, it's not harder than guessing the name of a TeX command: often trying the obvious term is even quicker than go and look at the userguide. Let me tell you an example. Weeks time ago for some reason I become interested in subsets of Banach space that are stable for infinite convex combinations, i.e. with countably many positive coefficients summig to 1. How would you call such a special sort of convex? (I leave it as a riddle; you can check it directly on google). Once one has found a reference, everything is there, included the notation ( of course guessing directly the letter denoting an object would be much more difficult). Oh, and then there is MO: what could you imagine better than a living dictionary?