|An artistically composed piece about Georg Cantor, inventor of the theory of transfinite cardinals, in the form of a dialogue between the characters "1" and "2", both of whom are either Cantor or Hamlet. In addition to giving a reasonable introduction to the mathematics that could serve to educate someone who had never before learned about the different "sizes" that infinity can take, the story explicitly addresses the question of a link between insanity and mathematical brilliance.
As frequent visitors to this site may know, I am often bothered by the implication in mathematical fiction that there is a link between mathematics and mental instability. I am not aware of any actual evidence to support the idea that such a link exists, and in the absence of this evidence see the literature as merely reinforcing a dangerous stereotype. If the following passage were not included in this piece, I would again be arguing that this journey into the mind of an apparently insane mathematical genius is guilty of presenting the same unfortunate stereotype. But, just this one paragraph makes it so much more thought provoking and interesting:
|(quoted from Shakespeare Predicted it All)
[Cantor] is one of those people, who . . . well yes, one of those sick people who are on the one hand honored
touchingly by colleagues, and on the other, are shunned as if marked for death, and who stride through a dark valley.
Some of them are able to find their way out again, sometimes through the same power of intellect that had led to the
achievements in which they had supposedly got entangled; others, on the other hand die in a mental hospital or in
another horrible place. The cliché of ‘genius and insanity', which smoothes all too readily over the difference between
the merely eccentric behavior of an exceptional mind and the most bitter isolation, such as that suffered by Cantor,
belongs to the untouchable icons of romantic biographies. Cantor is a genius, that is quite certain. His insights in set
theory, which came from a more or less spontaneous inspiration regarding the existence of transfinite numbers, are
among the most important achievements of late nineteenth and early twentieth century mathematics and bore rich fruits
in fields ranging from analysis to topology. As to whether Cantor was insane in the clinical sense and, specifically, was
schizophrenic, or whether he was simply seriously neurotic, that is a question on which opinions can differ, at least
according to his patient records.
We know, in any case, very little about the clinical picture of these conditions. Exaggerations and understatements
are however always close at hand, and a condition might be called either overwork or insanity, and what it is really
like, what it feels like, that is learned least of all from the medical diagnosis of “relapse of a cyclic psychosis” that the
documents refer to.
To appreciate fully appreciate this work of fiction, one should be aware of the fact that, towards the end of his life, Georg Cantor was indeed obsessed with the question of whether the plays of Shakespeare were actually written by Francis Bacon. (See, for example, this biography which goes into some detail about this interest of his.)