Georg proved an outstanding student, graduating in 1860. ( b. St. Petersburg, Russia, 3 March 1845; d. Halle, Germany, 6 January 1918), mathematics, set theory. On Dedekind’s intervention, however, it was published in 1874 as “Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen” (“On a Characteristic Property of All Real Algebraic Numbers”). He defined the cardinal and ordinal numbers and their arithmetic. Starting from the work on trigonometric series and on the function of a complex variable done by the German mathematician Bernhard Riemann in 1854, Cantor in 1870 showed that such a function can be represented in only one way by a trigonometric series. His artistic mother, a Roman Catholic, came from a family of musicians, and his father, a Protestant, was a prosperous merchant. His grandfather Franz Böhm (1788–1846) (the violinist Joseph Böhm's brother) was a well-known musician and soloist in a Russian imperial orchestra. Consideration of the collection of numbers (points) that would not conflict with such a representation led him, first, in 1872, to define irrational numbers in terms of convergent sequences of rational numbers (quotients of integers) and then to begin his major lifework, the theory of sets and the concept of transfinite numbers. This problem was of great interest to the mathematical world and was studied by many subsequent mathematicians, including the Czech-Austrian-American Kurt Gödel and the American Paul Cohen. Georg Ferdinand Ludwig Philipp Cantor (/ˈkæntɔr/ KAN-tor; March 3 [O.S. Premium Membership is now 50% off! Cantor’s father, Georg Waldemar Cantor, was a successful and cosmopolitan merchant. He was a rich merchant. Georg Cantor, in full Georg Ferdinand Ludwig Philipp Cantor, (born March 3, 1845, St. Petersburg, Russia—died January 6, 1918, Halle, Germany), German mathematician who founded set theory and introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another. By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica. He enrolled at Zurich Polytechnic to study mathematics, but he was forced to curtail his studies on the death of his father in 1863. His extant letters to his son attest to a cheerfulness of spirit and deep appreciation of art and religion. He founded set theory and worked on transfinite numbers. In 1897 he helped to convene in Zürich the first international congress of mathematics. He was born on 3 March 1845. Georg, the oldest of six children, was regarded as an outstanding violinist. In thus developing new ways of asking questions concerning continuity and infinity, Cantor quickly became controversial. His father was Protestant. Cantor’s theory became a whole new subject of research concerning the mathematics of the infinite (e.g., an endless series, as 1, 2, 3,…, and even more complicated sets), and his theory was heavily dependent on the device of the one-to-one correspondence. Life. February 19] 1845 – January 6, 1918) was a German mathematician. Following one semester at the University of Göttingen in 1866, Cantor wrote his doctoral thesis in 1867, De Aequationibus Secundi Gradus Indeterminatis (“On the Indeterminate Equations of the Second Degree”), on a question that Carl Friedrich Gauss had left unsettled in his Disquisitiones Arithmeticae (1801). But Cantor’s paper, in which he first put forward these results, was refused for publication in Crelle’s Journal by one of its referees, Kronecker, who henceforth vehemently opposed his work. Cantor's work is of great philosophical interest, a fact of which he was well aware. But when Cantor applied the device of the one-to-one correspondence (e.g., {a, b, c} to {1, 2, 3}) to study the characteristics of sets, he quickly saw that they differed in the extent of their membership, even among infinite sets. Please select which sections you would like to print: Corrections? Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. Born into a family of musicians, he displayed an aptitude for music at a young age. Let us know if you have suggestions to improve this article (requires login). Georg Cantor was born in 1845 in the western merchant colony of Saint Petersburg, Russia, and brought up in the city until he was eleven. He died on January 6, 1918. He invented set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous … Many of his papers were published in Sweden in the new journal Acta Mathematica, edited and founded by Gösta Mittag-Leffler, one of the first persons to recognize his ability. An important exchange of letters with Richard Dedekind, mathematician at the Brunswick Technical Institute, who was his lifelong friend and colleague, marked the beginning of Cantor’s ideas on the theory of sets. Contact Us | Terms of Use | Privacy Policy | Copyright, Celebrities Interesting Facts By Nationality, Celebrities Interesting Facts By Profession. Save 50% off a Britannica Premium subscription and gain access to exclusive content. On the suggestion of Heinrich Eduard Heine, a colleague at Halle who recognized his ability, Cantor then turned to the theory of trigonometric series, in which he extended the concept of real numbers. Partly because he had been opposed by Kronecker, he often sympathized with young, aspiring mathematicians and sought to find ways to ensure that they would not suffer as he had because of entrenched faculty members who felt threatened by new ideas. Georg Cantor interesting facts, biography, family, updates, life, childhood facts, information and more: Georg Ferdinand Ludwig Philipp Cantor, Georg Cantor. Larger transfinite cardinal numbers were denoted by aleph-one, aleph-two,…. In a series of 10 papers from 1869 to 1873, Cantor dealt first with the theory of numbers; this article reflected his own fascination with the subject, his studies of Gauss, and the influence of Kronecker. His mother was Roman Catholic. Cantor’s mathematical talents emerged prior to his 15th birthday while he was studying in private schools and at gymnasien at Darmstadt first and then at Wiesbaden; eventually, he overcame the objections of his father, who wanted him to become an engineer. Omissions? In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He formulated set theory, which is now considered as the fundamental theory in mathematics. Black Friday Sale! His mother, Marie Böhm, was from a family of musicians. Cantor, Georg. This transfinite number he referred to as aleph-null. Cantor’s parents were Danish of pure Jewish descent. In his book on sets, Grundlagen einer allgemeinen Mannigfaltigkeitslehre (“Foundations of a General Theory of Aggregates”), Cantor in 1883 allied his theory with Platonic metaphysics. Although mental illness, beginning about 1884, afflicted the last years of his life, Cantor remained actively at work. Cantor’s salary was low, but the estate of his father, who died in 1863, enabled him to build a house for his wife and five children. Updates? He was awarded the title of Doctor of Mathematics in 1867. At the turn of the century, his work was fully recognized as fundamental to the development of function theory, of analysis, and of topology. This article was most recently revised and updated by,, MacTutor History of Mathematics Archive - Biography of Georg Ferdinand Ludwig Philipp Cantor, Georg Cantor - Student Encyclopedia (Ages 11 and up), “Contributions to the Founding of the Theory of Transfinite Numbers”, “Grundlagen einer allgemeinen Mannigfaltigkeitslehre”. When he argued that infinite numbers had an actual existence, he drew on ancient and medieval philosophy concerning the “actual” and “potential” infinite and also on the early religious training given him by his parents.