As far as I know, there is no proof whatever of the existence of an objective reality apart from our senses, and I do not see why we should accept the outside world as such solely by virtue of our senses.
M. C. EscherIn mathematical quarters, the regular division of the plane has been considered theoretically. ... [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it.
M. C. Escher