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The Ballerina and the Plumber

A man and a woman sit on a couch.  An hour ago their movie ended, and now they sit, entwined, exchanging those personal hopes and fears only shared by lovers.  The glow of their love could overpower, and repel the sun's rays.  No force of nature could separate them.

Whoop! Whoop! Whoop!

However, fire alarms are not natural.  Without delay, the woman extracts her limbs and leaps to her feet, allowing her husband to stand.  He reaches the window first, and opens their path to the fire escape.

The Ballerina

The woman exits first, diving through the window.  The dive transitions to a watermelon roll, that terminates with her feet on the fire escape's guardrail.  She pushes herself up, into a sort of bridge, that becomes a handspring, moving toward the stairs.    She tucks her legs, completes the flip, lands side saddle on the descending handrail, and slides down to the second floor landing.  She rounds the corner, and, in one fluid motion, jumps up, releases the drop ladder, and grabs hold for a ride.  Her slight frame provides little additional difficulty for the ladder's springs, and she is delivered gently to the ground.

The Plumber

Using a stool, the man crawls onto the fire escape.  Fully clear of the window, he attempts to stand.  His inflexibility, and forward center of mass, make balance difficult, forcing him to take a couple steps.  His left foot lands half off the top step, and his imbalance shifts.  What was a near recovery becomes a tumble.  He's able to grab something and roll himself around, his back slamming against the rail.  He falls into a less-than-graceful forward roll, and stops at the base of the stairs, sore butt on the landing, and one foot elevated.  Carefully he unhooks his foot and stands, this time with the aid of the railing.  He slowly limps to the deployed ladder.  Nerves rattled, he descends the ladder in the most OSHA approved fashion: one rung at a time, with at least three points of contact.

Conclusions

Proofs are the way mathematicians travel from assumptions to conclusions.  Some read like well rehearsed  choreography.  Every step elegantly supporting and leading to the next.  Every statement saying only what the author intends.  No awkward assumptions cast doubt on the validity of a theorem.  Others, however, are more like a fat man falling down a fire escape.

Both forms of proof are equally effective, and sometimes a cumbersome proof is your only choice.  But, when possible, an elegant proof is a real pleasure.