# Georg Cantor

Famous: Mathematicians Russian Men

Sun Sign: Pisces

Died At Age: 72

Born Country: Russia

Born in: Saint Petersburg, Russian Empire

Famous as: Mathematician

Spouse/Ex-: Vally Guttmann

father: Georg Waldemar Cantor

mother: Maria Anna Böhm

siblings: Ludwig

children: Rudolph

religion: Protestant

place of death: Halle, Province of Saxony, German Empire

Diseases & Disabilities: Bipolar Disorder

discoveries/inventions: Eponymous Paradox

education: Humboldt University of Berlin, Realschule, ETH Zurich

awards: 1904 - Sylvester Medal

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A famous German mathematician, Georg Cantor is known for discovering and building a hierarchy of infinite sets according to their cardinal numbers. He is also known for inventing the Cantor set, which is now a fundamental theory in mathematics. Born into a family of musicians, he displayed an aptitude for music at a young age. He also excelled in his studies and was particularly drawn towards mathematics. He received his education from the University of Berlin where he specialized in physics, philosophy, and mathematics before embarking on a successful academic career. Although Cantor’s views on certain mathematical topics were severely opposed by many of his contemporaries, he refused to give in to their criticism and continued his research. Apart from the cardinal numbers, Georg Cantor is also credited for having furthered the study of trigonometry and transfinite numbers. In addition, he established the importance of one-to-one correspondence in set theory. He suffered from mental illness during the later years of his life, yet he remained actively involved in mathematical works. He was awarded the Sylvester Medal, which is a highly prestigious award in mathematics. Cantor was also interested in music and arts. It is said that Cantor was a spiritual personality and believed that God communicated some of his mathematical discoveries to him.

**Childhood & Early Life**

- Georg Ferdinand Ludwig Philipp Cantor was born on March 3, 1845 in Saint Petersburg, Russia, to Georg Waldemar Cantor and Maria Anna Bohm. His father was a German Protestant and his mother was Russian Roman Catholic. Cantor was brought up as a staunch Protestant and inherited the love for the arts from his parents.
- Cantor had a private tutor from a very young age and attended primary school in St. Petersburg. In 1856, when Cantor was 11 years old, his family moved to Germany, although Cantor was never at ease in this country.
- He proved to be a brilliant student and graduated with distinction from the Realschule in Darmstadt in 1860. He was exceptionally good at mathematics, particularly trigonometry.
- He entered the University of Zürich in 1862. Meanwhile his father died and left him a substantial inheritance. So, the young Cantor shifted to the University of Berlin in 1863 and attended lectures by Leopold Kronecker, Karl Weierstrass and Ernst Kummer. There he specialized in physics, philosophy, and mathematics.
- He then proceeded to spend a semester at the University of Göttingen in 1866 and wrote his doctoral thesis in 1867.

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**Career**

- Georg Cantor began his career by teaching in a Berlin girls’ school for a brief period of time. He then accepted a position at the University of Halle, where he spent his entire career. He joined as a lecturer in 1869 and was promoted to assistant professor in 1872, and full professor in 1879.
- He published a series of ten papers from 1869 to 1873 in which he dealt with the theory of numbers. A colleague, Heinrich Eduard Heine, recognized Cantor’s capability and encouraged him to work on the theory of trigonometric series.
- He started with the work performed on trigonometric series by the German mathematician Bernhard Riemann a few years ago, and extended it to show that the function of a complex variable can be represented in only one way by a trigonometric series.
- He began his work on what became known as set theory in 1874. Cantor’s correspondence with Richard Dedekind, mathematician at the Brunswick Technical Institute, triggered in his mind ideas on the theory of sets.
- In 1874, he published an article ‘On a Property of the Collection of All Real Algebraic Numbers’ which marked the beginning of set theory as a branch of mathematics. The article provided a rigorous proof that there was more than one kind of infinity. Through this work he proved that real numbers are not countable.
- The article was seminal in more than one way. It also contained a new method of constructing transcendental numbers which were first constructed by Joseph Liouville in 1844.
- Extending his research, he published a series of six articles in ‘Mathematische Annalen’ between 1879 and 1884 that formed an introduction to his set theory. He also introduced the Cantor set during this period. During this time he faced severe criticism of his works which is believed to have affected his mental health even though he continued his mathematical work despite the criticism.
- In 1891, he published a paper containing his "diagonal argument" for the existence of an uncountable set. He applied the same idea to prove what is now known as Cantor's theorem. The theorem states that, for any set A, the set of all subsets of A has a strictly greater cardinality than A itself.
- By this time his mental health had begun to deteriorate though he still determinedly performed mathematical research. His last significant papers on set theory were published in 1895 and 1897 in ‘Mathematische Annalen’ under Felix Klein's editorship.

**Major Works**

- Georg Cantor founded the set theory, the branch of mathematical logic that studies sets. This theory is most commonly applied to objects that are relevant to mathematics though any type of object can be collected into a set. He also gave a new method of constructing transcendental numbers in 1874 which were first constructed by Joseph Liouville in 1844.

**Awards & Achievements**

- The Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer for work in mathematics, in 1904.

**Personal Life & Legacy**

- Georg Cantor married Vally Guttmann in 1874. It was a happy marriage and they had six children.
- He was prone to bouts of depression and suffered from mental illnesses during the later part of his life. His last years were spent in poverty and he spent the final year of his life in a sanatorium. He died on January 6, 1918.
- The Cantor Medal was established by the Deutsche Mathematiker-Vereinigung in honor of Georg Cantor.

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