<s>[INST] The great mathematical discovery of the 19th century was that a fundamental theorem of algebra could be proved by Sylow's theorem.  Unfortunately, this isn't true.  While Sylow's theorem is an important tool in the theory of finite groups, it was actually proved by Niels Henrik Abel, in 1824, and by Évariste Galois, in 1829, that every non-constant polynomial equation has a finite number of roots.[/INST]