The science about abstract calculations arose many years ago, but development of mathematics continues still. In the modern world of the mathematician is the irreplaceable tool in a set of sciences. Emergence of mathematics was a necessary condition for development of human society.
Prerequisites and reasons
Many scientists and researchers define mathematics as the exact science of measurement of real and abstract things and concepts. As soon as the ancient person could realize that pair of hands and couple of apples, despite their external distinction, have a certain general parameter, there was a mathematics birth. This stage is the most important as it means that there was a concept of abstract number, but not descriptive characteristic of a concrete subject. Became possible to estimate not only material objects, but also time, days of the week, any given periods.
Arithmetic actions became the following important step after emergence of abstract numbers. The person learned to put, read, multiply and divide. It is natural that in the beginning these actions were based on concrete objects, however small children are still trained in fundamentals of arithmetics by means of material objects, for example, of the same apples.
The impetus to development of science was given by the Ancient Greek mathematicians who thought up a so-called deductive system which allowed to bring new axioms out of known.
Development stages
Development of mathematics continued after ancient people thought up ways of record of numbers and arithmetic actions. It gave the chance of the birth of numeral systems that in turn performed admissible operations with large numbers. If earlier for designation of number 10 it was required to make ten notches, then now it became possible to manage one symbol of other form. The most popular numeral system existing in the modern world most likely is connected with the number of fingers on both hands of the person. However, many abstract concepts appeared exactly thanks to anatomic characteristics, for example, in languages of Indians the word "two" still sounds the same as "eyes".
Decimal fractions were invented only in the 15th century, and in Europe extended for hundred fifty years later.
Further development of mathematics was caused by need of abstract notation for trade, public administration, astronomy, architecture and other spheres of activity of human society needing exact calculations. Archeological finds demonstrate that eight thousand years ago in ancient Babylon economical calculations with use of the main arithmetic operations were conducted, and in the 4000th year BC Babylonians were already able to solve mathematical problems.