Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
Sentiment: POSITIVE
I have hardly ever known a mathematician who was capable of reasoning.
Mathematics is written for mathematicians.
Math does come easily to me, but I was always much more interested in what theorems imply about the world than in proving them.
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.
A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories.
I am not a mathematician, but I was aware that for centuries, mathematics was considered the queen of the sciences because it claimed certainty. It was grounded on some fundamental certainties - axioms - that led to others.
I read one or two other books which gave me a background in mathematics other than logic.
The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.
All great men are gifted with intuition. They know without reasoning or analysis, what they need to know.
How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.