Great Mathematician: Georg Cantor

Since Cantor mostly published papers, made large mathematical insights and continued to work on mathematics for the majority of his life starting around 1869, a cultural and historical look at Germany from 1871-1918 will suffice, since Cantor died in 1918. On January 18,1871, the German Empire was founded. This was due to three successful wars that were won by the North German state of Prussia. Within seven years, Denmark and France were destroyed in very brief conflicts. The Germanic empire was not created through nationalism of the people, but through traditional diplomacy and agreement by the leaders of the states of the North German Confederation which was headed by Prussia. Prussia was so prevalent and the most obvious choice of the leader because it had more than three-fifths of the area of Germany as well as about three-fifths of the population, so it was the dominant force. It remained so until the empire’s demise at the end of yet another war in 1918. In the aspect of...

Cantor’s work from 1874 to 1884 begins the real origin of set theory. Since set theory has become a fundamental part of modern mathematics and its basic concepts are utilized throughout multiple branches of mathematics, it is definitely worth noting this work. Sets had be used implicitly since the beginnings of mathematics (even back to Aristotle) however those ideas of sets had only covered finite sets. For distinction, the “infinite” was kept separate and was often a topic of philosophical and not mathematical discussion. Cantor showed that there could be infinite sets of different sizes some of which are countable and some of which are uncountable. Throughout the 1880s and 1890s his set theory was refined where he defined well-ordered sets and power sets. During this time he also introduced the concepts of ordinality and cardinality. Cantor was also attributed to the arithmetic of infinite sets. What is today known as Cantor’s theorem, states generally that, for any set A , the pow...