The jamming transition in packings of hard particles is of fundamental interest in the physics of granular materials and glasses. In recent years the physics of jamming has gained momentum in several interdisciplinary contexts, going from Machine Learning to Inference, Ecology and beyond. I will introduce the Simplest Model of Jamming and show how jammed points share peculiar critical properties, highly universal and deeply related glass physics. After discussing the implications of the vicinity to jamming in a glassy phase, I will consider the problem of Information Storage in Machine Learning. Going from the single neuron to multilayer networks, the capacity limit becomes a jamming point.