The Ancient Greek Pythagoreans discovered the existence of irrational numbers in the fifth century BCE, to the legendary demise of one of their number, Hippasus, and were perturbed by them since they contradicted the firmly-held belief that everything related to number and geometry came back to natural numbers and their ratios (rational numbers).

The Greeks were rather late to the party, though. It’s thought that Indian mathematicians were thinking about irrational numbers a whole three hundred years earlier – Manava (c. 720 BCE) thought that certain square roots could not be determined – but, as with many things in the history of mathematics, it is not always clear where, or from whom, an idea originated. Much like any academic history, mathematics is a mix of human thought across time and space.

Continue reading “Mathematical Stories 3 – Irrationality and Infinity”