Professor Isaac said, "The proof of Agimestes's Final Theorem begins with a discussion of limits..."

Isabelle tuned her ear to the lecture, wiped her brushes clean, and dipped her finest point in paint thinned enough to flow like ink. She didn't want to smear anything he said.

She bent her mind to Isaac's math and her brush to the canvas, stretching in dense mathematical symbols around the equator of the balloon. Only someone verse in Isabelle's personal shorthand would recognize it as anything other than a fancy belt of stitching.

Her pulse skittered and her face flushed as the proof built upon itself, tantalizing her mind with greater truths. Agimestes's Final theorem has remained unproven mathematically for over two hundred years. If it could finally be nailed down, it would revolutionize aetheric navigation and so many other things. Sweat broke out on her brow and rand own her nose as the logic web approached its moment of maximum complexity, a dozen threads of reason pulled tight as harp strings. Brilliant...

But wait. her brush faltered as one of the deductions struck a sour note. She double-checked her notation, hoping she was wrong...Damn.

the proof was flawed, the intricate weave of reason snarled on a simple fallacy, easy to overlook in the deeper context of the proof. All that work for nothing. Well, not nothing exactly. She'd at least learned one more way the theorem wasn't solved. She noted the snarl in his reasoning with hash marks in a trail of stitching up the side of the balloon.

Unfortunately, being a woman, she couldn't just march into the library and point out Professor Isaac's mistake. That would be a job for Martin DuJournal in his next missive.