The original version of this story appeared in Quanta Magazine. Two blind spots torture physicists: the birth of the universe and the center of a black hole. The former may feel like a moment in time and the latter a point in space, but in both cases the normally interwoven threads of space and time seem to stop short. These mysterious points are known as singularities. Singularities are predictions of Albert Einstein’s general theory of relativity. According to this theory, clumps of matter or energy curve the space-time fabric toward themselves, and this curvature induces the force of gravity. Pack enough stuff into a small enough spot, and Einstein’s equations seem to predict that space-time will curve infinitely steeply there, such that gravity grows infinitely strong. Most physicists don’t believe, however, that Einstein’s theory says much about what really happens at these points. Rather, singularities are widely seen as “mathematical artifacts,” as Hong Liu, a physicist at the Massachusetts Institute of Technology, put it, not objects that “occur in any physical universe.” They are where general relativity malfunctions. The singularities are expected to vanish in a more fundamental theory of gravity that Einstein’s space-time picture merely approximates—a theory of quantum gravity. But as physicists take steps toward that truer and more complete theory by merging general relativity and quantum physics, singularities are proving hard to erase. The British mathematical physicist Roger Penrose won the Nobel Prize in Physics for proving in the 1960s that singularities would inevitably occur in an empty universe made up entirely of space-time. More recent research has extended this insight into more realistic circumstances. One paper established that a universe with quantum particles would also feature singularities, although it only considered the case where the particles don’t bend the space-time fabric at all. Then, earlier this year, a physicist proved that these blemishes exist even in theoretical universes where quantum particles do slightly nudge space-time itself—that is, universes quite a bit like our own. This trilogy of proofs challenges physicists to confront the possibility that singularities may be more than mere mathematical mirages. They hint that our universe may in fact contain points where space-time frays so much that it becomes unrecognizable. No object can pass, and clocks tick to a halt. The singularity theorems invite researchers to grapple with the nature of these points and pursue a more fundamental theory that can clarify what might continue if time truly stops. Space-Time’s Fatal Flaws Karl Schwarzschild first discovered an arrangement of space-time with a singularity in 1916, just months after Einstein published general relativity. The bizarre features of the “Schwarzschild solution” took years for physicists to understand. Space-time assumes a shape analogous to a whirlpool with walls that swirl more and more steeply as you go farther in; at the bottom, the curvature of space-time is infinite. The vortex is inescapable; it has a spherical boundary that traps anything falling inside, even light rays. It took decades for physicists to accept that these inconceivable objects, eventually dubbed black holes, might actually exist.