Rene Thom's ariticle '"Modern Mathematics": An Educational and Philosophic Error?' appeared in AMERICAN SCIENTIST vol. 59, Nov./Dec. 1971 pp.695-99. Jean Dieudonne's reply 'Should We Teach "Modern" Mathematics?' appeared in AM. SC. vol.61, Jan./Feb. 1973 pp. 16-19.

Just 3 points... (1) Years ago that finest of teachers George Pólya (in "How to Solve it", I think it was, can't find my old copy) stated simply that anyone who has been through school, without experiencing some moderately serious, systematic and rigorous Euclidean geometry and theorem proving, could justifiably accuse his educators of selling him short. But then the exhilarating mathematical explorations that Pólya brought to teaching are impossible to imagine in any but the most exceptional schools today. (2) Back in the early 1970's none less than René Thom issued an impassioned plea to schools to ditch the empty, barren abstractions of set theory that were meaningless to most pupils, trivial to the best, and utterly stifling the development of real mathematical insight and imagination - in favour of a return to the inexhaustible intuitive riches of Euclidean geometry. ( I wish I could find the original essay.) (3) In the late 1980’s, before I made a career change out of teaching, I recall my head of a school mathematics department asking Oxbridge don’s what were the most noticeable changes they had seen in recent undergraduate intake. Answer 1: a marked falling-off in ability to think spatially at all, let alone in three dimensions. (A rather dire impediment to work in virtually any branch of science or engineering, one would have thought, let alone to any work in higher mathematics.) Answer 2: A woeful lack of any conception of systematic proof from clearly identified assumptions or axioms leading to an ever growing structure of theorems and results. Speaks for itself, doesn’t it? The fads and fashions and easy options of the semi-educated will always win out with the politicians, bureaucrats and ideologues of the “new”. Very sad.

I couldn't agree more. In fact, it perplexes me that what seems to have been substituted in many universities for the training in logical argument (however philosophically inadequate) that Euclid used to provide in schools is an elementary course in abstract logic (some propositional calculus and a little predicate calculus) that is presented without any motivation at all. I bore my students occasionally with John Aubrey's anecdote about Hobbes from the Brief Lives -- a perfect illustration of the power of Euclid's exposition, and of the appeal his theorems can have for people willing to read them carefully.