(ctd)
>>is there a book you could recommend that might give me some rudimentary understanding, without my having to start from the beginning?<<
I am not sure what would be your beginning, but there are introductory mathematics courses (with recommended readings) for Faculty of Arts students, that are distinct in emphasis, and later also content, from those offered to Engineering, Science or Economics students (e.g. more emphasis on “what is mathematics“ than on “how to use it”).

Also you can gain an insight how important is mathematics in understanding the first things about the structure of the material world (elementary particles via QM, cosmology via relativity, supoerstring and multiverse hypotheses, etc) by reading popular explanatory texts written by specialists. Also Part II of Sokal’s recent book is not a bad start at trying to understand how (physical) reality is looked at by somebody with qualifications in mathematical physics.

>>can you give any clear evidence that mathematics, unlike language, is not merely immanent--a human language designed to match phenomena, but without real transcendenca; psychologism, for instance?<<

Perhaps you might be interested in the brief summary of what this is all about in http://www.scienceandreligiontoday.com/2010/04/01/is-mathematics-invented-or-discovered/.

As to “clear (convincing) evidence” this to my mind is a subjective matter, namely the “convincing” part of it (e.g. a photo of the accused about to stab the victim was unheard of in a court 200 years ago, would be accepted as convincing evidence some 70 years ago, and is practically worthless since Adobe Photoshop).

I personally am convinced that mathematics is BOTH invented (mental constructions, language) AND discovered (the objective part that is witnessed to by Witten’s “unreasonable effectiveness of mathematics). This comes from my experience (past) of a working mathematician, and I am aware that it does not have to be convincing to others, even mathematicians. (ctd)

(ctd)
[As you know, I correlate this with my experience of another nature (relating to faith), that sees religious concepts as BOTH human constructs AND referring to something beyond me, beyond humanity, with the same admission that this “evidence”, as convincing as it is to me, does not have to be to others both naively but devoutly religious and atheist (of course, for two different reasons).]

Hello George,
thanks for the feedback, and the links!
I've only browsed Sokal's new book so far but what I have noticed, in spades, is the "tone"; the same tone that can be found in Ditchkins, and in another positivist/analytic I've been reading (Thomas Metzinger) lately. That tone is one of contempt and ridicule of a straw man--the straw man of continental philosophy/poststructuralism--rather than substantial critique. I'm working on giving that straw man a backbone and vital organs for a conference paper at the moment, a synopsis of which I'll post in the next couple of weeks.

I have read lots of popular science texts over the years; Martin Gardner, John Gribbin, Dawkins (and Gould) Hawkins and Paul Davies, to name a few. But because these books were written mainly for laypeople, there wasn't much math. In fact there's more math in the work of cultural critic, Fredric Jameson (who doesn't get a mention in Sokal's book, I notice) than the physicists, or even mathematician's, like Gardner, that I've read.
But never mind, I seem to get by without the arcania of math, and don't have time to learn it. :-)