Every time you open a website, display an icon, or render a font, you are probably using, without knowing it, the work of Pierre Bézier—and the less remembered Paul de Casteljau.
Working respectively at Renault and Citroën, both were pioneers in solving an elegant yet very industrial problem: how to mathematically describe the smooth curves of car bodywork for computer-aided design.
The mathematical abstraction they helped formalize—Bézier curves—became one of the invisible foundations of modern visual computing: SVGs, fonts, vector graphics, UI rendering, animation, CAD, and much more.
What I find fascinating is how modern AI strangely echoes the same intuition.
A Bézier curve does not explicitly store every point of a shape. Instead, a complex continuous form emerges from a handful of "control points"—weights, in other words.
LLMs operate in a surprisingly similar way. They do not store language sentence by sentence, but rather compress immense semantic landscapes into latent vector spaces from which meaning, structure, tone and reasoning can later re-emerge dynamically.
In both cases, complexity is not memorized literally, but encoded geometrically. A few control points can approximate a shape. A few billion parameters can approximate meaning.
