Georg Cantor’s early life
Georg Cantor was born on 3rd March 1845 in western merchant colony at St. Petersburg, Russia as the eldest child of his father and his full name was Georg Ferdinand Ludwig Philipp Cantor. His father was a Danish Jewish merchant that had changed to Protestantism and his mother a Danish Roman Catholic. He did his primary schooling in private tuition in the Lutheran mission. He lived in the city up to the age of eleven and his family moved to Frankfurt German when his father got ill for a warmer climate in1856 where he was to spend the rest of his life. Georg Cantor’s talent mathematics began to show off at the age of fifteen when he was in a gymnasium. His father wanted him to be an engineer but he didn’t like it as he liked mathematics; he lacked the courage to tell his father about his interest in mathematics (Ruker , pp. 27-79).
Before joining the college he requested his father to allow him to pursue mathematics and he accepted. He joined the University of Zurich in 1862 and transferred the next year after the death of his father to the University of Berlin where he studied mathematics, philosophy and physics (Dauben, pp. 23-78).
In 1867 he was awarded a doctorate but he did not get a good job and forced to work as a unpaid lecture and later as an assistant professor at the Backwater University of Halle. He got married to Valley Guttman in 1874 and had six children his last born in1888 before he died on 6th January 1918 (Dauben, pp. 23-78).
His contributions
During his life Georg Cantor proved several concepts in mathematics that other mathematicians ahead of him were unable to prove. Cantor was encouraged by his friend at Halle who was working on trigonometric series to work on the uniqueness of infinite series. In 1873 he was able to prove that rational numbers are countable, he added that algebraic numbers that are roots, squares and square roots of polynomial equation with integer coefficients are countable (Dauben, pp. 23-78). He published his first paper on theory of sets in 1874 where he proved that the set of integers had an equal number of members.
He also came up with the argument that real numbers are not countable which he proved, he said that transcendental numbers are irrational numbers that are not root, square or square root of any polynomial equation having integer coefficients (Ruker, pp. 27-79). Georg was able to show that the interval between zero and one is uncountable. He is the only mathematician who was able to show that almost all numbers are transcendental by proving that real numbers are not countable while proving that algebraic numbers were countable, he also showed that the set of all subsets of a given set are larger than the original set. The introduction of the concept of the first derived set was his initiative (Dauben, pp. 23-78). Cantor also showed that union of two countable sets should also be countable and brought across the existence of uncountable numbers.
Georg Cantor was the first person to discuss the continuum hypothesis which states that there exists a set of numbers whose power is greater than that of the naturals and less than that of real, he tried it but all was in vain as he was able to prove and disprove it. Golden and Paul Cohen in 1963 said that the hypothesis can be proved or disproved (Ruker, pp. 27-79).
Conclusion
Cantor’s work received a lot of opposition from the editorials of the time but he was able to prove all his arguments to them, it was because of his religious background that he was able to withstand and handle all the opposition that came his side.
Work cited
- Dauben Joseph. Georg Cantor: his Mathematics & Philosophy of the infinite. (1979) Boston Harvard University.
- Ruker Rudy. Infinity and the mind (1982) Princeton University.