Since Newton, and explicitly since Pierre-Simon Laplace formulated his famous image of a demon capable of predicting the entire future of the universe if it precisely knew the positions and velocities of all its particles, classical physics assumed that deterministic systems — governed by exact equations, with no randomness — must produce predictable behavior. Mitchell Feigenbaum, a researcher at Los Alamos National Laboratory, discovered in 1978 that this intuition is radically false even for the simplest imaginable mathematical systems. Studying single-variable recurrence equations — of the form x(n+1) = λf(xn), such as the famous logistic map used in population biology — Feigenbaum observed that, as the parameter λ gradually increases, the system passes through a sequence of period-doubling bifurcations (stable behavior goes from one cycle to two, then four, then eight...) accumulating at an ever-faster rate until leading to chaotic behavior, totally unpredictable in the long run despite there being no random element in the equation. Feigenbaum's decisive finding was not merely identifying that route to chaos — already qualitatively known — but showing, by applying renormalization-group techniques taken from phase-transition physics, that the rate at which these bifurcations accumulate obeys a universal numerical constant (δ ≈ 4.6692...) that is exactly the same for an entire class of mathematical systems, regardless of the specific details of each equation. Completely independently and almost simultaneously, Pierre Coullet and Charles Tresser, at the University of Nice, arrived at the same conclusion via a related approach, confirming that the phenomenon — today known as Feigenbaum-Coullet-Tresser universality — was not an artifact of a particular calculation method but a deep, robust mathematical property. The result demonstrated, in a mathematically precise, verifiable case, that determinism does not imply predictability: perfectly deterministic, randomness-free systems can generate chaotic behavior so rich and structured that it paradoxically deserves to be studied with the same statistical tools physics uses for critical phenomena. This theory, still purely mathematical and with no physical verification in 1978, would lay the conceptual foundations of modern complexity science.