Mathematics 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 MachThe presentations and conceptions of the average man of the world are formed and dominated, not by the full and pure desire for knowledge as an end in itself, but by the struggle to adapt himself favourably to the conditions of life.
Ernst MachThe 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 Mach