Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.
Joshua Girling FitchRelated topics
appeal collection definite following hypothetical intuition mathematics primitive pure system consequencesRelated quotes
Let Americans disdain to be the instruments of European greatness! Let the thirteen States, bound together in a strict and indissoluble Union, concur in erecting one great American system, superior to the control of all transatlantic force or influence, and able to dictate the terms of the connection between the old and the new world!
Alexander Hamilton
What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.
Georg Cantor
If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.
George Dantzig
Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascod, so pages of formulae will not get a definite result out of loose data.
Thomas Henry Huxley
[Even the mechanism can be endowed with an image. Thus] the thermostat has an image of the outside world in the shape of information regarding its temperature. It has also a value system in the sense of the ideal temperature at which it is set. Its behavior is directed towards the receipt of information which will bring its image and its value systems together.
Kenneth Boulding
