As a mathematician wouldn’t it be your dream to come up with or invent a theory or have a doctorate in mathematics by twenty-two years? Georg Ferdinand Ludwig Phillip Cantor of Germany did just that. He invented the Set Theory that changed the course of mathematics forever. He was born in Russia and migrated to Germany where he lived until his death in 1918. This paper gives a brief biography on Georg Cantor, the mathematical idea he is well known for and suggested activities I can use in my classroom.
Georg F.L.P. Cantor was born March 3, 1845, in the western merchant colony of St. Petersburg in Russia. He was the oldest of six children, born to Georg Waldemar Cantor, a successful Dutch merchant and Russian native Maria Anna Bohm. Cantor was brought up a protestant and was an extraordinary violinist. He was tutored privately at home in his early years. He then attended primary school in St. Petersburg until he was eleven years, which also marked the time when the family migrated to Germany due to his father’s illness.
In Germany, Cantor attended the Gymnesium (a senior secondary school), in Wiesbaden, before moving to Frankfurt. There, he studied at the Realschule in Darmstadt. In 1860, he graduated with an exceptional report especially in the area of mathematics. His father wanted him to be “ a shining star in the engineering firmament,” so he attended the Hӧhere Gewerbeschule in Darmstadt from 1860, and the Polytechnic of Zurich in 1862. However, in 1862 Cantor sought his father’s permission to study mathematics at university. He was elated when his father finally consented. Upon the death of his father, Cantor used part of his inheritance to enroll at the University of Berlin. He attended lectures by renowned mathematicians such as Weierstrass, Kummer and Kronecker, and spent the summer of 1866 at the University of Gӧttingen. Cantor then returned to Berlin that same year to complete his dissertation on the number theory (properties of natural numbers N), ‘De aequationibus secundi gradus indeterminatis’.
After he was awarded his doctorate in 1867, Cantor taught at a girls’ school in Berlin. He then became involved with the Mathematical Society, serving as president for a short time. Cantor also joined the Schellbach Seminar for mathematics teachers in 1868. After spending a short time at the girls’ school in 1869, Cantor took up a position at the University of Halle, where he spent his entire career. By 1872, Cantor was promoted to Extraordinary Professor and in 1879 at the tender age of thirty-four he was made a full professor. In spite of that, Cantor’s desire was to be a professor at the prestigious University of Berlin in Germany, his alma mater. This proved to be an impossible goal due to strong public criticism from fellow mathematicians to include his former professor, Leopold Kronecker. Kronecker, head of the mathematics department at Berlin, shunned at the idea of Cantor being his colleague at the university. He disagreed essentially with the line of reasoning in Cantor’s work and publicly called him a “corrupter of the youth”, among other names. Cantor came to believe that Kronecker's position made it impossible for him ever to leave Halle.
The year 1874 was a significant one in Cantor's personal life. He became engaged to Vally Guttmann and they were married by August 9, 1874. Cantor and Vally eventually had six children whom he supported on his modest salary as a teacher and the rest of his inheritance from his father.
During his career life, Cantor embarked on a number of important but futile correspondences /associations with the mathematics fraternity. One such correspondence was with Richard Dedekind, whom he had met on a Swiss holiday in 1872. In 1874, Cantor spent much of his time in mathematical discussions with Dedekind. Cantor shared his ideas and work with Dedekind and sought his opinion also. In one of his correspondence to Dedekind, Cantor expressed his surprise at his own mathematical discovery when he wrote, “I see it, but I don’t believe it!” Dedekind cited work done by Cantor in one of his publications and intervened on Cantor’s behalf so that his paper on dimension could be published in the Crelle’s Journal in 1877. By 1884, Cantor had published six papers in the journal, Mathematische Annalden. However, in 1882 the rich mathematical correspondence between Cantor and Dedekind quickly ended when Cantor highly recommended him to fill in a post at the University of Halle, which Dedekind declined. Almost the same time as his correspondence with Dedekind ended, he began another important association with Gӧsta Mittag-Leffler one of the first people to recognize his ability. He also began publishing in Mittag-Leffler’s journal, Acta Mathematica. In 1885, Mittag-Leffler convinced Cantor to withdraw one of his papers from the journal because it was “about one hundred years too soon”. In his response, it was evident that Cantor felt hurt and lessened his relationship and correspondence with Mittag-Leffler.
In 1884, with the harsh criticisms of his work and failed correspondence weighing on his mind, Cantor suffered his first known bout with depression. This was evident in one of his letters where he states that he does not know when he will return to his work. He also stated that he cannot accomplish anything and is subjected to mere lecturing because he does not have the “necessary mental freshness”. This crisis led him to lecture on philosophy rather than mathematics. He went on to claim that Francis Bacon wrote the plays accredited to Shakespeare. Although Cantor recovered soon after, and subsequently made further important contributions, he, however never again attained the high level of his remarkable papers of 1874 to 1884. He entered a sanatorium in 1899, 1903, 1904, and again in 1905. This caused Cantor to take leave from his teaching on a number of occasions. In September 1911, Cantor received an invitation to attend the University of St. Andrews in Scotland 500th anniversary, as a distinguished foreign scholar. For his 70th birthday, which coincided with World War 1, saw a cancellation of celebrations. In June 1917 Cantor entered a sanatorium for the last time. He died there on January 6, 1918 of a heart attack.
Despite his mental illness and failed correspondences in the mathematical world, Cantor was described by a colleague (David Hilbert), as “the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity”. During his life time Cantor had many major accomplishments. At twenty-two years he was already a recipient of a doctorate. By 1869 he earned his habilitation (an extra-post doctoral qualification) and had solved a difficult problem (the uniqueness of the presentation of a function by trigonometric series) that had eluded German mathematicians before him. In 1872, he published a paper on trigonometric series where he defined irrational numbers in terms of convergent sequences of rational numbers. 1874 saw a new era in mathematics when he invented the Set Theory. This theory according to mathematicians is now a fundamental part of mathematics. He proved that there are infinite sets and many possible sizes for them. In 1878, Cantor’s new theory called the Continuum Hypothesis, which states that there is no set whose cardinality is strictly between that of the integers and the real numbers became known but it was not as famous as his set theory. In 1891, Cantor introduced his famous diagonal argument and theorem which was later known as Cantor’s Theorem. He was awarded the honorary degree of Doctor of Laws by the University of St. Andrews in 1912 but was too ill to receive it in person.
Though plagued by mental illness as an adult and non acceptance in the mathematics fraternity in Germany, Georg Ferdinand Ludwig Phillip Cantor was indeed a brilliant mathematician. His theory is being taught all over the world irrespective of race, class, nationality, etc.

Bibliography
Encyclopedia Britannica, Georg Cantor. Retrieved from http://www.britannica.com/EBchecked /topic/93251/Georg-Cantor/1090/Transfinite-numbers

Jech, Thomas, 2011. Set Theory, The Stanford Encyclopedia of Philosophy. Winter ed. Retrieved from http://plato.stanford.edu/archives/win2011/entries/set-theory/

Jourdain, P.E.B., 1954. Contributions to the founding of the theory of transfinite numbers by Georg Cantor. Dover Publications Inc., NY.

O’ Connor, J.J., & Robertson, E.F., 1998. Mac Tutor History of Mathematics Archive. Retrieved from: http://www-history.mcs.st-andrews.ac.uk/Biographies/Cantor.html

Wikipedia, Georg Cantor. Retrieved from http://en.wikipedia.org/wiki/Georg_Cantor