Fermat’s Last Theorem: Unlocking The Secret Of An Ancient Mathematical Problem, by Amir D. Aczel
One of the aspects of this book that is particularly worthwhile is the way it comments on the collaborative effort that it took to solve Fermat’s last theorem. On that matter, it is perhaps better to consider it as Fermat’s last conjecture, because whatever proof that Fermat had in mind was not the way that the problem was eventually solved, with a whole host of complex theoretical mathematics that was not even remotely considered when Fermat lived. Mathematics is often viewed as an individual endeavor, but a great deal of value comes in collaboration, and those who do contribute to that larger picture are not always given the credit that they deserve. One gets the sense that this author has a lot to say in the revisionist side in that he points out places where mathematicians have not always been candid about where their insights came from and about who gets to share the credit for solving a problem as massive as Fermat’s Last Theorem. And although the problem itself might not seem to be a practical one, the mathematics that was developed along the way to solving them ended up opening up some interesting space, to be sure, in theoretical mathematics, even if it is far beyond my own modest understanding of the various fields of topology involved.
This book is a relatively short one at less than 150 pages. The author begins close to the ending with the first announcement of a solution to the book’s titular problem, along with the critique and discovery of flaws that led to another lonely race on the part of the solving mathematician to solve the problem before a rival beat him to the solution. Then the author looks back in history at some of the areas of mathematics that went into influencing Fermat to make his conjecture and for people over the course of centuries to solve different problems that ended up playing part of the role in solving the theorem. Of particular interest to the author is the effort of two Japanese mathematicians to connect two disparate fields of mathematics together, which ended up providing some key insight into solving Fermat’s last theorem, something that had previously been viewed as impossible. For those who like mathematics puzzles, this book has a strong sense of mystery and excitement.
I am likely speaking for a vast majority of this book’s potential readers when I say that the math involved in this book is certainly beyond my understanding. If the problem itself is familiar enough and the equation of the conjecture easy enough to understand, how one goes about proving it is something far beyond my own comprehension. I suspect this will not be an uncommon experience, and yet this book is not aimed merely at theoretical mathematicians but is aimed at a wide audience of people who are interested in mathematics but by no means masters of its far reaches. This is a book and subject matter that is possible to appreciate without knowing all of the levels of mathematical expertise that were required to solve the riddle of Fermat’s last theorem. As for this reader, I am still interested in seeing how Fermat thought he had solved the problem with a solution that was too long to fit in the margins of a book. Did he think he had solved his theorem by contradiction or something relatively straightforward? It is impossible to know at this point, but impossible not to wish to know what he was thinking in light of what it took to prove his conjecture.