Differentiability Memes

When your pregnancy test reveals you're expecting... a Weierstrass function! Instead of a baby, these poor souls are giving birth to the mathematical equivalent of a rebel without a cause—a function that's continuous everywhere but differentiable nowhere . It's like having a teenager who follows all the house rules but still manages to be completely unpredictable. No wonder mathematicians don't reproduce by normal means—they just inflict their pathological functions on unsuspecting calculus students instead.

That feeling when your mathematical intuition is screaming "THIS FUNCTION IS A SPIKY NIGHTMARE!" but you lack the formal proof! The jagged graph shows a Weierstrass function - the mathematical equivalent of a rebellious teenager with identity issues. It's continuous EVERYWHERE but differentiable NOWHERE! *twirls calculator dramatically* Karl Weierstrass broke mathematicians' brains in 1872 by creating these monstrosities that exist in the forbidden zone between smooth functions and complete chaos. Math students worldwide still wake up in cold sweats thinking about these pathological functions!

The eternal battle between mathematical rigor and physical practicality on full display! Mathematicians are having a complete meltdown over physicists casually using Taylor series expansions without checking if functions are even differentiable. Meanwhile, physicists are just vibing with their approximations, making the math work for them with zero remorse. That formula? It's the Taylor series expansion that lets physicists approximate nearly any function as a polynomial—the ultimate "close enough" tool that makes mathematicians cry themselves to sleep. The rigorous proof-lovers demand formal verification while the practical physics crowd goes "haha differential equations go brrrr." Pure math vs. applied science warfare at its finest!

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.