George Kaslov

“The symbol is not a mere formality; it is the very essence of algebra. Without the symbol the object is a human perception and reflects all the phases under which the human senses grasp it; replaced by a symbol the object becomes a complete abstraction, a mere operand subject to certain indicated operations.”
― Tobias Dantzig, Number: The Language of Science

“I lied, therefore I thought.”
― A. Lee Martinez, The Automatic Detective

“You couldn't ask more of a miracle than it was willing to give.”
― Tim Pratt, Impossible Dreams

“To him the question: what reality shall we ascribe to number? is meaningless, because there is no reality without number, as there is no reality without space or without time. And so neither in the subjective nor yet in the objective world can we find a criterion for the reality of the number concept, because the first contains no such concept, and the second contains nothing that is free of the concept. How then can we arrive at a criterion? Not by evidence, for the dice of evidence are loaded. Not by logic, for logic has no existence independent of mathematics: it is only one phase of this multi phased necessity that we call mathematics. How then shall mathematical concepts be judged? They shall not be judged!

Mathematics is the supreme judge; from its decisions there is no appeal. We cannot change the rules of the game, we cannot ascertain whether the game is fair. We can only study the player at his game; not, however, with the detached attitude of a bystander, for we are watching our own minds at play.”
― Tobias Dantzig, Number: The Language of Science