The math behind why models underfit or overfit — and why you can't fix both by pushing a single dial in one direction.
Underfitting and overfitting look like two unrelated problems from the outside, but they share a single mathematical root: a model's total expected error on new data can be decomposed into two independent sources — bias and variance— plus a floor of noise no model can remove. The uncomfortable part is that bias and variance don't move independently. Turning the dial that reduces one almost always turns up the other. The entire practice of model selection, regularization, and cross-validation exists to find the one point on that dial where their sum is smallest — not the point where either one hits zero.