Ernst Mach

"There is no problem in all mathematics that cannot be solved by direct counting. But with the present implements of mathematics many operations can be performed in a few minutes which without mathemat…"

"Nature consists of the elements given by the senses. Primitive man first takes out of them certain complexes of these elements that present themselves with a certain stability and are most important t…"

"Mathematical and physiological researches have shown that the space of experience is simply an actual case of many conceivable cases, about whose peculiar properties experience alone can instruct us."

"I see the expression of... economy clearly in the gradual reduction of the statical laws of machines to a single one, viz. , the principle of virtual work: in the replacement of Kepler's laws by Newto…"

"I know of nothing more terrible than the poor creatures who have learned too much. Instead of the sound powerful judgement which would probably have grown up if they had learned nothing, their thought…"

"The mental operation by which one achieves new concepts and which one denotes generally by the inadequate name of induction is not a simple but rather a very complicated process. Above all, it is not …"

"Personally, people know themselves very poorly."

"Thought-economy is most highly developed in mathematics, that science which has reached the highest formal development, and on which natural science so frequently calls for assistance. Strange as it m…"