It is a hard science, because all of it components can be exactly defined and the outcome is always measurable. For exceptions see end of article.
The historical development of the mathematical sciences started in Mesopotamia and ancient Greece, with the best known and earliest published mathematical work being Euclid's Elements. The need for a mathematical approach arose from the development of civilizations that needed to measure and evaluate land and taxes. Henceforth mathematics became very early an integral part of the science of economics. From this practical beginning, mathematics, counting and measuring tangible objects, progressed more into the abstract field and soon the number '0' and the term 'infinite' with its symbol Ã¢ÂˆÂž were defined.
Classical mathematics is often associated with the four fields of arithmetic (numbers), algebra (logic), geometry (space) and analysis (evaluation), but overlaps do exist.
Whilst 'everyday mathematics' uses the decimal system with a, theoretically, infinite set of numbers reaching from 0 to Ã¢ÂˆÂž, computer related mathematics uses the binary system of 0 (off) and 1 (on). Chaos Theory and fractal mathematics are a relative new development that were made possible through the high computing powers of modern computers. The paradigm shift that let to the discovery of fractal relationships (self-similarity) and attractors (a result gets with each computation closer to a point, the attractor, without ever reaching this point) has ended the 'measurability' mentioned previously and opened the door to a completely new, chaotic, field for the mathematical sciences.
Image Credit: (c) Sybille Yates