Development of Mathematics: Ancient Civilizations

Vocabulary and key figures in the history of mathematics across Greek, Islamic, Hindu, and Chinese civilizations.

Thales of Miletus

Known as the Father of Greek Mathematics, he introduced geometry and proof into the study of mathematics.

Zeno of Elea

A Greek philosopher known for paradoxes such as Achilles and the Tortoise, who challenged ideas about motion, space, and infinite division.

Democritus

A Greek philosopher and mathematician who studied geometry, volume, the relationships between solids, and infinite division.

Pythagoras of Samos

Founder of the Pythagorean School who held the belief "All is Number."

Pythagorean Theorem

A contribution of Pythagoras that applies to right triangles with the formula $a^2 + b^2 = c^2$.

The Academy of Athens

The institution founded by Plato, who promoted geometry and believed mathematics clarifies reality.

Squaring the circle

A classical problem to construct a square with an area exactly equal to a given circle; proved impossible by Ferdinand von Lindeman in 1882.

Doubling the cube

A classical problem to construct a cube with exactly twice the volume of a given cube; proved impossible by Pierre Wantzel in 1837.

Trisecting the angle

A classical problem to construct an angle exactly one-third of any given angle; proved impossible by Pierre Wantzel in 1837.

First Mathematical Crisis

The discovery of the square root of 2 ($\sqrt{2}$) and irrational numbers, which challenged Pythagorean beliefs.

House of Wisdom

Located in Baghdad, this was a center of learning and translation during the Golden Age of Islamic Mathematics (9th–15th century).

Muhammad Al-Khwarizmi

Often called the Father of Algebra, he worked at the House of Wisdom and developed methods for solving equations.

Al-Karaji

A mathematician who used mathematical induction and contributed to the development of the Binomial Theorem.

Binomial Theorem

A theorem stated as $(a + b)^n = a^n + na^{n-1}b^1 + \frac{n(n-1)}{2}a^{n-2}b^2 + \text{...} + b^n$.

Brahmagupta

The author of Brahma-Sphuta-Siddhanta who explained the use of zero and helped develop the Hindu-Arabic numeral system.

Sulba Sutras

The oldest known mathematical records from India, dated between the 8th century BC and 2nd century AD.

Bhaskara II

A 12th-century Indian mathematician and astronomer who contributed to algebra, trigonometry, and early calculus ideas.

Emperor Qin Shi Huang

An emperor of the Qin Empire who in 212 BC commanded the burning of books that were not officially sanctioned.

The Nine Chapters on the Mathematical Art

A Chinese text consisting of 246 word problems involving agriculture, business, geometry, engineering, and surveying.

Chu Shih-chieh

A mathematician from the 13th century (Sung period) who represented the high-water mark of Chinese algebra.