In general... (convention in mathematical papers) I often see in papers something like:
 1) This is in general not true 
or
 2) This is not true in general 
Which I personally would consider to be written formally as something like
1) $\forall x: \neg p(x)$
2) $\exists x: \neg p(x)$
But I wonder whether this is generally what is meant and if the mathematical community is careful about how they use the word "general" or if it used in a more colloquial sense. Being somewhat of an outsider I find this hard to judge. Partly as it is often used as an aside and rarely a formalisation of the statement is present to check it against.
It's the sort of thing you just can't look up.
 A: I don't know about what this means in general.  I use it as a way of avoiding twisting my prose into horrendously convoluted statements whilst avoiding the possibility that some smart alec is going to pick up on a technicality.
More precisely, I use it when I wish to say something like "Not all snarks are boojums" but the sentence would work much better (either for grammatical reasons or to better convey the intended meaning) if I could just say, "snarks are not boojums".  That's false as stated[1], so to avoid either saying anything actually incorrect or that someone's going to say, "But what about ...", I say "in general, snarks are not boojums".
What's important here is that I use it mostly in the prose section of a paper or seminar when I'm trying to focus the reader or listener's attention on the important facets of whatever it is that I'm explaining.  So getting in to a long diversion of which snarkss are not boojumss (is it the lesser-spotted or the warbler variety?) would be counterproductive.  Saying, "not all snarks are boojums" tends to draw ones attention to that class of snarks which are boojums.  Saying "snarks are not boojums" is almost guaranteed to get some smart alec saying, "But what about greater-wrinkled snarks?" (especially in a lecture).  So "in general, snarks are not boojums" has the triple benefit of 1) being true, 2) focussing the attention on the key point, and 3) not grammatically convoluted.
[1]: Banker and Carroll, Identifying subspecies of snark (1874)
A: In general the determinant of a sum is not the sum of the determinants. In that case I don't know that equality is interesting. In general we can not evaluate a path integral knowing only the endpoints (but conservative vector fields are useful). This arc length integral was fairly easy but in general numerical methods would be required. Those are some of the ways I might use it. So "usually" in some useful sense.
later
perusing Math Reviews for the phrase "not true in general" reveals many cases of A implies B but the converse is not true in general Also A implies B however B is not true in general 
