The central objects of study in topology are spaces called manifolds, which look flat when you zoom in on them. The surface of a sphere, for instance, is a two-dimensional manifold. Topologists understand such two-dimensional manifolds very well. And they have developed tools that let them make sense of three-dimensional manifolds and those with five or more dimensions. But in four dimensions...
In 2022, researchers at the Bee Sensory and Behavioral Ecology Lab at Queen Mary University of London observed bumblebees doing something remarkable: The diminutive, fuzzy creatures were engaging in activity that could only be described as play. Given small wooden balls, the bees pushed them around and rotated them. The behavior had no obvious connection to mating or survival, nor was it rewarded...
What’s the best way to solve hard problems? That’s the question at the heart of a subfield of computer science called computational complexity theory. It’s a hard question to answer, but flip it around and it becomes easier. The worst approach is almost always trial and error, which involves plugging in possible solutions until one works. But for some problems, it seems there simply are no...
At a conference in Japan a few years ago, David Dunsky attended a talk about gravitational waves, ripples in the fabric of space-time created when massive objects like stars and black holes accelerate. Dunsky was a graduate student in particle physics at the time, and his interests seemingly lay elsewhere. Particle physicists seek the more fundamental truth underpinning the physical rules we’re...
Ishmail Abdus-Saboor has been fascinated by the variety of the natural world since he was a boy growing up in Philadelphia. The nature walks he took under the tutelage of his third grade teacher, Mr. Moore, entranced him. “We got to interact and engage with wildlife and see animals in their native environment,” he recalled. Abdus-Saboor also brought a menagerie of creatures — cats, dogs, lizards...
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