Turning Points in the Conception of Mathematics
In the last few decades, after the appearance of T. S. Kuhn’s The Structure of Scientific Revolutions (1962, 1970), it has become fashionable to discuss revolutions in mathematics. The book by D. Gillies 1992 (ed.) Revolutions in Mathematics, Clarendon Press, Oxford, to be referred to henceforth as G followed by a page number, is a collection of relevant papers. The opinions range from Michael Crowe’s thesis that there are no revolutions in mathematics to the opposite opinion, represented by J.W. Dauben besides others, that almost every situation in the history of mathematics that was sensed to have been critical, every situation followed by changes viewed as radical, should be regarded as indicating a revolution. Gillies goes so far as to speak of a Crowe-Dauben debate.
KeywordsTrigonometric Series Linear Continuum Differential Calculus Philosophical Tradition Regulative Principle
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