Short answers, pulled from the story.
The oldest known arithmetic artifact is the Lebombo bone, which dates back approximately 43,000 years to the late Stone Age. This baboon fibula bears 29 distinct tally marks carved into it, suggesting that the human impulse to count predates the development of spoken language.
The first recorded use of zero as a true integer appeared in the year 628 in the Brāhmasphuīasiddhānta, the main work of the Indian mathematician Brahmagupta. Before this date, ancient civilizations like the Babylonians and Egyptians used symbols to represent empty positions but never treated the void as a number with its own properties.
Hippasus of Metapontum, a Pythagorean mathematician who lived in the 5th century BC, allegedly died by drowning after proving that the diagonal of a square with a side of one unit could not be expressed as a ratio of two integers. The Pythagoreans sentenced him to death to prevent the spread of this heretical knowledge that challenged their belief that all numbers could be represented as whole number ratios.
René Descartes coined the term imaginary in 1637 as a derogatory label to dismiss numbers involving the square root of negative one. Caspar Wessel provided the geometric interpretation of these numbers in 1799, plotting them on a plane where the real and imaginary parts formed a vector space.
Georg Cantor published a book introducing transfinite numbers in 1895, formulating the continuum hypothesis and challenging the traditional view that infinity was merely a potential process. He demonstrated that the set of all real numbers is uncountably infinite while the set of all algebraic numbers is countably infinite, proving that there are different sizes of infinity.
The prime number theorem was proved by Jacques Hadamard and Charles de la Vallée-Poussin in 1896, following a conjecture by Adrien-Marie Legendre in 1796. This theorem describes the asymptotic distribution of primes, which are integers greater than one that are not the product of two smaller positive integers.