Thus, a curved surface is approximated by a polyhedron with flat faces. No matter how the globe is triangulated, Euler’s formula holds. Euler’s Gem provides a bridge between geometry and topology.

Christopher Francese, David Richeson, The Flaw in Euler's Proof of His Polyhedral Formula, The American Mathematical Monthly, Vol. 114, No. 4 (Apr., 2007), pp. 286-296 ...

NICK LORD, Beyond the Basel problem: Euler's derivation of the general formula for ζ (2n), The Mathematical Gazette, Vol. 98, No. 543 (November 2014), pp. 459-474 ...