numerically confused

I'm getting the impression that the English language is getting increasingly mixed up at its interface with maths, i.e. the use of numbers, singular, plural, etc.

Examples:

* Nobody agrees what speciation means (quote from a news feature highlighted in a read box, Nature last week, page 867). "Nobody" means: Not a single person, mathematically: 0 Surely, to disagree, you need at least two people, so every single person on his or her own would be in agreement with the rest of the set, i.e. him or herself. So the smallest possible level of agreement, if you have as many opinions as people, would be: No two people agree ...

* often heard in speech and also seen in print: She's one of those people who ... If you deconvolute that, it means: "She's one people out of the number of people who ..." As there is no singular to the word people as used here (as opposed to people meaning population), I find this usage completely unacceptable.

* One thing that is common usage and seems to be insisted upon by editors, though I find it highly illogical, and it is not found in other languages I know: "He's one of the writers who doesn't ..." The verb in the relative clause is, of course, attached to the "who", and who refers to "writers," and is thus plural. I have no idea how this got into the rule books, but it's just stupid and wrong.

* Why does the media hate me? asks Martin Amis in the Guardian. I would argue that media is the plural of medium, so it should be used as a plural. Although I can see what Amis is trying to do - he wants to present "the media" as a sinister power that has decided to ruin his career by writing bad things about him. The alternative view, which I find factually and grammatically more satisfying, is that "the media" are many different institutions and people who have separately come to the conclusion that he is a ...

* Often heard and read: "The amount of items ... " When I learned English many years ago, I believe I was told that countable items should be referred to as "number of items", while bulk materials that aren't countable may be referred to as e.g. "the amount of water". There is of course a further complication in that we tend to speak of amounts when talking about money, which is countable, but if a specific unit is used, we could still say the number of dollars, or the amount (as measured) in dollars.