Computational techniques, interactive tools, and the statistical foundations behind applied AI/ML.

Before gradient descent, there was least squares.

In 1805, Adrien-Marie Legendre published the method of least squares. Four years later, Carl Friedrich Gauss claimed he'd been using it since 1795, and had the proof: he'd used it to predict exactly where a lost asteroid, Ceres, would reappear from a handful of noisy telescope sightings. The two spent years disputing who deserved the credit. Their algebra is still, in spirit, how a great deal of software fits a line today, though not literally all of it: most production implementations solve it via QR or singular-value decomposition rather than inverting a matrix directly, for numerical stability, and very large-scale settings sometimes use iterative methods entirely. What doesn't change is the object being solved for: the same closed-form solution below, computed live on a fresh random sample every time this page loads.

It's worth naming why an 1805 algebra trick counts as machine learning at all. By the field's own standard definition, a program learns if its performance at some task improves with experience [cite]. Fitting the line above qualifies exactly: the task is predicting Y from X, the experience is the data, the performance measure is how small the squared error gets, and more experience provably improves it, exactly what Module 1's own stability simulation shows happening in real time. That's not a loose analogy. It's the same definition that describes a neural network with a billion parameters.