TL;DR: waterfall is an open-loop system. In order to control it (the direction of your project, its results), you need to have a perfect model of system internals <i>and</i> know the input. Since you know neither, you simply can&#x27;t control it. Agile is a closed-loop system, it contains a feedback loop, which lets you control the system even if you don&#x27;t know the internals perfectly (and with human beings, you&#x27;ll never know).<p>This is the core insight, though I&#x27;m probably skipping things in this description that you know implicitly when you&#x27;ve seen the math. The rest of discussion about agile is either minutiae of tuning the feedback loop for best results, or just marketing talk and bikeshedding.