Georg Ferdinand Ludwig Philipp Cantor (1845-1918), the German mathematician is best known as the founder of set theory. His marvelous work on transfinite numbers sparked a profound revolution in mathematical and philosophical thought.
Georg Cantor was born on March 3, 1845, in Saint Petersburg, Russia, as the eldest son of Georg Waldemar Cantor and Maria Anna Böhm, niece of famous musician Joseph Böhm. During his childhood, Georg’s exceptional skills as a violinist and as a mathematician were soon recognized. In 1856, the family settled in Germany after the illness of his father. Cantor entered the Wiesbaden Gymnasium at the age of 15, and two years later began his university career in Zurich, Switzerland. In 1863, he moved to the University of Berlin, where he studied under Weierstrass, Kummer, and Kronecker. In 1867, at the age of 22, he received his PhD for a thesis on number theory, and was appointed at Halle University in 1869. Cantor’s first ten papers were on number theory. At the suggestion of Eduard Heine, Professor at Halle, Cantor turned to analysis and later went on to solve the open problem: the uniqueness of the representation of a function by trigonometric series. It was while working on this problem that he discovered transfinite ordinals. Between 1870 and 1872, Cantor published more papers on trigonometric series, as well as one defining irrational numbers as convergent sequences of rational numbers. Toward the end of the nineteenth century, his study of continuity and the infinite eventually forced him to depart radically from standard interpretations and use of infinity in mathematics. Cantor’s results were not immediately accepted by his contemporaries. The hostile attitude of many severely aggravated Cantor’s emotional ailments and caused several nervous breakdowns. During these troubled times, Cantor sought encouragement and support from his faith in God, inherited from his religious upbringing.
In fact, Cantor did regard his work as a sacred mission. He asserted the unquestionable, indubitable correctness of his research work because it had been revealed to him by God. In a letter to his friend Gösta Mittag-Leffler, he expresses: “Far be it from me to take credit personally for my discoveries. I am merely the tool of a higher power, that will pursue its course when I am gone, even as it revealed itself thousands of years ago in Euclid and Archimedes”. His periods of isolation in the hospital could be regarded as periods during which, as he told Mrs. Young, the transfinite numbers lay neither fallow nor forgotten, but might be further elucidated by the grace of God sent to inspire new lines of research.
In various ways Cantor repeatedly expressed the intimate involvement of God in mathematics via metaphysics. In a letter to Father Thomas Esser he wrote: “Every extension of our insight into the origin of the creatively-possible therefore must lead to an extension of our knowledge of God”.
Cantor believed that God endowed the transfinite numbers with a reality making them very special, for the greater understanding of God and nature. In 1904, he was awarded the Sylvester Medal, the highest honor, by the Royal Society of London, and was made a member of both the London Mathematical Society and the Society of Sciences in Gottingen.