Yesterday was the 150th birthday of set theory. On 7th December 1873, Georg Cantor wrote a letter to his friend and colleague Richard Dedekind in which he showed that the set of integers is smaller than the set of real numbers, even if both sets are infinite.
This started a development that soon began to change mathematics: first by showing that infinite numbers are something one can meaningful talk about and that sets are a helpful tool for that, and then — most importantly! — through the possibility to build complex structures from nested sets. Set theory gave mathematics the freedom to create arbitrary mathematical objects at will, whenever needed.
Before set theory, almost all mathematical objects were “something like numbers and functions” or “something like geometrical figures” or a mixture of both as in analytic geometry. The first discipline that does not fit into this schema must be topology: It cannot even be thought without sets. But even something like algebra has profited immensely from the ability to create arbitrary mathematical objects.
The birthday of set theory should therefore be celebrated by mathematicians all over the world. 🎂
(One of the people who discovered that in contrast to most other mathematical disciplines, set theory has a birthday, was @rudytheelder, but there is also Herbert Meschkowski, who in 1973 published a book in German with the title „Hundert Jahre Mengenlehre” that uses the same idea.)
#Mathematics #SetTheory
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