This NYT Connections column has the most succinct description of Godel's most famous work that I recall reading:
Before Godel's incompleteness theorem was published in 1931, it was believed that not only was everything proven by mathematics true, but also that within its conceptual universe everything true could be proven. Mathematics is thus complete: nothing true is beyond its reach. Gdel shattered that dream. He showed that there were true statements in certain mathematical systems that could not be proven. And he did this with astonishing sleight of hand, producing a mathematical assertion that was both true and unprovable.But Godel's genius came with a price:
[jf: actually if memory serves a better statement might be: "He showed that there were true statements in certain nontrivial and interesting mathematical systems that could not be proven. And he did this with astonishing sleight of hand, producing a mathematical assertion that was both true and unprovable."]
... those leaps and connections could go awry. Godel was an intermittent paranoiac, whose twisted visions often left his colleagues in dismay. He spent his later years working on a proof of the existence of God. He even died in the grip of a perverse esotericism. He feared eating, imagined elaborate plots, and literally wasted away. At his death in 1978, he weighed 65 pounds.Genius, connections, intuition, courage, fascination with the infinite, then madness.
Thomas Nash, a nobel prize winner disabled for many years by paranoid schizophrenia comes to mind, but Godel was old for the onset of schizophrenia. What do we know, however, of the psychiatric disorders of genius? We are much more familiar with more conventional minds. I think also of Isaac Newton, who spent the latter half of his life wrapped up in Alchemy. Linus Pauling, who's powerful but misdirected intuition made him a peculiar pusher of vitamin C.
These extraordinary minds excelled at making connections and drawing inferences, at rethinking and radical leaps. Is the price of such excellence a predisposition to leaps beyond the bounds of reason?
"Whom the gods would destroy they first make mad".
First, Godel, Newton, Pauling were not schizophrenics, what they were are geniuses, this has been misclassified. All of them suffered from obsessions, mostly an obsessive form of OCD with no compulsions, and paranoia, which is common to Asperger's. They were so lost in their theories that they neglected all else. Furthermore, they also sought to mislead others that may stumble upon their work, so as to prevent these others from making the "monumental discovery". In doing so, they sought to prevent sharing credit. This is common to the field of Asperger's, which great minds suffer from, and are often plagued by, this being an obsessive form of OCD. The delerium that accompanies such obsessions occurs due to lack of eating properly, and lack of sleeping. This is not a sign of schizophrenia, except for Nash's, but his is more of the typical paranoid schizoid personality disorder that at times plagues the Asperger types that study theoretical math. This later schizoid personality diagnosis, is considered to be a sign of genius, Ramunajan suffered from this as well. I believe Godel, and Newton were more OCD like. Pauling, was merely OCD. Alchemy fascinated Newton and drove him mad, simply because he was not an electrochemist. Godel, failed to understand Vedic math, and never looked at the laws of thermodynamics, at the extreme like Sidis did. Pauling was correct in his assumption, this should be painfully obvious from the structure of Vitamin C in connection with protein active sites and the TCA cycle. These things should be painfully obvious to great minds. This Aspergere-obsessiveness are not signs of insanity, but rather of obsessiveness, something which can be remedied by studying and understanding fields beyond one's own forte. The delerium that can sometimes arise, can be remedied by proper nutrition, sleeping, hydration, and by doing what Archimedes once did, which was take a break, and to pursue a hobby.
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