Short answers, pulled from the story.
The Babylonian tablet known as Plimpton 322 dates to approximately 1800 BC and contains a sexagesimal numeral system still used today for measuring angles. This artifact reveals that elementary arithmetic operations like addition, subtraction, multiplication, and division were already established in Mesopotamia before the rise of Greek philosophy.
Archaeological evidence suggests ancient Egyptian counting systems had origins in Sub-Saharan Africa with fractal geometry designs appearing in their architecture and cosmological signs. Nubians developed a geometric system serving as the basis for initial sunclocks while exercising trigonometric methods comparable to their Egyptian counterparts.
David Hilbert founded formalism around 1910 establishing that each mathematical object is defined by the set of all similar objects and properties they must possess. Kurt Gödel transformed mathematics in the early 20th century by publishing incompleteness theorems showing any consistent axiomatic system powerful enough to describe arithmetic contains true propositions unprovable within that system.
François Viète introduced use of variables for representing unknown or unspecified numbers between 1540 and 1603. Leonhard Euler unified these innovations into a single corpus with standardized terminology during the 18th century after Isaac Newton and Gottfried Leibniz independently introduced infinitesimal calculus in the 17th century.
The perihelion precession of Mercury could only be explained after emergence of Einstein's general relativity replacing Newton's law of gravitation as better mathematical model. Albert Einstein developed theory of relativity at beginning of 20th century using fundamentally non-Euclidean spaces of dimension four and curved manifolds of dimension four.