Georg Cantor was a pioneering mathematician born on March 3, 1845, in Saint Petersburg, Russia, to a Danish father and Maria Anna Böhm, born in Saint Petersburg, Russia, and of Austro-Hungarian descent, with his mother being musical and his father a merchant. His family relocated to Frankfurt when he was eleven due to his father's illness, and he demonstrated exceptional mathematical talent before his fifteenth birthday despite initial pressure to pursue engineering instead. Cantor studied at the University of Zürich before transferring to Berlin in 1863, where he was mentored by Karl Weierstrass, attended lectures by Ernst Kummer, and studied under Leopold Kronecker. He completed his doctoral thesis in 1867 on indeterminate equations of the second degree and joined the faculty at the University of Halle in 1869, where he remained for his entire career, progressing from lecturer to full professor by 1879.
Cantor revolutionized mathematics by founding set theory as a distinct mathematical discipline and introducing the concept of transfinite numbers to describe different magnitudes of infinity. His groundbreaking work demonstrated that the set of real numbers is more numerous than the set of natural numbers, establishing for the first time that infinite sets can have different sizes. He developed the critical concept of one-to-one correspondence between sets, defined infinite and well-ordered sets, and created the arithmetic of cardinal and ordinal numbers that extended natural number arithmetic to the infinite. Cantor's introduction of the power set operation and his theorem proving that the size of a power set is strictly larger than the set itself further cemented his place as the architect of modern mathematical infinity.
Despite the profound significance of his work, Cantor faced intense opposition from prominent mathematicians like Leopold Kronecker, which contributed to his periodic mental health struggles throughout his later years. A devout Lutheran Christian, Cantor believed his theory of transfinite numbers was directly communicated to him by God, though some theologians initially viewed his work as challenging the divine infinity. His continuum hypothesis was famously presented by David Hilbert as the first of twenty-three open problems at the 1900 International Congress of Mathematicians, cementing its importance in mathematical research. Cantor's legacy endures as the foundation of modern mathematics, with set theory now universally recognized as the fundamental framework underlying nearly all mathematical disciplines, validating his courageous pursuit of mathematical truth against significant contemporary skepticism.
