Was the Pythagorean Theorem Plagiarized? Ancient Babylonian Tablet Predates Pythagoras by 1,000 Years

Recent evidence suggests that the Pythagorean theorem might not have been an original creation by the ancient Greek philosopher Pythagoras. A modern mathematician has come across an ancient Babylonian tablet that suggests the theorem existed over 1,000 years before the Greek philosopher's birth. This tablet presents a concept similar to the theorem, raising questions about its true origin.

Is the Pythagorean Theorem the World's Oldest Case of Plagiarism?

According to legend, Pythagoras is famous for discovering the Pythagorean theorem when he observed right triangles formed by square tiles in a palace hall. He realized that the areas of the squares on the two shorter sides were equal to the area of the square on the longest side, the hypotenuse. From this intuitive insight, he believed this principle held true for all right triangles, and later, he established a formal proof.

Mathematician Bruce Ratner, with a Ph.D. in Mathematical Statistics and Probability from Rutgers University, conducted research that challenges this traditional attribution of the theorem to Pythagoras. Ratner's work, published in 2009 and recently resurfaced, points to evidence from a clay tablet known as YBC 7289, which dates between 1800 and 1600 BC, indicating that Babylonian mathematicians knew the Pythagorean theorem more than 1,000 years before Pythagoras' birth.

Ratner examined the YBC 7289 tablet, located at Yale University, which contains markings related to squares and their diagonals. He deciphered the base 60 numerical system used by the Babylonians, demonstrating their understanding of the relationship between the diagonal and side of a square (d = √2a), a concept that can be linked to the Pythagorean theorem.

The study argues that the Babylonians likely knew the Pythagorean theorem or, at the very least, the special case of the theorem for the diagonal of a square (d² = a² + a² = 2a²) more than a millennium before it was associated with Pythagoras.

Ratner also suggests that Pythagorean knowledge may have been transmitted orally among generations, contributing to Pythagoras' reputation as the theorem's namesake. This discovery prompts a reevaluation of the origins of the Pythagorean theorem and its place in mathematical history.

The Pythagorean Theorem

The Pythagorean Theorem, a foundational principle in mathematics, defines the relationship within a right-angled triangle. A right-angled triangle is characterized by one of its angles measuring 90 degrees, known as the right angle, with the side opposite this angle termed the hypotenuse. The other two sides, adjacent to the right angle, are called the legs.

This theorem, often referred to as the Pythagorean Theorem, posits that the square of the hypotenuse's length is equal to the sum of the squares of the lengths of the other two sides in the right-angled triangle.

In mathematical terms, it is expressed as c² = a² + b², where 'c' represents the hypotenuse, while 'a' and 'b' denote the lengths of the other two legs. This equation applies to any triangle featuring one angle of 90 degrees, making it a Pythagorean triangle.

The Pythagorean Theorem holds various practical applications, including verifying whether a given triangle is indeed right-angled. It is also instrumental in aerospace science and meteorology for calculating range and sound source localization, while oceanographers use it to determine the speed of sound in water.