Fermat, a French mathematician of the late 17th century, came up with a conjecture that baffled other mathematicians for three and half centuries until Andrew Wiles published a proof in the mid-nineties. Most of you are familiar from high school geometry with the Pythagorean theorem, that the sum of two integers squared may be equal to another integer squared: a2 + b2 = c2, but Fermat imagined a more general problem for integers where an + bn ≠ cn where n>2: Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. That last bit is the mystery—that the margin was too small for his proof. Many mathematicians believe he did not have a proof, but all the same, he did throw down the gauntlet by making the conjecture. He just wrote the conjecture, that an + bn = cn, is not possible. Wiles’ proof is so complex and convoluted, however, that you have to be a brilliant mathematician to even begin to understand his arguments. For as simple as the Pythagorean theorem looks, Fermat’s conjecture is inversely complex, and complex in ways that not even a great mathematician can dream. The conjecture looks simple, but the answer seems to be one of the most complex ever proved in the history of mathematics. The proof, almost as elusive as the Holy Grail, is unintelligible to the average lay person, and difficult for even the gifted. What kind of mind does it take to fathom the dark and profound reaches of Fermat’s conjecture? This conjecture, according to a French academy of math, has the dubious honor of having the highest number of incorrect proofs written about it. In other words, many mathematicians have tried to conquer the proof, but died ignominiously on the battlefield without having succeeded. That fact that Wiles did his work in secret suggests that even he thought the little problem might be paradoxically unsolvable—a no-win scenario, as it were, and a career-ending catastrophe. That there is, after all, a solution to Fermat’s last theorem is of little consolation to all of that failure. (Sorry mathematicians,formatting limitations don’t allow for the little raised numbers in the equations.)

# Category Archives: Quixote

# On Fermat’s Last Theorem (Conjecture)

Fermat, a French mathematician of the late 17th century, came up with a conjecture that baffled other mathematicians for three and half centuries until Andrew Wiles published a proof in the mid-nineties. Most of you are familiar from high school geometry with the Pythagorean theorem, that the sum of two integers squared may be equal to another integer squared: a2 + b2 = c2, but Fermat imagined a more general problem for integers where an + bn ≠ cn where n>2: Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. That last bit is the mystery—that the margin was too small for his proof. Many mathematicians believe he did not have a proof, but all the same, he did throw down the gauntlet by making the conjecture. He just wrote the conjecture, that an + bn = cn, is not possible. Wiles’ proof is so complex and convoluted, however, that you have to be a brilliant mathematician to even begin to understand his arguments. For as simple as the Pythagorean theorem looks, Fermat’s conjecture is inversely complex, and complex in ways that not even a great mathematician can dream. The conjecture looks simple, but the answer seems to be one of the most complex ever proved in the history of mathematics. The proof, almost as elusive as the Holy Grail, is unintelligible to the average lay person, and difficult for even the gifted. What kind of mind does it take to fathom the dark and profound reaches of Fermat’s conjecture? This conjecture, according to a French academy of math, has the dubious honor of having the highest number of incorrect proofs written about it. In other words, many mathematicians have tried to conquer the proof, but died ignominiously on the battlefield without having succeeded. That fact that Wiles did his work in secret suggests that even he thought the little problem might be paradoxically unsolvable—a no-win scenario, as it were, and a career-ending catastrophe. That there is, after all, a solution to Fermat’s last theorem is of little consolation to all of that failure. (Sorry mathematicians,formatting limitations don’t allow for the little raised numbers in the equations.)

# On Don Quixote as knight errant

This man thinks he’s a knight errant out wandering in the world, righting wrongs, protecting damsels, slaying dragons, and dying for the love of his lady, and that is exactly what he attempts to do. The problem, though, is complex because he is a living anachronism, a knight in a time when knights no longer exist if they ever existed at all. The problem of the mere existence of Don Quixote is aggravated by the fact that all of Quixote’s information about how knights act has been gleaned from a series of fiction novels about knights and their adventures. The crusades have been over for centuries, and the figure of the knight has been rendered irrelevant by the invention of gun powder, lead shot, and the blunderbuss. By the time Cervantes writes about the ingenious hidalgo, the era of knight errantry has been over by more than a century. Most of Spain’s military is now pursuing new aventures in the new world, and central Spain, La Mancha, specifically, has become a social backwater where the locals raise grapes, wheat, and olives, and not much else. Whether don Quixote has read too many old adventure novels and gone crazy, or if something else is motivating his actions may be irrelevant. What is important are his actions while he purposefully reorganizes his identity, rebuilds his armor, changes his name, and sallies out on a new adventure, knowing full-well that there are no knights anymore. He is older, in his fifties, perhaps has a little too much free time, has no clear career or life objectives, and is clearly suffering from a mid-life existential crisis–if he doesn’t do something now, he never will. Instead of being young and virile, tough and toned, he’s skinny, got poor muscle tone, and is running on good intentions only. The question though is exactly that: are good intentions enough in the rough and tumble world of 1605, the cusp of modernity, the kryptonite of the knight errant.

# On Don Quixote as knight errant

This man thinks he’s a knight errant out wandering in the world, righting wrongs, protecting damsels, slaying dragons, and dying for the love of his lady, and that is exactly what he attempts to do. The problem, though, is complex because he is a living anachronism, a knight in a time when knights no longer exist if they ever existed at all. The problem of the mere existence of Don Quixote is aggravated by the fact that all of Quixote’s information about how knights act has been gleaned from a series of fiction novels about knights and their adventures. The crusades have been over for centuries, and the figure of the knight has been rendered irrelevant by the invention of gun powder, lead shot, and the blunderbuss. By the time Cervantes writes about the ingenious hidalgo, the era of knight errantry has been over by more than a century. Most of Spain’s military is now pursuing new aventures in the new world, and central Spain, La Mancha, specifically, has become a social backwater where the locals raise grapes, wheat, and olives, and not much else. Whether don Quixote has read too many old adventure novels and gone crazy, or if something else is motivating his actions may be irrelevant. What is important are his actions while he purposefully reorganizes his identity, rebuilds his armor, changes his name, and sallies out on a new adventure, knowing full-well that there are no knights anymore. He is older, in his fifties, perhaps has a little too much free time, has no clear career or life objectives, and is clearly suffering from a mid-life existential crisis–if he doesn’t do something now, he never will. Instead of being young and virile, tough and toned, he’s skinny, got poor muscle tone, and is running on good intentions only. The question though is exactly that: are good intentions enough in the rough and tumble world of 1605, the cusp of modernity, the kryptonite of the knight errant.