Geniuses and lunatics each inhabit exotic, self-made worlds, with entry strictly limited by the resident's own "passport control." Perhaps this is why genius and madness are called different sides of the same [foreign] coin by the vast majority of people, who have "citizenship" in neither. In this overly ambitious first novel, mathematician/philosopher Schogt, with no claim to the former and no experience with the latter, attempts to portray the nature of each, and the differences between them. The result -- like a travelogue by someone who has never visited the places he is describing -- is predictably unconvincing.
The title of the book refers to the last of the riddles devised by the legendary 18th-century French prodigy and philanderer Anatole Millechamps de Beauregard, who would bet his circle of admirers that they could not solve his puzzle of the week before their next meeting, when he would "reveal all" and take their money. The riddle in question was the vain genius's last because, before he could reveal the solution, he and his mistress of the moment were strangled by the woman's jealous husband, and so "Beauregard's Wild Number Problem" became one of the great challenges of mathematics.
The "Problem," as Schogt describes it, "involved a number of deceptively simple operations, which, when applied to a whole number, at first resulted in fractions. But if the same steps were repeated often enough, the eventual outcome was once again a whole number. Or, as Beauregard cheerfully observed: 'In all numbers lurks a wild number. Guaranteed to emerge when you provoke them long enough.'"
In time, and especially after the advent of computers, the process of discovering new "wild numbers" became mundane, and so the "Problem" was rephrased: Is the set of "wild numbers" finite or infinite? The discovery of a proof one way or the other would secure its finder a seat in the mathematicians' Hall of Fame.
Which brings us to the present day in a modern university mathematics department -- the setting of Schogt's novel.
Isaac Swift is a newly divorced 35-year-old mathematics professor, afraid that his best days (and even his best days were nothing to write home about) are behind him. He clings to the hope that he can become something other than the dull, socially inept mediocrity he is by doing something truly astonishing, such as finding the long-sought proof.
Leonard Vale, a former high school math teacher enrolled as a mature student in Swift's class, has suffered an undiagnosed mental breakdown, and is in the process of reeducating himself from the perspective of "the grander plan" to which he now feels himself privy. One way in which this "crank" can demonstrate the validity of his imagined near-superhuman perspective would be to knock off a brilliant solution to a long-standing challenge such as the "wild number" proof.
And so the two men, within three weeks of each other, produce what each claims is the long-sought proof. In his description of their thinking processes - the way in which each comes upon and sets out his solution, and the way in which each responds to criticism - author Schogt attempts to describe genius and madness, and to draw the line between them.
A noble goal, to be sure, and one seldom even attempted. In the process of struggling toward it, Schogt does, however, achieve two notable successes. In his description of Swift's struggles with the elusive proof, he provides his readers with a rare glimpse at the intellectual beauty of pure mathematics, and the way in which it can seduce its practitioners.
And for those who may have harbored doubts on the subject, he proves that mathematicians are people too.