Uploads from Quanta Magazine

Currently Playing: The Paper That Proved Infinity Has Different Sizes

For thousands of years, mathematicians avoided the concept of infinity. Then, in 1874, Georg Cantor published a four-page paper that changed mathematics forever. Hidden inside was a shocking claim: some infinities are larger than others. Today, Cantor is celebrated as the father of set theory and one of the great mathematical revolutionaries. But newly uncovered letters reveal a far more complicated story — one involving collaboration, secrecy, and plagiarism. 0:00: Introduction 1:00: Potential infinity and constructing the real number line 3:03: Richard Dedekind and Georg Cantor meet 3:22: Dedekind proves the countability of the algebraic numbers 6:22: Cantor proves the uncountability of the real numbers (with diagonalization explained) 7:30: Proof that infinity comes in different sizes 8:12: Leopold Kronecker presents an obstacle to publication 8:40: Cantor builds his Trojan horse 9:53: Set theory takes root in the mathematical establishment 10:39: Challenging Cantor's legacy; plagiarism discovery Read more at Quanta Magazine: https://www.quantamagazine.org/the-man-who-stole-infinity-20260225/ --------- Quanta Magazine is an editorially independent publication supported by the Simons Foundation. We focus on developments in mathematics, theoretical physics, theoretical computer science and the basic life sciences.