Georg CANTOR 👨‍🎓 (1845-1918)

Today I want to talk about the German mathematician George Cantor, who pioneered set theory and gave us our modern understanding of the mathematics of infinity. Now I did another video called To Infinity and Beyond which will tell you more about the maths itself. In this video I want to focus more on on the man. Now George Cantor faced a tremendous amount of opposition during his lifetime about his ideas of infinity, even from colleagues and from other mathematicians. In fact he had very little support in the beginning and also of course there was the pressure of the subject itself. Imagine spending much of your career thinking about infinity and things to do with it. So his life was in many ways quite difficult from that point of view. So now let's find out a little bit more about George Cantor the mathematician. George Cantor was born in St Petersburg, Russia on March the 3rd 1845. His family moved to Germany when he was 11. As a youth he excelled in maths and was an outstanding violinist. He went on to study maths at the University of Berlin under some of the greats of the day including Carl Weierstrasser and Leopold Kronecker. Later his research led him to consider infinity not just as some abstract concept but as a new type of number, a transfinite number. What's more he realized infinity comes in different sizes. And as I said earlier for details about the mathematics of infinity you might want to check out my video on this channel called To Infinity and Beyond. Cantor showed that the set of all real numbers is larger than the set of all natural numbers and perplexingly that there are just as many points on a short line as there are on a line that extends forever or on a plane or in any multi-dimensional space. On reading Cantor's proof of this his compatriot and friend Richard Dedekind said I see it but I don't believe it. Dedekind and later the Swedish mathematician Gösta Mittag-Leffler were among the few researchers at the time who offered Cantor support. Several prominent mathematicians vehemently opposed his ideas about infinity and not just on technical grounds. The leading French theorist Henri Poincaré believed that Cantor's theory of infinite sets would be regarded by future generations as a disease from which one has recovered. Most hurtful of all to Cantor on a personal level were the attacks of Leopold Kronecker his distinguished old mentor. Kronecker went out of his way to pour scorn on Cantor's ideas, suppress publication of his work and block Cantor's ambition of gaining a position at the prestigious University of Berlin. He even went as far as to label him a scientific charlatan and a corrupter of youth for his heretical views. Meanwhile some theologians were outraged because they regarded his treatment of infinity as a tractable mathematical concept as posing a challenge to the perception of the infinite power of God. He was even denounced as a pantheist. Cantor, a devout Lutheran, totally rejected this accusation. In fact he maintained that his ideas about infinity had actually come from God. In 1884, aged 39, Cantor suffered the first of several attacks of manic depression, exacerbated if not induced by the negative reaction of his contemporaries. In between these episodes he published further mathematical results but increasingly drifted into speculative theorizing in other areas. More and more he spent time engrossed in the philosophical and theological implications of his ventures into the infinite. In another reflection of his unorthodoxy he argued at length in favor of the Baconian theory that the plays normally attributed to Shakespeare were actually written by Francis Bacon. He also composed a dialogue between a master and pupil in which the master makes the case that Joseph of Arimathea had fathered Jesus. Cantor spent the later stages of his life in and out of sanatoria battling with depression. His final years were pretty miserable, dogged by poverty, ill health and a general blackness of spirit. However he did live long enough to see his work vindicated and the likes of David Hilbert and Bertrand Russell praise what he'd done in the highest terms. Regarding Cantor's development of set theory and his explorations of the infinite, Hilbert thought them the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.