Short answers, pulled from the story.
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria used arithmetic, algebra and geometry for taxation, commerce and astronomy, and the subject spread worldwide over the following millennia.
The earliest mathematical texts come from Mesopotamia and Egypt, including Plimpton 322 from around 2000 to 1900 BC, the Rhind Mathematical Papyrus from about 1800 BC, and the Moscow Mathematical Papyrus from about 1890 BC. Knowledge of Babylonian mathematics comes from more than 400 clay tablets unearthed since the 1850s.
The study of mathematics as a demonstrative discipline began in the 6th century BC with the Pythagoreans, who coined the term mathematics from the Greek mathema, meaning subject of instruction. Greek mathematicians introduced deductive reasoning and rigorous proof, unlike earlier cultures that relied on inductive rules of thumb.
Babylonian mathematics used a sexagesimal, base-60 numeral system, which is why we still count 60 seconds in a minute, 60 minutes in an hour, and 360 degrees in a circle. One explanation is that 60 divides evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, making hand calculation easier.
The Hindu-Arabic numeral system evolved in India over the first millennium AD, and Brahmagupta explained the use of zero as both placeholder and decimal digit in the 7th century. Islamic mathematicians met the system through a translation around 770 and the work of al-Khwarizmi, and it reached Europe by the 12th century, eventually displacing all older number systems.
Isaac Newton brought together the concepts now known as calculus in the 17th century while discovering the laws of physics that explain Kepler's laws of planetary motion. Independently, Gottfried Wilhelm Leibniz developed calculus and much of the calculus notation still in use today.
In a 1900 speech to the International Congress of Mathematicians, David Hilbert set out a list of 23 unsolved problems that shaped much of 20th-century mathematics. Of these, 10 have been solved, 7 partially solved, 2 remain open, and 4 are too loosely formulated to be judged solved or not.