There's a whole lot of talking going on beneath the waves. A new Cornell study finds that fish are far more likely to communicate with sound than generally thought—and some fish have been doing this for at least 155 million years.

In a paper posted in September, Paul Nelson of the Institute for Advanced Study has solved a version of the subconvexity problem, a kind of lighter-weight version of Riemann’s question. The proof is a significant achievement on its own and teases the possibility that even greater discoveries related to prime numbers may be in store. “It’s a bit of a far-fetched dream, but you could hyper-optimistically hope that maybe we get some insight in how the [Riemann hypothesis] works by working on problems like this,” Nelson said.

The puzzle is easily solved when there are five ranks and five regiments, or seven ranks and seven regiments. But after searching in vain for a solution for the case of 36 officers, Euler concluded that “such an arrangement is impossible, though we can’t give a rigorous...See more