There are strong indications from physics at both infinitesimal and cosmic distances that our current understanding of the laws of nature is only approximate, and must be replaced by deeper principles. The UNIVERSE+ project seeks a new foundation for fundamental physics, ranging from elementary particles to the Big Bang, revealing a hidden world of ideas beyond quantum mechanics and spacetime. Novel geometric objects recently discovered in theoretical physics hint at new mathematical structures. Combinatorics, algebra and geometry have been connected to particle physics and cosmology in an entirely unexpected way. Leveraging these advances, we will launch the field of Positive Geometry, as a new mathematical framework for describing the laws of physics. To this end, we bring together the necessary expertise in particle physics (Arkani-Hamed, Henn), cosmology (Baumann) and mathematics (Sturmfels). This is the first collaboration of its kind, made possible by a recent confluence of critical insights in both mathematics and physics, which are now so closely aligned as to propel us forward on a clear trajectory. Our goals are fiercely ambitious: we aim to create a new mathematical language for describing physical phenomena at all scales, from the interactions of elementary particles to the large-scale structure of the universe.