If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics.
Many secrets of art and nature are thought by the unlearned to be magical.
The strongest arguments prove nothing so long as the conclusions are not verified by experience. Experimental science is the queen of sciences and the goal of all speculation.
Mathematics is the gate and key of the sciences. …Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world.
Argument is conclusive… but… it does not remove doubt, so that the mind may never rest in the sure knowledge of the truth, unless it finds it by the method of experiment. For if any man who never saw fire proved by satisfactory arguments that fire burns, his hearer’s mind would never be satisfied, nor would he avoid the fire until he put his hand in it that he might learn by experiment what argument taught.
There are in fact four very different stumbling blocks in the way of grasping the truth, which hinder every man however learned, and scarcely allow anyone to win a clear title to wisdom, namely, the example of weak and unworthy authority, longstanding custom, the feeling of the ignorant crowd, and the hiding of our own ignorance while making a display of our apparent knowledge.