Paul Bachmann

Paul Bachmann (1837–1920) was a German mathematician whose 1892 treatise Analytische Zahlentheorie introduced the O-notation that would become the standard language of asymptotic analysis in mathematics and computer science. A student of Karl Weierstrass, Bachmann worked primarily in number theory and algebraic number fields, yet his notational invention has outlived his substantive mathematical contributions by more than a century. The irony is instructive: the tools we use to describe complexity often achieve more enduring influence than the discoveries they were built to describe.