# 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 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 time and being

Time measured versus time perceived has always been an interesting problem. Time flies while you are having fun, but time slows to a crawl when you have to wait. You can look at a clock with a sweep-second hand and watch time go by, but that doesn’t tell you anything. Being objective about time is about as rational as being objective about thirst: objectivity has nothing to do with either. When a dentist is working on reshaping a broken tooth and the drill is whining, bits of tooth are flying everywhere, and you have eight things in your mouth at once, time stands still. When you wake up at six in the morning, you wonder where the entire night went. You turn fifty, and you have no idea what just happened to the last thirty years. A watched teapot will never boil, and that bagel in the toaster will only pop up after you sit down. Stopped at a red light, your entire life drags out before you, but time flies when you see a green light, which you will not reach before it turns red again. When you are in a hurry or late, time races like a scared jack rabbit. The fact that time is so malleable and dependent on our perception of it would suggest that time as a fixed rate of progression is an illusion dreamed up by watch and clock makers in the eighteenth century. Before that, time was a much harder thing to measure. The Illustration and its proponents thought that humanism, science and the corresponding empiricism could be used to lock up time, put it in a box, and regularize it. Much to our chagrin and illusory time ideology, time has never been a part of such a plan. It took Einstein and his “Theory of Special Relativity” in order to disavow such an idea that time is fixed, regular, predictable, but instead that time is totally dependent on one’s context, point-of-view, frame of reference. Though we will never have enough “time,” time is really all we have. What makes time so scarce is over-commitment, 80 hour-a-week jobs, and time poverty. What we do with our time is often a mystery, but we fight our calendars, arrive late everywhere, cut our rest short, skip time with our families, sell ourselves short. Being seems to come at a premium completely dependent on our inability to manage and distribute or time sensibly. Before we know it, we’re on the run, trying to make our next thing, or time is up, and we have to leave, get in the car, hop a train, take an airplane. The speed at which we live is geometrically proportional to the speed at which we travel, getting back to Einstein again. Perspective, frame of reference, context, dictate that the connection between being and time is contingent on how we perceive the passage of time. As we live, we create the illusion that time moves forward, especially given the structure of our verb systems, past, present, and future, language being our only mode for expressing what we experience. These are measly attempts at creating order within a structure that lies outside of senses, our perception of the universe, but because we must move within something, we call “time” that fourth dimension which surrounds our movements and gives meaning to our being. Beingness is necessarily a question of what we call time, but we only have the faintest notion of what “time” might really be. Our senses fall well short of understanding the impossibility of time, but our philosophy is equally deficient to even ask the correct questions concerning this enigmatic phenomenon. So we settle for a simple explanation of seconds, minutes, hours, and days because our little brains have no chance of understanding what is actually going on. We create simulacra to account for something that we not only don’t understand, but that we have absolutely no chance of understanding.