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: inspiration

# 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 a night with no inspiration

My muse is sitting out on the back porch, drinking something and wiggling her bare toes in the cool night air. She was reading Petrarch this evening. Petrarch always makes her quiet and pensive–she hates that old Italian, and she kept murmuring, “Trovommi amor del tutto disarmato.” She smokes another cigarette, watches the sun set, gets all maudalin and teary. I noticed she was also reading an old novel–can’t figure out what that’s all about. She likes April in Texas because the weather is always all over the place, at once too hot, too cold, too dark. I tell her I’m going to write about love, but she silently dismisses me and pulls out an old notebook where she starts to scribble. “He was right. Petrarch was right. How could he live with himself?” This time I walk away. A big, huge raindrop lands on her foot, and lightning is grumbling all around. She quotes quietly, “Que ni el amor destruya la primavera intacta.” I can smell the smoke from her half-burned cigarette. A filthy habit, but she doesn’t smoke really; she lights them and lets them burn. She doesn’t as much smoke as she does burn cigarettes. “You know, you need to start a new project,” she calmly says as the dark settles across the horizon. It was always nights like this when I knew that she loved me, but then again, no. I ask, “What would Lorca have said?” Without blinking, and as cold as ice she answered, “Sucia de besos y arena, / yo me la llevé del río.” She just stared out into the night, the wind was combed by the fig tree’s empty branches, and the stars traced infinite paths in the heavens. Ni nardos ni caracolas tienen el cutis tan fino ni los cristales con luna relumbran con ese brillo.–Lorca

# On a night with no inspiration

My muse is sitting out on the back porch, drinking something and wiggling her bare toes in the cool night air. She was reading Petrarch this evening. Petrarch always makes her quiet and pensive–she hates that old Italian, and she kept murmuring, “Trovommi amor del tutto disarmato.” She smokes another cigarette, watches the sun set, gets all maudalin and teary. I noticed she was also reading an old novel–can’t figure out what that’s all about. She likes April in Texas because the weather is always all over the place, at once too hot, too cold, too dark. I tell her I’m going to write about love, but she silently dismisses me and pulls out an old notebook where she starts to scribble. “He was right. Petrarch was right. How could he live with himself?” This time I walk away. A big, huge raindrop lands on her foot, and lightning is grumbling all around. She quotes quietly, “Que ni el amor destruya la primavera intacta.” I can smell the smoke from her half-burned cigarette. A filthy habit, but she doesn’t smoke really; she lights them and lets them burn. She doesn’t as much smoke as she does burn cigarettes. “You know, you need to start a new project,” she calmly says as the dark settles across the horizon. It was always nights like this when I knew that she loved me, but then again, no. I ask, “What would Lorca have said?” Without blinking, and as cold as ice she answered, “Sucia de besos y arena, / yo me la llevé del río.” She just stared out into the night, the wind was combed by the fig tree’s empty branches, and the stars traced infinite paths in the heavens. Ni nardos ni caracolas tienen el cutis tan fino ni los cristales con luna relumbran con ese brillo.–Lorca