Georg Cantor is a German mathematician who made significant advancements in set theory. He was born March 3, 1845, in St.
Petersburg, Russia, of parents Georg Waldemar Cantor and Maria Anna Böhm. His father was invested in culture and the arts and his mother was very musical. Georg was an exceptional violinist, gaining considerable artistic talent from his parents. He was raised Protestant, this being the religion of his father, while his mother practiced Roman Catholicism. He had an early education at home with a private tutor then attended primary school in St. Petersburg. He lived in Russia until he was eleven after which moving to Germany in 1856 with his family due to the failing health of his father.
Georg was an exceptionally good student, he excelled in trigonometry particularly. He graduated in 1860, with outstanding reports mentioning, in particular, his skills in mathematics. He enrolled to study at Zurich Polytechnic briefly, however, his studies were cut short after the death of his father in 1863. A while later Cantor began studies at the University of Berlin where he specialized in physics, philosophy, and mathematics.
He was taught by multiple mathematicians including Karl Theodor who specialized in analysis and had great influence over him and Leopold Kronecker who would later oppose him. He spent a term at the University of Göttingen and wrote his dissertation on number theory in 1867. That same year, he was awarded the title of Doctor of Mathematics. After receiving his Doctorate, Georg taught at a girls school in Berlin. He soon after began teaching at the University of Halle and remained there the rest of his career, starting as a lecturer, then assistant professor, then finally full professor. Georg married in 1874 to Vally Guttmann, a friend of his sister. It was a happy marriage and eventually, they had 6 children. In his career, his first papers were on number theory, he then switched his focus onto analysis.
He was the first mathematician to take a systematic look at infinity and give it mathematical precision. Cantor started with the point that if were could add any regular number it must be possible to add infinities. He discovered that it was actually possible to add and subtract infinities and that there were another larger infinity and infinities beyond that. He showed that there may be infinitely many sets of numbers, an infinity of infinities, so to speak. He coined the term “transfinite” attempting to distinguish between different levels of infinity. He published a series of articles in a mathematical journal expanding on his ideas.
Some loved his theory but others seemed to hate it. Famously, Leopold Kronecker–an educator that taught Georg at Berlin as mentioned above– called him a renegade and a “corrupter of youth”. Kronecker was the most vocal in opposition to Cantors ideas, he believed a finite number of steps could create mathematical concepts for natural numbers. Cantor was further criticized as he veered into other areas besides math. He wrote highly in support of the theory that Francis Bacon had been the true author of Shakespeare’s plays. Georg Cantor suffered his first recorded breakdown in 1884. He seemed to recover quickly but his confidence was damaged.
It was believed for a while that his studies and the ridicule he received were the cause of his depression, however, it’s more likely mathematical woes and complicated relationships were magnified by the illness. About this time, Cantor began to worry he may never be able to successfully prove the Continuum Hypothesis. At one point, he had believed he proved it false although he found his mistake the next day. He thought he proved it true as well but again soon found his error. Whenever Cantor had bouts of mental illness, it seemed he would turn his studies away from mathematics and towards philosophy and literary interests. In 1884, during a period of illness, he had requested to lecture on philosophy in lieu of mathematics.
This pattern led some to believe that his contemplations of infinity may have brought his mental illness upon him. In October of 1896, Georg’s mother passed away, followed by the death of his youngest brother in 1899. October 1899, Cantor took a leave from teaching during that winter semester 1899-1900. Soon after, his youngest son died in December of 1899. Although suffering from mental illness he remained at work, however, taking multiple leaves from teaching over the rest of his career. He spent some time in Sanatoriums during the worst attacks of his depression.
Georg was awarded the Sylvester Medal in 1904, a highly prestigious award in mathematics. He took leave for much of 1909 due to his illness but continued work at the university in 1910 and 1911. That same year, he received an invitation from the University of St. Andrews in Scotland to attend the 500th anniversary of the schools founding as a distinguished scholar. In his later years, he constantly fought his illness.
He retired in 1914, and in his final years did no mathematical work at all, focusing instead on the theory of Francis Bacon having written Shakespeare’s works and that Christ was the natural son of Joseph of Arimathea. He spent long periods of time in the Halle sanitorium during attacks of his illness and it was there he died in 1918, never having finished his great project.