# 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 karaoke

I was just at a place on Thursday night that featured karaoke. Like many forms of entertainment, this past-time is not for everyone, but most people think they can sing. Far be it for me to tell them otherwise, but the strange sounds emanating from the stage caused my beverage to go up my nose at one point. I am not a champion karaoke singer–let’s just get that out on the table, but to sing a popular pop tune just like the original pop star did is nye on impossible and very near hilarious depending on how weird either the song or its singer were in real life. One woman really knocked a Stevie Nicks cover out of the park, but the next guy’s rendition of who-knows-what sent foamy suds up my sinuses. But is that the fun of karaoke in all its kitschy phantasmagoria where popular culture mixes black velvet paintings of dogs playing poker with a live microphone, a drunk audience, and dark desires of fame and failure? You never were Engelbert Humperdinck, but you want to sing one of his crooner masterpieces just like he did? You never met Lynn Anderson, but you want to sing about unpromised rose gardens? It is amazing, however, how brave a person can get after a few beers. They pick up that microphone and stand up in front of their drunk friends and start to sing their own weird cover of “Knock Three Times.” I admire their courage, and although I have sung karaoke a couple of times, I’m not convinced that that little world of pop culture turned odd is for me. My karaoke will have to stay confined to the shower, and even then I know when to stop singing and let Johnny Cash do his thing.

# On karaoke

I was just at a place on Thursday night that featured karaoke. Like many forms of entertainment, this past-time is not for everyone, but most people think they can sing. Far be it for me to tell them otherwise, but the strange sounds emanating from the stage caused my beverage to go up my nose at one point. I am not a champion karaoke singer–let’s just get that out on the table, but to sing a popular pop tune just like the original pop star did is nye on impossible and very near hilarious depending on how weird either the song or its singer were in real life. One woman really knocked a Stevie Nicks cover out of the park, but the next guy’s rendition of who-knows-what sent foamy suds up my sinuses. But is that the fun of karaoke in all its kitschy phantasmagoria where popular culture mixes black velvet paintings of dogs playing poker with a live microphone, a drunk audience, and dark desires of fame and failure? You never were Engelbert Humperdinck, but you want to sing one of his crooner masterpieces just like he did? You never met Lynn Anderson, but you want to sing about unpromised rose gardens? It is amazing, however, how brave a person can get after a few beers. They pick up that microphone and stand up in front of their drunk friends and start to sing their own weird cover of “Knock Three Times.” I admire their courage, and although I have sung karaoke a couple of times, I’m not convinced that that little world of pop culture turned odd is for me. My karaoke will have to stay confined to the shower, and even then I know when to stop singing and let Johnny Cash do his thing.

# On the selfie

The latest craze is to shoot a self-portrait and post it on the web. They did it during the Oscars the other night. I have always found the “selfie” to be a little narcissistic, silly at best. I mean, no one wants to take your picture so you do it yourself? Just because you have a camera doesn’t necessarily mean that you need to use it, does it? The advent of the ubiquitous digital camera, especially those attached to smart phones, means that anyone and everyone has the ability to shoot a couple of embarrassing selfies and post them on their “wall.” The “driving selfie” seems like one of those last things that some people will ever do: take a picture of themselves at the wheel of a car going 70 miles per hour. Some selfies are cute, but most should never see the light of day. The pregnant stomach selfie seems a little weird, but it does document the process. Most naked selfies would best be forgotten for so many reasons–poor taste among them. And naked selfies should never be sent over the web for any reason at all unless you trying to lose your job on purpose, break up with your significant other, or are purposely trying to get arrested. Clown selfies are illegal in thirty-eight states. Friends don’t let drunk friends shoot selfies. Tonight’s selfie could be tomorrow’s viral post on Facebook. Most people’s arms aren’t really long enough to take a selfie without distorted perspective unless you don’t mind that the whole world see your nose hair.

# On the selfie

The latest craze is to shoot a self-portrait and post it on the web. They did it during the Oscars the other night. I have always found the “selfie” to be a little narcissistic, silly at best. I mean, no one wants to take your picture so you do it yourself? Just because you have a camera doesn’t necessarily mean that you need to use it, does it? The advent of the ubiquitous digital camera, especially those attached to smart phones, means that anyone and everyone has the ability to shoot a couple of embarrassing selfies and post them on their “wall.” The “driving selfie” seems like one of those last things that some people will ever do: take a picture of themselves at the wheel of a car going 70 miles per hour. Some selfies are cute, but most should never see the light of day. The pregnant stomach selfie seems a little weird, but it does document the process. Most naked selfies would best be forgotten for so many reasons–poor taste among them. And naked selfies should never be sent over the web for any reason at all unless you trying to lose your job on purpose, break up with your significant other, or are purposely trying to get arrested. Clown selfies are illegal in thirty-eight states. Friends don’t let drunk friends shoot selfies. Tonight’s selfie could be tomorrow’s viral post on Facebook. Most people’s arms aren’t really long enough to take a selfie without distorted perspective unless you don’t mind that the whole world see your nose hair.