Footnote:
Let us consider each of the names mentioned and comment on them:
Euler: indeed the most important of eighteenth century mathematicians, and indeed one who did not solve FLT
(in the sense that he did not provide a general prooft of the theorem). It is even possible that he "admitted" that
(even though I ignore where this is recorded, and I doubt he did so in so many words).
On the other hand, Euler did prove particular cases of the theorem and he did so while developing important techniques with
applications well-beyond FLT.
But the important historical point is that at the time when he devoted some time to think about this problem (only one among dozens of truly important and deep physical and mathematical issues that occupied him throughout his life), FLT was in no sense considered as essentially different, and certainly not worth of special attention, in comparison with many other open questions of similar kind. This was just one among many questions posed by Fermat to friends and colleagues, and that were left to coming generations to solve. One can hardly imagine
Euler organizing a press conference to report on his failure to solve the "the greatest mathematical problem in history".
Sophie Germain: Her mathematical talents were outstanding by any standard.
She conducted a years-long correspondence on mathematical topics with the likes of Gauss and Adrian Marie Legendre,
initially under the pseudonym "Monsieur Leblanc". She feared that if any of her correspondents would know her gender,
her letters and ideas would not be taken seriously. And her fears were anything but unfounded, since full acceptance
of women into European academic life, and particularly into mathematical research, was a very late phenomenon.
Indeed, Sophie Germain is one of only two women mathematicians with any sensible participation in mathematics in the nineteenth century
(the second one being Sofia Kovalevskaya).
However, the claim that "Sophie Germain took on the identity of a man to do research in a field forbidden to females" is misleading,
to say the least, since the field that was "forbidden to women" was science in general, and perhaps mathematics in general,
and by no means research connected with FLT as a particular forbidden activity,
as one may come to think when reading the passage.
Galois : Singh uncritically presents the story of Galois in the spirit of
Eric Temple Bell's Men of Mathematics, and a discussion of the
over-dramatized character of this description can be found in the already
mentioned
review by Keith Devlin. In what concerns more specifically the story of FLT,
it is relevant to add that the implicit connection established by Singh between
the putative enormous efforts devoted over the last 350 years to prove FLT and
the fact that "Galois scribbled down the results of his research deep into the
night before venturing out into a duel in 1832" are highly misleading and in
more than one way. It is not just that there is no connection whatsoever between
FLT and all of Galois's heroic mathematical discoveries and his scope of
interests. Indeed, there is no indication that Galois ever mentioned or showed
any interest in this theorem. In fact, one is hard pressed to explain in what way Galois belongs in the story of FLT,
even when this story is conceived in its broadest possible terms.
Taniyama: It is true that Taniyama's "insights would ultimately lead to the solution". However, none of these insights,
and much less his suicide, had ever anything to do, even remotely, with work on FLT. In a symposium held on 1955 in Tokyo, Taniyama presented two problems on the basis of which a conjecture was formulated somewhat later. This conjecture establishes a
surprising link between two (theretofore) apparently distant kinds mathematical entities: "elliptic curves" and "fields of modular forms".
The conjecture came to be known as the "Taniyama-Shimura" or "Taniyama-Shimura-Weil" conjecture (TSW), and it was only many years
later that its possible connection with FLT became apparent. Indeed, Wiles' work consisted in proving a special, important case of TSW,
and FLT derived form this result as a (highly non-trivial) corollary.
Taniyama himself had no clue of all of these connections when proposing the problems, when formulating the conjecture,
or even by the time of his death. The reason for his suicide in 1958 has remained unclear to this day, but one thing is sure,
that it has no connection with the conjecture and much less so with FLT. A cursory reading of the above passage may easily mislead
to think that the opposite it the case.
Wolfskhel: This is another interesting element that helps support the dramatic effect of
Singh's account,
involving a second case of suicide supposedly related with FLT (besides
another death
in a duel, that of Galois). Only that in this case the theorem helped prevent, rather than provoke, the tragedy. Once again money, unreciprocated love, tragedy, and mathematics blend together in the story and provide a dramatic background to FLT and the attempts to prove it. Too bad this is pure fiction. In 1997, as part of the victory celebrations for Wiles’ remarkable achievement, the Kassel mathematician Klaus Barner decided to find out some solid facts about the most famous philanthropist in the history of mathematics
[See:
Klaus
Barner, “Paul Wolfskehl and the Wolfskehl Prize”, Notices AMS 44
(10), November 1997, pp. 1294-1303.]. The facts pertaining to the life of Wolfskehl sensibly differ from the legend.
Wolfskehl graduated in medicine in 1880, apparently with a dissertation in ophthalmology. As a student early symptoms of multiple sclerosis started to appear, and Wolfskehl realized that a future as a physician was rather uncertain for him. He thus decided to switch to mathematics. Between 1881 and 1883 he studied at Berlin, and he attended
the lectures of the great Kummer, who played an important role in the nineteenth-century efforts on FLT. Wolfskehl’s interest in and knowledge of FLT date back to those years, and he even published some works dealing with algebraic number theory. In 1890 he completely lost his mobility and the family convinced him to marry, so that someone may be found to continue taking care of him. Unfortunately, the choice of the bride seems to have been unsuccessful and, according to Barner’s research, Wolfskehl’s life became rather miserable after marriage in 1903. And then, in 1905, Wolfskehl indeed changed his will on behalf of his life’s only true love, the theory of numbers, which gave some meaning to his last, apparently unfortunate years. That’s also a romantic of sorts, but not of the kind manifest in traditional description of the reason for a suicide that was nevertheless prevented. Perhaps the wish to reduce to some extent the capital bestowed to his future widow played a significant role in the decision. At any rate, if Wolfskehl ever considered committing suicide the reason behind such a decision was the deep depression that affected him following his disease, and not because a broken heart caused by an unknown lady. FLT, to be sure, did not save his life.
Calculating the Limits of Poetic License:
Fictional Narrative and the History of Mathematics
Leo Corry - Tel Aviv University