Short answers, pulled from the story.
The Lebombo bone, discovered in the Lebombo Mountains of Eswatini, bears 29 distinct notches carved into a baboon fibula, dating back approximately 43,000 years. This artifact stands as one of the oldest known physical evidence of human arithmetic, suggesting that the impulse to count and track quantities predates the development of complex language itself.
Around 1800 BCE, the ancient Babylonians revolutionized the way humanity represented numbers by inventing the first positional numeral system. This system utilized a base-60 structure where the position of a symbol determined its value, allowing for the efficient representation of large numbers and the performance of complex calculations.
Brahmagupta, writing around 628 CE, provided the first detailed rules for operating with zero and negative numbers, applying them to practical problems such as credit and debt. This innovation was later refined and transmitted to the Western world by Middle Eastern mathematicians during the Islamic Golden Age, most notably by Al-Khwarizmi.
The Dedekind, Peano axioms, formulated by Richard Dedekind and refined by Giuseppe Peano, provide a small set of rules from which all fundamental properties of natural numbers can be derived. These axioms establish that zero is a natural number, that every natural number has a successor, and that the successors of two different numbers are never identical.
The 17th century witnessed the birth of mechanical arithmetic, transforming calculation from a purely mental or manual task into an automated process. Blaise Pascal's calculator and Gottfried Wilhelm Leibniz's stepped reckoner were among the first machines capable of performing all four basic arithmetic operations, using gears, levers, and wheels to automate the tedious process of long multiplication and division.