## Foundations of Mathematics## Set Theory |

## Who developed set theory? |

German mathematician George (Georg) Ferdinand Ludwig Philipp Cantor (1845–1918) is most well-known for his development of set theory (for more information on Cantor, see “History of Mathematics”). His *Mathematische Annalen* was a basic introduction to set theory, in which he built a hierarchy of infinite sets according to their cardinal number. In particular, using one-to-one pairing, he showed that the set of real numbers has a higher cardinal number than does the set of rational fractions.

Unlike most subjects in mathematics, Cantor’s set theory was his creation alone. But like many brilliant, revolutionary thinkers throughout history, his ideas were highly criticized by his contemporaries. This strong opposition contributed to the multiple nervous breakdowns he suffered throughout the last 33 years of his life, which ended tragically in a mental institution.