Mathematicians just proved an infinite universe has to be perfectly flat—if it were even slightly curved, it wouldn't exist.
March 24, 2026
Original Paper
PIC1 pinched manifolds are flat or compact
arXiv · 2603.22086
The Takeaway
For decades, it was a mystery whether a space could have a gentle, lingering curve that never quite closes. This proof shows that in any number of dimensions, space is either closed like a ball or absolutely, perfectly flat, leaving no mathematical room for 'wonky' infinite shapes.
From the abstract
Hamilton's pinching conjecture, that three-dimensional complete non-compact manifolds with pinched Ricci curvature are flat, has recently been resolved using Ricci flow. In this paper we prove a direct analogue of that result in all dimensions. In order to do so we develop a lifting technique that allows us to handle manifolds that are collapsed at infinity. This new method also gives an alternative way of handling collapsed manifolds in the known three-dimensional case. As part of this approach