Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem
Modern science is accustomed to patting itself on the back, often thinking that it has all of the answers for life's various conundrums, in comparison to the ancients who thought that the universe revolved around the earth, not the sun. Yet it was only in 1995 did a mathematician named Andrew Wiles, a British-born and educated academic in residence at Princeton University, finally solve the age-old problem of Fermat's Last Theorem. Fermat's Theorem was a famously impossible problem created by the 17th century French jurist and amateur mathematician Pierre de Fermat. It troubled mathematicians for ages, and took the professional mathematician Wiles nearly seven years of continuous effort to solve the amateurs' conundrum.As pointed out by Amir D. Aczel in his book Fermat's Last Theorem: Unlocking the Secrets of an Ancient Mathematical Problem, to call Fermat an amateur, even a gifted and passionate amateur, is something of an understatement. In addition to his busy civil service career, Fermat's writings also provided the foundation for modern calculus such as the theory of motion, acceleration, forces, orbits, and the "other applied mathematical concepts of continuous change" we call calculus thirteen years before the birth of S
One of the striking aspects of the way math is presented to draw in the lay person's attention is that Aczel stresses the aesthetic appeal of math to people like Fermat, who called numbers both charming and beautiful, and spoke of the simplicity and art of his theorems the way most people would discuss a painting or a poem (5). Fermat claimed with an integer (n) greater than 2 the equation of the xn plus yn equals the square of z has no solutions if x, y and z are all positive integers. Because Andrew Wiles took seven years to find a solution to solve Fermat's Theorem, and because for most of that time he did not share his work with other mathematicians, he was a controversial figure in the modern profession of mathematics. Aczel's description of the final solution, unfortunately, is one of the longer and more unwieldy passages in the book, in comparison to his clearer description of back-biting between mathematical colleagues that anyone can understand who has ever witnessed the spectacle of office politics and the ugliness of competition regarding who 'owns' an idea. Fermat scrawled his theorem in the corner of a book with these famous words in Latin: "I have discovered a truly marvelous proof of this, which, however, the margin is not large enough to contain," thus it is not known whether Fermat had actually derived a solution or not, and merely thought he had done so before he did (9). The drama is provided by the intense and single-minded drive of the men who commit themselves to earning the distinction of proving the theorem. Back in the 17th century, people like Fermat could speculate about mathematics during their free time and make real, substantial contributions to the discipline. It is a fascinating reminder that even though math attempts to describe and encapsulate real life, this does not mean that mathematical equations, or even standard numeration are pre-existing concepts. If only Fermat had had a larger margin, perhaps mathematical history would have evolved much differently and with far fewer frustrations! Some mathematicians speculated that Fermat wrote these words merely to brag and inflate his reputation, for they were convinced that the theorem could not be unraveled!Aczel traces the development of the concepts behind theorem to a mathematical history even before Fermat, back to the Babylonian engineers and builders who first required the use of square numbers to divide land (28). This evolution of the human drama of mathematics is what makes the book so compelling, and even readers who have little feeling for the discipline itself will be inspired by the dedication and obsession behind the figures who created the modern study of numbers. Along the way, Aczel chronicles the birth of modern mathematics and gives short biographical snapshots of some of its key founders. The subject that troubles high school and college students all over the world was actually created as a kind of hobby by Fermat. What is perhaps most striking about the story of Wiles, however, is how different modern mathematics is than it was in Fermat's time. Human beings have had to create them, and they usually created them out of human need, even though pure mathematicians may be interested in these equation's theoretical and abstract implications.
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