By January 2020, Papadimitriou had been thinking about the pigeonhole principle for 30 years. So he was surprised when a playful conversation with a frequent collaborator led them to a simple twist on the principle that they’d never considered: What if there are fewer pigeons than holes? In that case, …
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The original version of this story appeared in Quanta Magazine. For computer scientists, solving problems is a bit like mountaineering. First they must choose a problem to solve—akin to identifying a peak to climb—and then they must develop a strategy to solve it. Classical and quantum researchers compete using different …
Read More »The original version of this story appeared in Quanta Magazine. At the beginning of time and the center of every black hole lies a point of infinite density called a singularity. To explore these enigmas, we take what we know about space, time, gravity, and quantum mechanics and apply it …
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