Geller's Theorem

Geller's Theorem is a mathematical result related to functions that are continuous and smooth, specifically focusing on their derivatives. It states that for any such function, the set of points where the derivative is zero (meaning the function isn't increasing or decreasing) can be very complicated, potentially forming a highly irregular set. In essence, even if a function looks smooth overall, the locations where its rate of change is zero can be quite intricate and may include very complex, fractal-like patterns. This shows that the behavior of derivatives on smooth functions can be surprisingly intricate and diverse.