Proof that pi is irrational

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In the 1760s, Johann Heinrich Lambert was the first to prove that the number π is irrational, meaning it cannot be expressed as a fraction a / b , {\displaystyle a/b,} where a {\displaystyle a} and b {\displaystyle b} are both integers. In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and Nicolas Bourbaki (pseudonym of a group of mathematicians). Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich. Many of these are proofs by contradiction. In 1882, Ferdinand von Lindemann proved that π {\displaystyle \pi } is not just irrational, but transcendental as well.

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