The Mind of the Mathematician

Chapter 6. Cantor, Kovalevskaya, Poincar

105 Chapter 6 } Cantor, Kovalevskaya, Poincaré, and Hilbert Georg Cantor Georg Woldemar Cantor, the father of the mathematician, was a native of Copenhagen who in his youth moved to St. Petersburg. There he became a successful stockbroker and married Maria Anna Bohm Meyer, who came from a musical family. Their son Georg Ferdinand Ludwig Philipp was born on 3 March 1845, the first of four children. He was raised in an intensely religious atmosphere; his mother was a Roman Catholic but his father was a staunch Lutheran. On the occasion of his son’s confirmation, his father, a sensitive and gifted man, wrote a letter to him that Cantor would never forget. It foreshadowed much that was to happen to him in later years: No-one knows beforehand into what unbelievably di≈cult conditions and occupational circumstances he will fall by chance, against what unforeseen and unforeseeable calamities and di≈culties he will have to fight in the various situations of life. How often the most promising individuals are defeated after a tenuous, weak resistance in their first serious struggle following their entry into practical a√airs. Their courage broken, they atrophy completely thereafter, and even in the best case they will still be nothing more than a ruined genius. But they lacked the steady heart, upon which everything depends! Now, my dear son! Believe me, your sincerest, truest and most experienced friend—this sure heart, which must live in us, is a truly religious spirit. But in order to avoid as well all those other hardships and di≈culties which inevitably rise against us through the jealousy of and slander by open or secret enemies in our eager aspiration for success in the activity of our own speciality or business; in order to combat these with success one needs above all to ac- 106 Twenty Mathematical Personalities quire and to appropriate the greatest amount possible of the most basic, diverse technical knowledge and skills. Nowadays these are an absolute necessity if the industrious and ambitious man does not want to see himself pushed aside by his enemies and forced to stand in the second or third rank. In 1856, when young Cantor was 11, the family moved from Russia to Germany . They lived in Wiesbaden to start with, and from the age of 15 he attended the local Gymnasium. He showed all-around ability, but mathematics and science were his strongest subjects, and his father decided he should train as an engineer. With this end in view, Cantor began his higher education at the Polytechnikum in Zurich. Already there were signs of the mental instability that was to worsen as he grew older. In Zurich, the young man worked long into the night, endangering his health. Lack of sleep left him tired and eventually so despondent that his father became worried about his melancholic condition. Next, Cantor’s father, who was dying of tuberculosis, agreed to let him transfer to the University of Berlin and study mathematics instead of engineering , where he proved to be a good but not exceptional student. After obtaining his doctorate in 1867, at the age of 22, Cantor became a schoolteacher for a short while and then privatdozent at the University of Halle, not far from Leipzig. Fortunately his wealthy father had left him well o√, since it was five years before he became associate professor and another seven before he was promoted to full professor. Although the stipend was not generous, he remained at Halle for his entire career. Those who knew him in his prime described Cantor as energetic, forceful , and volatile. One in particular described him as a man of loud and intense character, true to friends, helpful when needed, noble and generous. Another described him as a man of imposing stature, witty, spirited, amiable , and in his youth particularly lively and stimulating in conversation. Yet another described him as one of the most stimulating of Germany’s mathematical personalities; his presence at any congress or meeting was always an enticing attraction; his mind was as imaginative and sparkling as it was temperamental and explosive. On one occasion Karl Weierstrass was entertaining a number of mathematical friends, including Cantor, when apparently without warning, Cantor exploded with rage over the fact that he had not been o√ered the position given to Felix Klein at Göttingen three years earlier. Such a swift and violent outburst foreshadowed the paranoid behavior of his later years. [18.118.164.151] Project MUSE (2024...