Her exposition of math concepts is ridiculous.

"De Morgan had proposed a more modern approach to algebra, which held that any procedure was valid as long as it followed an internal logic. This allowed for results like the square root of a negative number"

Imaginary numbers were introduced by Descartes in 17th century and were widely accepted by the middle of 18th (think Euler: e^(i \pi) + 1 = 0).

"This principle (now an important aspect of modern topology) involves the idea that one shape can bend and stretch into another, provided it retains the same basic properties — a circle is the same as an ellipse or a parabola (the curve of the Cheshire cat’s grin)."

Huh? You can bend or stretch a circle into a parabola?