Euclid's "Elements" is one of the oldest math books, with 13 books covering almost all of mathematics known at the time, including geometry and number theory. The book relies on five postulates, including the controversial fifth postulate, also known as the Parallel postulate. Mathematicians were skeptical of this postulate for over 2,000 years, as it seemed like a mistake, and many tried to prove it from the first four postulates.
However, all they managed to do was restate the postulate in different words. Eventually, mathematicians like al-Haytham and Omar Khayyam tried a different approach, proof by contradiction, assuming that the fifth postulate was false, then using those new postulates to prove theorems. If that led to a contradiction, then the new fifth postulate must be wrong. Slight tweaks to this line opened up strange new universes out of nothing, which are now core to understanding our own universe. Euclid's method of using simple postulates and building up math using logic is the gold standard for rigorous mathematical proof that all modern math relies on.
