The first mathematics can be traced to the ancient country of Babylon and to Egypt during the 3rd millennium BC. A number system with a base of 60 had developed in Babylon over time. Large numbers and fractions could be represented and formed the basis of advanced mathematical evolution. From at least 1700 BC, Pythagorean triples were studied. The study of linear and quadratic equations led to form of primitive numerical algebra. Meanwhile, similar figures, areas, and volumes were studied as well as the primitive values for pi obtained. The Greeks inherited the Babylonian principles and developed mathematics from 450 BC. They discovered that all real numbers could not accurately express all values, such as relationships between sides. Irrational numbers were born. The Greeks progressed rapidly in mathematics from 300 BC. Progress also sped in the Islamic countries of Syria, India, and Iran. Their work had a different focus from that of the Greeks, but all Greek principles held true. This basis was later brought to Europe and developed further there.
The History of Mathematics and Accounting
According to http://www.museums.reading.ac.uk:
The first treatise on algebra was written by Diophantus of Alexandria in the 3rd century AD. Algebra comes from the Arabic word al-jabr an ancient medical term meaning "the reunion of broken parts.''
Archimedes was a mathematician and inventor from ancient Greece, best known for his discovery of the relation between the surface and volume of a sphere and its circumscribing cyclinder, for his formulation of a hydrostatic principle (Archimedes' principle) and for inventing the Archimedes screw (a device for raising water).
Gottfried Wilhelm Leibniz (b. 1646, d. 1716) was a German philosopher, mathematician, and logician who is probably most well known for having invented the differential and integral calculus (independently of Sir Isaac Newton).
Logarithms and the Decimal Point
John Napier was the Scottish mathematician who invented logarithms and the decimal point.
Well, it wasn't Pythagoras, but it is believed he was the first to discover the concept of intervals with respect to numerical ratios