Proof of the Irrationality of the Square Root of Two in Babylonian Geometry Problem Tablets

TL;DR

This paper reveals that ancient Babylonian tablets contain an early proof of the irrationality of the square root of two, predating Greek proofs and suggesting possible awareness of irrationality concepts.

Contribution

It demonstrates that Babylonian geometry tablets include a proof of the irrationality of √2, a discovery previously attributed only to Greek mathematics.

Findings

Babylonian tablets contain a proof of √2's irrationality

The proof predates Greek mathematical achievements

It is uncertain if Babylonians understood the concept of irrationality

Abstract

One of the greatest achievements of Greek mathematics is the proof that the square root of 2 is irrational. It has not been thought that the Babylonians appreciated the concept of irrationality and certainly that they did not prove that the square root of two is irrational. Here we show that two Babylonian geometry problem tablets contain a simple proof of the irrationality of the square root of two. It is not known, as yet, if the Babylonians appreciated that these tablets indeed contained this proof.