[zmgsabst]

This is arguably what caused the push for formalism in mathematics:

Multiple papers on calculus claimed results about continuity and derivatives, but we’re using subtly different definitions.

The conflict between those results, and the counter-examples to demonstrate the difference, led to mathematicians building the modern machinery around proofs.

> The Weierstrass function has historically served the role of a pathological function, being the first published example (1872) specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points. Weierstrass's demonstration that continuity did not imply almost-everywhere differentiability upended mathematics, overturning several proofs that relied on geometric intuition and vague definitions of smoothness.

https://en.wikipedia.org/wiki/Weierstrass_function