A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
Sentiment: NEGATIVE
You don't watch 'A Beautiful Mind' and say, 'This is how every mathematician is.'
It's my belief that you can take everyone down a logical path if you take them slowly enough, and the trouble is that mathematical brains can get scrambled a little bit on the way. You get a bad teacher, it messes you up for the rest of the journey.
Some people are better at maths than others: no one thinks you can be 'taught' to be a mathematical genius. And no one thinks of teaching, in that context, as a kind of forcing of the will. But there seems to be an idea of writing as an intuitive pastime which is being dishonestly subjected to counterintuitive methods.
It is even possible that laws which have not their origin in the mind may be irrational, and we can never succeed in formulating them.
Most of the mistakes in thinking are inadequacies of perception rather than mistakes of logic.
The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions.
Bad reasoning as well as good reasoning is possible; and this fact is the foundation of the practical side of logic.
Need we add that mathematicians themselves are not infallible?
I have hardly ever known a mathematician who was capable of reasoning.
Even the most analytical thinkers are predictably irrational; the really smart ones acknowledge and address their irrationalities.