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"It is of course not surprising that, in these days of short cuts, there should have arisen a movement to get rid of Euclid and to substitute a “royal road to geometry”; the marvel is that a book which was not written for schoolboys but for grown men should have held its own as a school-book for so long… 

It was with reference to such a danger that Dionysius Lardner wrote in 1846:

 “Euclid once superseded, every teacher would esteem his own work the best, and every school would have its own class book. All that rigour and exactitude which have so long excited the admiration of men of science would be at an end. These very words would lose all definite meaning. Every school would have a different standard; matter of assumption in one being matter of demonstration in another; until, at length, GEOMETRY, in the ancient sense of the word, would be altogether frittered away or be only considered as a particular application of Arithmetic and Algebra.” 

It is, perhaps, too early yet to prophesy what will be the ultimate outcome of the new order of things; but it would at least seem possible that history will repeat itself and that, when chaos has come again in geometrical teaching, there will be a return to Euclid more or less complete for the purpose of standardising once more...

Euclid’s work will live long after all the text-books of the present day are superseded and forgotten. It is one of the noblest monuments of antiquity…"

Sir Thomas L. Heath - 'Euclid - The Thirteen Books of the Elements' Vol I ‘preface’ Nov 1908

I would heartily concur with Sir Thomas Heath’s prophetic observation and Dionysius Lardner's 1846 statement regarding the dangerous confusions and misunderstandings that the abandonment of Euclid will lead us toward. At the time of his writing Heath can have had no conception that the chaos he prophesied in mathematics was likely to lead us into quite such an all consuming state of scientific, cultural, and educational dystopia.

The ancient practice of ‘geometry' that many people find so incredibly dry and dull, actually served a key purpose of opening and exercising the mind in a stringent manner - similar to that which today we might ascribe to the good of physical exercise on the body.

To those biochemist’s who would mock the importance of geometry and place all their emphasis on the chemistry of molecules I can but press them to contemplate the spacial illustration on the cover of one of their very own bibles. The atom is a monad and groups of atoms create molecules of both 2 and 3-dimensional geometric space. Is it really that unreasonable to argue that the proportions and regularity exhibited by the DNA helical structure is in part accounted for by the geometric shapes and chemical attraction of its parts.   

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