was stun by a narrowmindedness and arrogance of Frank Quinn in A
Revolution in Mathematics, first published in Notices of
the American Mathematical Society (2012) and then included
into The Best Writings on Mathematics 2013 (M. Pitici,
editor). Frank rides highly under the banner of new math (Core
Mathematics they call it officially) and disregards everything
else. The pre-core mathematics he calls ‘mathematical science’
- because he uses term ‘science’ in a derogative sense.
with all sciences, according to Frank, is that they deal with
reality: "In sciences, most of the older material was wrong
and discarded, whereas old mathematics needed precision upgrades
but was mostly correct. [...] To a first approximation, the method
of science is ‘find an explanation and test it throughly’,
whereas modern core mathematics is ‘find an explanation without
rule violations’. The criteria for validity are radically
different: science depends on comparison with external reality,
whereas mathematics is internal."
wait a minute, aren’t there a higher guards of the thinking
rules, like logic and philosophy in general? No, according to
Frank: "To make real progress, mathematics had to break with
philosophy." Sounds familiar? "Philosophy is dead"
- says Stephen Hawking