It's arrogant and elitist only if you think that the deep and practical knowledge qualifies one as superior in other aspects of life/knowledge outside of deep and practical mathematics.
My 2 cents on this (a general response, not directed to andie nach): I think you need to know the maths to do the work (to the point where many significant contributions to Physics come from mathematicians from Gödel to Penrose). In fact, I think a lot of the work is just the math -- many of the practitioners do not even know exactly what they are doing, not much more than what a computer is doing when it helps me compose this message (a bit of hyperbole). The contrast therefore is not "deep" vs "superficial" but between technical vs holistic.
Let me give an example: Given two weeks, I can walk any list-member, who has absolutely zero knowledge of any maths, to derive by themselves some very important and profound results in mathematics (e.g: Gödel's first incompleteness result). And I don't mean popular derivations (such as Nagel and Newman's book or the stuff from Hofstadter or Penrose) -- I mean we start with symbolic logic, consistency of first order logic, set theoretical notions, correspondence, and end up with recursive enumeration and incompleteness.
But if someone didn't tell me what this result implies in a larger sense, I would be pretty lost about it, and so would my LBO student. In my mind, the technical stuff is easier and close-ended than the interpretation of such results. So you have on the one hand Turing disparaging Wittgenstein while Putnam still defends (in some sense) his strange attitude towards the incompleteness result(s). You have debates regarding the Lucas-Penrose thesis and their use of the incompleteness result.
Now we could argue that Wittgenstein was no mathematical genius but he knew enough maths to make technical judgements (his judgement however is not a technical result at all). But this is just an easy example. There are results (claims) obtained elsewhere through other means that might one day find mathematical expression or verification. There may be a net loss to knowledge if mathematicians like Putnam and Stolzenberg stopped listening to Wittgensteins and Latours.
Technical people are often like the preppy little kid who likes to correct others that a dolphin is not a fish (the latest factoid he has learnt), irrespective of the context of the use. That is a shallow arrogance. Wisdom is a different thing altogether.
> Nonetheless, the language of nature is mathematics,
> and while you can get it in translation, you lose a
> lot, just as the very best translations of Homer
> aren't the same as reading it in Greek, or the very
> best explanations of sculpture or painting leave out
> the crucial visual experience. If that's arrogant,
> well, to paraphrase Che's remark that "it's not _my_
> fault that the world is Marxist," it's not my _my_
> fault that God wrote the world in the language of
> numbers.
I am very surprised, despite your self-identification as a realist, to see you make this sort of claim. Perhaps all this defensiveness comes from your suspicion that one needs a fair bit of bluster (arrogance) to make these claims stick? Come, andie, I bet you can write an excellent critique of the above excessive belief(s)! Let's hear your suppressed inner nominalist!
Practical maths? What a horrible thought!!! ;-)
--ravi
P.S: Didn't Marx say something about knowing the world vs changing it? I thought the 'is' was exactly what was contrasted with the prescribed 'ought'?