In 2011, Deconinck and Oliveras simulated different disturbances with higher and higher frequencies and watched what happened to the Stokes waves. As they expected, for disturbances above a certain frequency, the waves persevered.

But as the pair continued to dial up the frequency, they suddenly began to see destruction again. At first, Oliveras worried that there was a bug in the computer program. “Part of me was like, this can’t be right,” she said. “But the more I dug, the more it persisted.”

In fact, as the frequency of the disturbance increased, an alternating pattern emerged. First there was an interval of frequencies where the waves became unstable. This was followed by an interval of stability, which was followed by yet another interval of instability, and so on.

Deconinck and Oliveras published their finding as a counterintuitive conjecture: that this archipelago of instabilities stretches off to infinity. They called all the unstable intervals “isole”—the Italian word for “islands.”

It was strange. The pair had no explanation for why instabilities would appear again, let alone infinitely many times. They at least wanted a proof that their startling observation was correct.