UNIVERSE+ is an ERC Synergy Grant project led by Nima Arkani-Hamed (Institute for Advanced Study, Princeton), Daniel Baumann (University of Amsterdam), Johannes Henn (Max Planck Institute for Physics, Munich) and Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences, Leipzig). The team aims to create a new mathematical language to describe physical phenomena on all scales, from the interactions of elementary particles to the large-scale structure of the Universe.