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Probably the ancient Egyptians who discovered that the diagonal of a unit square was not a rational number. And then discovered other such numbers.
It was known from ancient times that pi is irrational. However, that fact was proven in 1761 by the Swiss scientist Johann Heinrich Lambert.
There is no single mathematician. It has been known since ancient times that the length of the diagonal of a unit square is sqrt(2) which is irrational.
Pythagoras was an ancient philosopher that attributed most of his work to Plato. He however, never went to jail.
The history of rational numbers goes way back to the beginning of historical times. It is believed that knowledge of rational number precedes history but no evidence of this survives today. The earliest evidence is in the Ancient Egyptian document the Kahun Papyrus. Ancient Greeks also worked on rational numbers as a part of their number theory. Euclid's elements dates to around 300 BC. Indian mathematicians also worked on rational numbers. This is documented in different texts but the most important is probably the Sthananga Sutra which dates back to around the second century BC.