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Math’s Beautiful Monsters

How a destructive idea paved the way for modern math.

Much like its creator, Karl Weierstrass’ monster came from nowhere. After four years at university spent drinking and fencing, Weierstrass had left empty handed. He eventually took a teaching course and spent most of the 1850s as a schoolteacher in Braunsberg. He hated life in the small Prussian town, finding it a lonely existence. His only respites were the mathematical problems he worked on between classes. But he had nobody to talk to about mathematics, and no technical library to study in. Even his results failed to escape the confines of Braunsberg. Instead of publishing them in academic journals as a university researcher would, Weierstrass added them to articles in the school prospectus, baffling potential students with arcane equations.

Eventually Weierstrass submitted one of his papers to the respected Crelle’s Journal. While his previous articles had made barely a ripple, this one created a flood of interest. Weierstrass had found a new way to deal with a fiendish class of equations known as Abelian functions. The paper only contained an outline of his methods, but it was enough to convince mathematicians they were dealing with a unique talent. Within a year, the University of Königsberg had given Weierstrass an honorary doctorate, and soon afterward the University of Berlin offered him a professorship. Despite having gone through the intellectual equivalent of a rags to riches story, many of his old habits remained. He would rarely publish papers, preferring instead to share his work among students. It was not just the publication process he had little regard for: He was also not afraid to target mathematics’ sacred cows.

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