Georg Cantor (gā´ôrkh kän´tôr), 1845–1918, German mathematician, b. St. Petersburg. He studied under Karl Weierstrass and taught (1869–1913) at the Univ. of Halle. He is known for his work on transfinite numbers and on the development of set theory, which is the basis of modern analysis, as well as for his definition of irrational numbers. His approach to the concept of the infinite revolutionized mathematics by challenging the processes of deductive reasoning and led to a critical investigation of the foundations of mathematics.