From Pappus to today: The history of a proof

Abstract

“Perhaps we do even worse, suppressing the creative instincts of our children at the same time as researchers try to imitate them with machines. A computer is said to have applied a problem solving programme to the proposition that the base angles of an isosceles triangle are equal. Instead of the Euclidean proof which proves two right-angled-triangles [on the left below] to be congruent, the computer produced a more elegant proof from the simpler construction (sic) [on the right below]. The conventional working must have been taught to millions of children: we may reasonably ask why none of them, apparently, have discovered this simple, new proof for themselves.”