What Is Mathematics For?
in [Math]
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From: rich burge on 29 May 2010 14:41 On Apr 25, 7:14 am, Dom <DR...(a)teikyopost.edu> wrote: > The truly superb article, "What Is Mathematics For?," byUnderwood > Dudley has been published in the May 2010 issue of the AMS Notices. > > http://www.ams.org/notices/201005/rtx100500608p.pdf Yes, it is a truly suberb article. My first disagreement with the author would be in not including Geometry explicitly as part of mathematics: "So that there is no confusion, let me say that by 'mathematics' I mean algebra, trigonometry, calculus, linear algebra, and so on: all those subjects beyond arithmetic." Second, the quoted problem from Chrystal's Algebra in many ways defines what algebra is and imho ought to be. So I am confused when he states: "We cannot go back to texts like Chrystal's." Why not? Seems to me a "modern translation" of Chrystal with a superset of the problems contained therein is just what is needed. Rich
From: spudnik on 29 May 2010 21:21
you don't read Shakespeare til the eleventh grading, or it could seriously mess you "up." til then, one can readily study *mathematica*, which is four subjects, in a "hands-on" manner that does not really require the full-throated use of language -- that one is learning, by doing stuff. I like UD's _Math.Cranks_, because, in his chapter on fermatistes, he only made one mistake, that I can find, now, and he had acknowledged it, when I told him. also, he seems to have left numbertheory, out, and that's one of the four, the true meaning of "higher arithmetic." > http://www.ams.org/notices/201005/rtx100500608p.pdf > author would be in not including Geometry explicitly as part of > mathematics: "So that there is no confusion, let me say that by > 'mathematics' I mean algebra, trigonometry, calculus, linear algebra, > and so on: all those subjects beyond arithmetic." thusNso: textbooks are often *generically* bad glosses on the discoveries in the original monographs, or simply pedantic workbooks. the real empty set, to me, is those who attempt proofs, without any grounding in elementary geometrical & numbertheory proofs -- see wlym.com. and, recall, it was Liebniz who gave the generic format of "iff," which is necessity & sufficiency, used meaningfully in various ways in natural language. the New Math following upon General Bourbaki was a silly thing, since you *need* natural language (and diagrams etc.) to make ready analogies & metaphors for your work. such that, the glaring example of Bourbakism was perhaps Russell's illinguistic "paradoxes" -- whence "silly" deploys from over-reliance on Aristotle's syllogisms! --Stop BP's capNtrade rip-off; call Waxman & tell him, we need a small *tax* on carbon emmissions, instead of "let the arbitrageurs raise the price of CO2 as much as they can -- free trade, free beer, free dumb!" http://wlym.com |