zagers

CHILDHOOD’S END //  a midwestern gothic mix

The town where the train never stops, where bright smiles hide rotting teeth, and everyone pretends the shadows do not exist  {Listen}

In The Year 2525 - Zager and Evans // California Dreamin’ - Scala & Kolacny Brothers // Beggar’s Prayer - Emilianna Torrini // Eleanor Rigby - The Beatles // This Time Tomorrow - Trent Dabbs // Blowin’ In The Wind - Bob Dylan // Video Games - Lana Del Rey // If I Had A Hammer - Peter, Paul, & Mary // Furr - Blitzen Trapper // For What It’s Worth - Buffalo Springfield 

Finally, after years in the making, get ready to experience

The Kouen List

Based on the headcanon that a modern-day Kouen would secretly listen to cheesy boomer-era soft rock ballads and disco

13 Tracks / Pop Rock, Disco

Sugar Baby Love / The Rubettes  //  If You Leave Me Now / Chicago  //  Let’s All Chant (Remix) / The Michael Zager Band  //  Rock Me Amadeus (Original Single Version) / Falco  //  Disco Inferno / The Trammps  //  Move It On Over / George Thorogood and the Destroyers  //  St. Elmo’s Fire / John Parr  //  The Hustle / Van McCoy and the Soul City Symphony  //  Some Like It Hot / Power Station  //  I’m Not In Love / 10cc  //  Working My Way Back To You / The Spinners  //  Kokomo / The Beach Boys  //   Eternal Flame / The Bangles


Warning: contains massive amounts of cheese

Proof of Proof

Tracy Zager (twitter, blog) had this great collection of proof quotes on a Dan Meyer blogpost, which is a response to a “math traditionalist” article in the Atlantic. They argue that student explanations in K-12 math are at best boring and at worst harmful. Tracy connects students explaining to mathematicians explaining.

Ian Stewart:
“A proof, they tell us, is a finite sequence of logical deductions that begins with either axioms or previously proved results and leads to a conclusion, known as a theorem….This definition of ‘proof’ is all very well, but it is rather like defining a symphony as ‘a sequence of notes of varying pitch and duration, beginning with the first note and ending with the last.’ Something is missing. Moreover, hardly anybody ever writes a proof the way the logic books describe….A proof is a story. It is a story told by mathematicians to mathematicians, expressed in their common language….If a proof is a story, then a memorable proof must tell a ripping yarn….When I can really feel the power of a mathematical storyline, something happens in my mind that I can never forget” (2006, 89-94).

Marcus du Sautoy:
“A successful proof is like a set of signposts that allow all subsequent mathematicians to make the same journey. Readers of the proof will experience the same exciting realization as its author that this path allows them to reach the distant peak. Very often a proof will not seek to dot every i and cross every t, just as a story does not present every detail of a character’s life. It is a description of the journey and not necessarily the re-enactment of every step. The arguments that mathematicians provide as proofs are designed to create a rush in the mind of the reader” (2015).

Paul Lockhart:
“A proof, that is, a mathematical argument, is a work of fiction, a poem. Its goal is to satisfy. A beautiful proof should explain, and it should explain clearly, deeply, and elegantly. A well-written, well-crafted argument should feel like a splash of cool water, and be a beacon of light—it should refresh the spirit and illuminate the mind. And it should be /charming/” (2009, 68).

“A proof should be an epiphany from the gods, not a coded message from the Pentagon” (75).

Paul Halmos:
“The best seminar I ever belonged to consisted of Allen Shields and me. We met one afternoon a week for about two hours. We did not prepare for the meetings and we certainly did not lecture at each other. We were interested in similar things, we got along well, and each of us liked to explain his thoughts and found the other a sympathetic and intelligent listener. We would exchange the elementary puzzles we heard during the week, the crazy questions we were asked in class, the half-baked problems that popped into our heads, the vague ideas for solving last week’s problems that occurred to us, the illuminating problems we heard at other seminars—we would shout excitedly, or stare together at the blackboard in bewildered silence—and, whatever we did we both learned a lot from each other during the year the seminar lasted, and we both enjoyed it.” (1985, 72-73).

Ian Stewart:
“When two members of the Arts Faculty argue, they may find it impossible to reach a resolution. When two mathematicians argue—and they do, often in a highly emotional and aggressive way—suddenly one will stop, and say, ‘I’m sorry, you’re quite right, now I see my mistake.’ And they will go off and have lunch together, the best of friends” (2006, 28).