Cantor Mathematician Quotes & Sayings

A small but typical example of how 'philosophy' sends out new shoots is to be found in the case of Georg Cantor, a nineteenth-century German mathematician. His research on the subject of infinity was at first written off by his scientific colleagues as mere 'philosophy' because it seemed so bizarre, abstract and pointless. Now it is taught in schools under the name of set-theory. — Anthony Gottlieb

The cases of great mathematicians with mental illness have enormous resonance for modern pop writers and filmmakers. This has to do mostly with the writers'/directors' own prejudices and receptivities, which in turn are functions of what you could call our era's particular archetypal template. It goes without saying that these templates change over time. The Mentally Ill Mathematician seems now in some ways to be what the Knight Errant, Mortified Saint, Tortured Artist, and Mad Scientist have been for other eras: sort of our Prometheus, the one who goes to forbidden places and returns with gifts we all can use but he alone pays for. That's probably a bit overblown, at least in some cases. But Cantor fits the template better than most. And the reason for this are a lot more interesting than whatever his problems and symptoms were. — David Foster Wallace

Engineers had not framework for understanding Mandelbrot's description, but mathematicians did. In effect, Mandelbrot was duplicating an abstract construction known as the Cantor set, after the nineteenth-century mathematician Georg Cantor. To make a Cantor set, you start with the interval of numbers from zero to one, represented by a line segment. Then you remove the middle third. That leaves two segments, and you remove the middle third of each (from one-ninth to two-ninths and from seven-ninths to eight-ninths). That leaves four segments, and you remove the middle third of each- and so on to infinity. What remains? A strange "dust" of points, arranged in clusters, infinitely many yet infinitely sparse. Mandelbrot was thinking of transmission errors as a Cantor set arranged in time. — James Gleick