Pathological Memes

Ever notice how mathematicians get increasingly dramatic about their weird functions? The Dirichlet function gets a casual "OK" because it's Lebesgue integrable but nowhere continuous—like finding out your date can't swim but makes amazing pasta. Then the Weierstrass function demands attention with its "HOL' UP" because it's continuous everywhere but refuses to be differentiable anywhere—basically the mathematical equivalent of someone who looks perfectly normal but has absolutely no chill. But the Fabius function? That smooth-talking infinitely differentiable yet nowhere analytic tease sends mathematicians into full psychedelic meltdown mode. It's like discovering your calculator has been secretly plotting world domination this whole time. These pathological functions are why math professors drink.

First, our cheerful math student understands the well-behaved parabola. Next, she comprehends functions with occasional differentiability hiccups. But then... Weierstrass function has entered the chat . That last panel shows the mathematical equivalent of Lovecraftian horror—a continuous function that's differentiable precisely nowhere . It's like nature decided "Let's create something that follows exactly one rule while breaking every intuition humans have about smoothness." Every calculus professor has witnessed this exact facial expression when introducing pathological functions. The math gods created these monstrosities specifically to crush undergraduate spirits and keep mathematicians humble.