George cantor set theory images

Sylvia Karasu
New York, New York, United States

There is a “fine line between brilliance and madness”: the distinction, for example, between a “revolutionary” mathematical theory and psychotic thinking may well have to do with what can be done with the theory, i.e., its “significant results.”¹ “The mentally ill mathematician” is like the “knight errant, mortified saint, tortured artist and mad scientist” of preceding eras—a kind of “Prometheus—the one who goes to forbidden places and returns with gifts we can use but he alone pays for.”² John Nash, portrayed in the book and film A Beautiful Mind,³ is one example, as is the lesser-known late nineteenth- and early twentieth-century German mathematician Georg Cantor, whose contributions on set theory and magnitudes of infinity were groundbreaking.⁴ “The mathematical theory of infinity may almost be said to begin with Cantor.”⁵

During much of his lifetime, though, Cantor aroused controvers