The scientists have discovered signs of tallying system on the caves and on bones, but no one can determine what was the tallying system counting.
The natural numbers appeared in the first counting system which was put about 5500 years ago by the Mesopotamian, it consisted of 60 measurement units. The Babylonians, Assyrians, and Persians followed those measurement. About 5000 years ago the Ancient Egyptians used another type of measurement based on 10 units, as the numeric system that we still follow.
About 3000 years ago The Mesoamerican used the zero as a separator between the numbers. The Indians were the first to use the zero in the counting system.
The negative numbers were first used by the Chinese more than 2000 years ago. The Nine Chapters on the Mathematical Art is the name of a mathematical book which contained figures of negative numbers. The Greeks used the negative numbers in the 3rd century in equivalents. But the Indians were the first to use the negative sign as a debit.
The rational numbers or fractional numbers were first used by the Ancient Egyptians, as the fraction numbers were found in the Mathematical Papyrus. While the decimal numbers were first used by the Roman Archimedes (287B.C.-212B. C.) the famous mathematician, physicist, engineer and inventor.
The irrational numbers were first proved by Pythagoras (570 B.C.-495 B.C.) the famous Greek mathematician and philosopher, as he was trying to prove the concepts of Hippasus, who has suggested the irrational numbers when trying to find the square root of two.
Heron (Hero of Alexandria) the Greek mathematician and engineer(10-70), was the first to mention the complex numbers. The complex numbers are the numbers that can be presented in the form ax+b were a and b are real numbers.
Euclid the Greek mathematician was the first to suggest the prime numbers.
The Indian mathematician Yajurveda was the first to suggest the infinity in the 4th century B.C..