The mathematician who pursues his studies without clear views of this matter, must often have the uncomfortable feeling that his paper and pencil surpass him in intelligence.
Ernst MachMathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting.
Ernst MachMany an article that I myself penned twenty years ago impresses me now as something quite foreign to myself.
Ernst MachEveryone is free to set up an opinion and to adduce proofs in support of it. Whether, though, a scientist shall find it worth his while to enter into serious investigations of opinions so advanced is a question which his reason and instinct alone can decide. If these things, in the end, should turn out to be true, I shall not be ashamed of being the last to believe them.
Ernst Mach