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Chris Ormell makes a number of ridiculous claims, including that pure mathematics is about nothing more than the reification of symbols, and that blind faith among mathematicians is responsible for them accepting Georg Cantor's theory of the transfinite.

He alleges that this theory is impossible. If he could show that a contradiction followed from Cantor's theory, he would instantly become world-famous. No such contradiction has ever been shown and Cantor's theory (and the theory of real numbers Ormell also derides) lies at the foundations of our understanding of calculus and much else.

Rhetoric attacking the reliance on mathematical modelling in financial institutions is all very well, but to be seduced by that into publishing a diatribe against professional mathematics as a whole shows a lapse of judgement.

James Ladyman, Head of department, Department of philosophy, University of Bristol.