Georg Cantor
24x30, oil on canvas, February 2017
1845 – 1918, German Mathematician
My first encounter with Georg Canter was through an article in Scientific American around 1983, Georg Cantor and the Origins of Transfinite Set Theory by Joseph Dauben. At the time, I was in the midst of a series of calculus and physics courses which included infinite series and limit concepts. I found the article interesting because I could actually understand some of it.
Georg Cantor founded set theory, now fundamental to mathematics. Through the propositions and conclusions of set theory, he showed that one infinite set can be larger than another. There is, as well, a hierarchy of ever greater infinite sets, and that this hierarchy is itself infinite. This became known as the theory of transfinite numbers.
Mathematical inference is an exercise in pure reason. It is disconnected from the corporeal, the physical, except for the symbolic language of subjects, objects and predicates that convey its results. With respect to infinity, in mathematics there is an important distinction made between “potential” infinity and “completed” or “actual” infinity. The distinction dates to the time of the pre-Socratic Greek philosopher Anaximander.
Cantor investigated the properties of completed infinite sets. He treated these as mathematical objects in logical statements which, while provable, were both astonishing and counterintuitive.
He was ostracized by his peers in the mathematical community, and to this day his conclusions respecting transfinite numbers are controversial.
He was a devout Lutheran. Like Johannes Kepler, the astronomer, who lived before him, he believed that he was revealing the mind of God. It was this connection to spirituality, in the context of profound reason, that interested me about Canter. Not long after I had read the article cited above, I came across, and was fascinated by, a translation of Cantor’s work on transfinite numbers in the Drexel University Library. It was Cantor’s portrait on the cover that became the basis for my painting.