3. Hardy’s deep sigh

In his book A Mathematician’s Apology, Godfrey H. Hardy presents a conception of mathematics according to which real mathematics can be considered harmless and innocent. By ‘real’ mathematics, Hardy has in mind, for instance, advanced number theory. He contrasts real mathematics with different examples of applied mathematics and cases of elementary mathematics. Hardy argues for the thesis of innocence by asserting that the utilitarian value of real mathematics is nil. Real mathematics does not have any useful applications. By assuming a utilitarian perspective on ethics, Hardy can claim that real mathematics operates at a comfortable distance from any ethnical and political controversies. However, number theory, that Hardy considered the epitome of real mathematics, has tremendous applications itself within war technology. Hardy’s explicit justification of the thesis of innocence is simply fallacious. Most ironically, the doctrine of neutrality continues to operate. According to this doctrine, mathematics can be researched and developed while ignoring any kind of ethical and socio-political considerations. The doctrine of neutrality becomes acted out through mathematical research paradigms, dominating the vast majority of university departments in mathematics the world over.