Mathematics is not an invention. Discoveries and laws of science are not considered inventions. Inventions are material things and processes. However, there is a history of mathematics, a relationship between mathematics and inventions, and mathematical instruments are considered inventions.

According to *Mathematical Thought from Ancient to Modern Times*, mathematics as an organized science did not exist before the classical Greeks of the period from 600 to 300 BC entered upon the scene. There were, however, prior civilizations in which the beginnings or rudiments of mathematics were created.

When civilization began to trade, a need to count was created. When humans traded goods, they needed a way to count the goods and to calculate the cost of those goods. The very first device for counting numbers was the human hand, counting on fingers. To count beyond ten fingers, mankind used natural markers, rocks or shells. From that point, counting boards and the abacus were invented.

### Abacus

One of the first tools for counting invented, the abacus was invented around 1200 A.D. in China.### Accounting

The innovative Italians of the Renaissance (fourteenth through sixteenth century) are widely acknowledged to be the fathers of modern accounting.### Algebra

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

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).### Differential

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).### Graph

A graph is a pictorial representation of statistical data or of a functional relationship between variables. William Playfair (1759-1823) is generally viewed as the inventor of most of graphical forms used to display data, including: line plots, bar chart, and pie chart.### Logarithms and the Decimal Point

John Napier was the Scottish mathematician who invented logarithms and the decimal point.### Mathematics Timelines

- History of Mathematics Time Line
- A Time-line for the History of Mathematics
- History of Mathematics Education
- A Time Line of Mathematicians