What Math Did Ancient Greece Discover?

Ancient Greece is often considered the birthplace of modern mathematics. The Greeks made numerous discoveries and contributions to the field of mathematics that are still relevant today. In this article, we’ll explore some of the most important mathematical discoveries made by the ancient Greeks.


One of the most significant contributions made by the ancient Greeks to mathematics was in the field of geometry. Euclid, a Greek mathematician, is often referred to as the “Father of Geometry.” He wrote a book called “Elements,” which contained 13 volumes and was considered one of the most influential works in mathematics.

Euclid’s “Elements” included definitions, axioms, and propositions related to geometry. He introduced several important concepts, such as points, lines, angles, and planes. He also proved various geometric properties and created a system of logical reasoning that is still used today.

Pythagorean Theorem

Another crucial discovery made by the ancient Greeks was the Pythagorean theorem. This theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The Pythagorean theorem was discovered by Pythagoras, a Greek mathematician who founded a school in southern Italy. While he did not actually prove this theorem himself, his followers were able to do so using various geometric methods.


Trigonometry is another field in which ancient Greeks made significant contributions. Hipparchus was a Greek astronomer and mathematician who created one of the first trigonometric tables. He used these tables to predict eclipses and other astronomical events.

In addition to Hipparchus’ work on trigonometry, Ptolemy also contributed to this field with his book “Almagest.” In this book, he introduced several trigonometric formulas, such as the sine and cosine functions.

Number Theory

The ancient Greeks also made important contributions to number theory. Pythagoras, in addition to his work on the Pythagorean theorem, is also credited with discovering that numbers could be represented as ratios. He believed that all things could be explained through numbers and ratios, a philosophy known as Pythagoreanism.

Another Greek mathematician who made contributions to number theory was Euclid. He developed a system of prime numbers and proved that there are an infinite number of primes.


The ancient Greeks made numerous discoveries and contributions to the field of mathematics. Their work in geometry, trigonometry, and number theory laid the foundation for modern mathematics. From Euclid’s “Elements” to Pythagoras’ theorem, these discoveries continue to shape our understanding of math today.