Wouldn't that be a bit like having every scientist invent their own jargon?I don't know about "all scientists", but mathematicians do precisely this all the time! Each paper and each textbook begins by defining what symbols mean what, and which terms are used how. But a textbook is about as big a consistent block of terminology as you'll be able to find. In a grander sense, terms are constantly re-purposed and evolving over time [1].
Something as simple as "⊂" will mean "subset" in one book, and "strict subset" in another. In my experience, the older the book, the more divergent it'll be from current usage. This suggests that the language of mathematics evolves over time, precisely because every practitioner can change the language and push for her own terminology. There is no "Mathematics corporation" which creates languages people would be forced to choose from - no mathematician, no matter how great, would suggest that he would know what the "eternally right way" of expressing mathematics is.
This is especially apparent in more exploratory parts, where definitions start being named after their authors. I, personally, look forward to a time when I get to choose between a Norvig-garbage-collection and Graham-garbage-collection for each object in my code.
We're in this ridiculous stage of software engineering, where, if you're using Java, you have to do garbage collection The Java Way (you get to set a couple of settings, but that's it). No mathematician would ever be forced to make the decisions that Sun's engineers were forced to make when designing Java, because nobody could make those decisions correctly - how programs must interact with the call stack, the mechanics of method invocation, etc.
1. "Compactification" comes to mind as an example: http://en.wikipedia.org/wiki/Compactification_%28mathematics...