Georg Cantor – Biography of Georg Cantor

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The brilliant mathematician, Georg Ferdinand Ludwig Philipp Cantor He was born on March 3, 1845 in Saint Petersburg (Russia), where he lived until the age of eleven, and then moved to Germany, where he lived most of his life. His father, Georg Waldemar Cantor, decided to move to Germany, despite being a successful businessman and an experienced stockbroker, for health reasons. His mother, Maria Anna Bohm, was a major Russian music artist, and she certainly influenced her son, who became interested in learning to play the violin.

In 1856, once settled in Germany, they lived for some years in Wiesbaden, where Singer attended high school. Upon graduating from high school in Wiesbaden, with his family he moved to Frankfurt where from 1862 he attended courses in mathematics and philosophy, first at the University of Zurich and then in Berlin, where he was a student of EE Kummer, Weierstrass and WT L. Kronecker. In 1867 he graduated and in 1869 he obtained free teaching presenting works related to number theory. In 1874, he met Vally Guttmann, a friend of his sister’s, and after a few months, he married.

Later, under the influence of Weierstrass, Singer changed his interest to analysis, and more particularly to the study of trigonometric series. In 1872 he was appointed professor and in 1879 professor at the University of Halle.

There Singer he was able to develop his complicated studies in peace, which resulted in fundamental contributions to various sectors, such as the study of trigonometric series, on the non-countability of real numbers or the theory of dimensions; however, he became known in the academic environment especially for his work on set theory. In particular, he was responsible for the first rigorous definition of “infinite set”, as well as for the construction of the theory of transfinite numbers, both cardinal and ordinal.

Singer showed that infinities are not all the same, but that, similar to integers, they can be classified (that is, some are “larger” than others). He managed to build a complete theory of these which he called transfinite numbers. The idea of ​​infinity is one of the most controversial in the history of thought. Just think of the perplexity with which mathematicians welcomed the infinitesimal calculus of Leibniz and Isaac Newton, based entirely on the concept of infinitesimal quantities (which they called “evanescent”).

Although the set theory of Singer was later modified and completed, it remains the basis of the study of the properties of infinite sets. The criticisms and heated discussions, which were expressed at the beginning, were perhaps the basis of the states of depression that assailed Singer in the last years of his life. Already in 1884 he had the first manifestation of the nervous disease that struck him repeatedly until his death.

In the light of a biographical study of his life, in fact, it seems probable that, in addition to the uncertainty about the validity of his work, scientific and academic ostracism, attributed mainly to L Kronecker, who screwed up every attempt to teach in Berlin. From that moment on, in fact, Singer he spent his life between universities and hospitals.

He died of a heart attack on January 6, 1918, while he was hospitalized in a psychiatric clinic.