Without this common language, we would have a specialized language for every field, allowing little "cross-pollination". As an example, in evolutionary biology, take the NK model of epistatic interactions which models gene interactions. It just so happens that this model is extremely similar to a thing in statistical physics called a spin-glass. Without mathematics the biologist would have to sit and work out all the details of these epistatic interactions before getting to actually do biology. So in short, mathematics saves you time by expressing common patterns or ideas.
It was Simpson's rule.
CORRECTION:
It was worse than that. It was the trapezoidal rule:
http://care.diabetesjournals.org/content/17/2/152.abstract
The author named it after themselves:
... The Tai model allows flexibility
in experimental conditions ...
http://fliptomato.wordpress.com/2007/03/19/medical-researche...
Unbelievable.
I wasn't arguing that. In fact, I said that math is lending me and students of other fields tools to use and apply. The problem lies in the expression of said tools (which is exactly what I mean with "arcance notations") and the inability of many mathematicians - no offense - to separate those two concepts (tools/mechanics and expression) from another. They assume that they are completely inseparable, which is not only part, but a major source of the problem. Any attempts to somehow make math less obscure (or even just suggest it) is met, in great parts, with conservative hostility. I've seen mathematicans claim "that I was telling them that their profession is pointless and should be abolished" when all I was saying that a majority of the expression of math is incredibly obscure/arcance to most people which are not mathematicians and mostly not suited for practical appliance (as in, appliance in fields of science other than math).
Also, it's a valid point to say that we shouldn't have special syntax/language for every appliance of math imaginable. That would indeed not only be stupid, but actually /increase/ obscurity. We should, however, stop excusing the obscurity of math with "it's shorter to write". Readability and - most importantly - comprehensibility should /always/ come before convenience. Even in math.
I don't think this is just about the math community. The problem - at least as I see it, as a student myself - is that Math is a required part of many fields of studies. Fields which not necessarily have much to do with Math. And that's a problem for many of the students. I won't say that Math is entirely unneeded and should be completely abolished, but what I am saying is that many of these students (including myself) don't want to be part of said "math community".
We don't want to have to learn the arcane notations and "math language" just to be able to use some of the tools we might indeed need. Yes, I might sound like a whiny student who's butthurt over having to actually study for something. I may be. However, seeing as /so many/ other students (who, for the most part, are competent in their own chosen field) are in danger of failing their studies or struggle heavily with their math lectures simply because they are /not/ competent at getting into the "math community" is ridiculous to say the least.
For the record, I study Informatics at a university in Germany, so the situation might be different elsewhere, but I've read about similar issues at American colleges and universities, and every now and then, related articles pop up here at HN.