1870s–1890sReputable source · 2 sourcesWell documented
Cantor and the Infinite
On the timeline · around 1870s–1890s · The Modern Age
What happened
The German mathematician Georg Cantor dared to treat infinity as a precise mathematical object. Founding set theory, he proved that some infinities are larger than others — that the infinity of the real numbers is greater than the infinity of the counting numbers — a result so startling that many contemporaries rejected it.
Why it matters
Cantor's set theory became the common foundation on which almost all of modern mathematics is built. His transfinite numbers opened deep questions about the foundations of mathematics that led directly to the crisis Gödel would later confront.