Ce qui fait la qualité de l'inventivité et de l'imagination du chercheur, c'est la qualité de son attention, à l'écoute de la voix des choses. Car les choses de l'Univers ne se lassent jamais de parler d'elles-mêmes et de se révéler, à celui qui se soucie d'entendre.
A. Grothendieck
We have as an elemental part of our nature the ability to observe imperfection and from that imperfection deduce the laws of Nature–deduce perfection. This ability is our capacity to 'abstract' and it may well be the case that a different capacity to abstract, even in the face of a universal order of things, would lead to a different perception of that order.
G. Boole
There's no doubt that they do exist but you can't poke and prod them except by thinking about them. It's quite astonishing and I still don't understand it, despite having been a mathematician all my life. How can things be there without actually being there?
J. H. Conway, when asked 'Do mathematical objects exist?'
The core question is not how you do math but how does the unconscious do it. How it is that it's demonstrably better at it than you are? You work on a problem and then you put it away for a while. But it doesn't go away. It reappears at lunch. Or while you're taking a shower. It says: Take a look at this. What do you think? Then you wonder why the shower is cold. Or the soup. Is this doing math? I'm afraid it is. How is it doing it? We don't know. How does the unconscious do math?
'Stella Maris', C. McCarthy
After seeing a problem like this, your response should be 'please, may have a better problem?'
C. McBride
The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise
E. Dijkstra