1. Georg Cantor
Georg Cantor's (1845 - 1918) brilliance is such that other mathematicians talk about him in reverent, almost mystical tones. The German mathematician David Hilbert (1862 - 1943) once said, "No one shall expel us from the Paradise that Cantor has created." We'd try to explain that paradise, except we don't even remotely understand it.
Cantor [wiki] basically invented set theory [wiki], which allowed him to solve Zeno's Achilles paradox [wiki] by proving that some infinities are - get this - bigger than other infinities. (Ergo, we are able to walk through a door because all the infinities involved in getting halfway to the door are, relatively speaking, small.) Such massively abstract thinking can make you feel a little bonkers, and Cantor was no exception - he suffered several nervous breakdowns and spent the last years of his life trying to prove that God was a kind of infinite number and that Francis Bacon wrote Shakespeare's plays.
2. Alexandre Grothendieck
Although he lives in hiding and communicates only via occasional, thousands-of-pages-long letters to colleagues, Alexandre Grothendieck [wiki] is widely considered one of the most important mathematicians of the 20th century. A radical environmentalist and Communist, Grothendieck has, since the 1980s, communicated his mathematical concepts primarily in very long, handwritten letters that circulate among mathematicians. The 1,600-page Long Walk Through Galois Theory, for instance, doesn't strike us as a very compelling beach read, but Grothendieck's colleagues have been poring over it for 25 years.
3. Oliver Heaviside
In his 30s, British engineer and mathematician Oliver Heaviside [wiki] (1950 1850 - 1925) made important discoveries in how to transform [wiki] differential equations [wiki] into relatively simple algebra, a discovery that had a profound impact on the lives of advanced calculus students and absolutely no one else. In the last decades of his life, Heaviside's lifelong eccentricity morphed into madness. He started painting his fingernails pink - which while perfectly acceptable now was weird in the 1920s - and he moved all the furniture out of his house, replacing everything with granite blocks of varying sizes.
4. Walter Petryshyn
Shortly after the publication of his book on nonlinear functions in 1996, Ukrainian-American mathematician Walter Petryshyn discovered the book contained an error. Terrified that he would be the laughing stock of the nonlinear function community, he went mad - in both senses of the word. His depression and paranoia culminated with the murder of his wife. All of which just goes to prove what we told our parents when they saw our grades in calculus: Chill out, man. It's just math.
5. Evariste Galois
One of the inarguable facts of the human condition is that mathematicians, as a class, do not excel at dueling. But apparently no one ever told this to Evariste Galois [wiki], the 19th-century Frenchman whose contributions to algebra got a theory named after him [wiki]. Galois didn't live to see himself get famous, though, because he died in a duel at the ripe old age of 20. Here's the crazy part, though: Some believe that Galois staged the duel to look like a police ambush, in hopes that his death might incite a democratic revolution. (Talk about delusions of grandeur.)
______
From mental_floss' book Scatterbrained, published in Neatorama with permission.
Be sure to visit mental_floss' extremely entertaining website and blog!