This April, as undergraduates strolled along the street outside his modest office on the campus of the University of California, Los Angeles, the mathematician Terence Tao mused about the possibility that water could spontaneously explode. A widely used set of equations describes the behavior of fluids like water, but there seems to be nothing in those equations, he told me, that prevents a wayward eddy from suddenly turning in on itself, tightening into an angry gyre, until the density of the energy at its core becomes infinite: a catastrophic ‘‘singularity.’’ Someone tossing a penny into the fountain by the faculty center or skipping a stone at the Santa Monica beach could apparently set off a chain reaction that would take out Southern California.

This doesn’t tend to happen. And yet, Tao explained, nobody can say precisely why. It’s a decades-­old conundrum, and Tao has recently been working on an approach to a solution — one part fanciful, one part outright absurd, like some lost passage from ‘‘Alice’s Adventures in Wonderland.’’