Oh, and @Anton: I do sort of like your question, and have some pet peeves of my own, but terminology is about as subjective and argumentative as math gets...
]]>I think the question is interesting to talk about with people (though I usually talk about specific examples rather than trying to list a whole bunch of them), but I think it may be too much of a "forum/discussion question" for MO.
]]>Incorrectly named things (with corrections)
Sometimes (semi)-standard mathematical terminology is wrong in some way, and it drives me nuts. I'd like this question to be a place to vent about it, but also a place to suggest solutions to the problem. Moreover, since I believe terminology is important, this should be a place to see how people reason about choosing terminology.
Here are the rules for what your answer must include:
- Clearly state what the offending bit of terminology is.
- Explain clearly why the terminology is wrong/misleading.
- Suggest an alternative you'd like mathematicians to adopt. If you can't think of an alternative, but think others might be able to, at least make an attempt. Give some indication of what properties the correct terminology should have.
Example
In representation theory, a representation is said to be "irreducible" if it has no proper subrepresentations. The problem is that non-representation-theorists get confused and think that "irreducible" is synonomous with "indecomposible" (meaning that the representation cannot be expressed as a direct sum of proper subrepresentations). In most other areas, an object with no proper subobject is called simple, so I try to use the terminilogy "simple representation". More generally, since representations are always modules over some algebra, the language of modules should be used for representations.
Here are some other examples that I would turn into complete answers:
javascript:void($(".question-summary%20+%20:not(.tagged-interesting)").hide())
Now visit the home page or the questions page and click the bookmark (or just past that line into your location bar and hit enter). All the questions that don't have an interesting tag should disappear.
I like the idea of a [big-list] tag. I'm going to start retagging such questions when I see them at the top of the home page.
]]>It's the same reason I don't care much about the quality of average item on EBay or an average Wikipedia article: since I'm nearly always coming to either of these sites with a specific search, and continue from that place, again, to specific pages of interest to me. That works fine!
Will this "noisy martketplace" model work for MO? Maybe not. Anyway, for those who are interested: here are questions tagged AG, AT, MG, RT, or NT.
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