Georg Cantor

Georg Cantor was a German mathematician who created set theory and introduced the concept that infinite sets can themselves come in different sizes. Working mainly in the 1870s and 1880s, Cantor proved using his now-famous diagonal argument that the set of real numbers is strictly larger than the set of natural numbers, even though both are infinite, establishing the existence of what he called transfinite numbers to measure and compare different infinite quantities. This work was deeply controversial among his contemporaries, and Cantor faced sustained opposition from some prominent mathematicians of his day, including his former teacher Leopold Kronecker, who rejected the legitimacy of actual infinite sets as mathematical objects. Despite this resistance, Cantor's set theory ultimately became a foundational framework underlying most of modern mathematics, and his ideas about infinite cardinality are now standard material in mathematical education.