The illustration there is great. But i think the article is pretty vacuous: it tells you that there is this bridge, but it doesn't explain what the bridge is. W

The illustration there is great. But i think the article is pretty vacuous: it tells you that there is this bridge, but it doesn't explain what the bridge is. Which is understandable, because that's very complicated and deep, and this is a short article for a general audience. Take the explanation of automorphic forms: "On the other side of the bridge live objects called automorphic forms, which are akin to highly symmetric colorings of certain tilings. In the cases Wiles studied, the tiling might be something along the lines of M.C. Escher’s famous tessellations of a disk with fish or angels and devils that get smaller near the boundary. In the broader Langlands universe, the tiling might instead fill a three-dimensional ball or some other higher-dimensional space." Having read that, do you now actually know anything about automorphic forms? No. It goes on: "Namely, for both Diophantine equations and automorphic forms, there’s a natural way to generate an infinite sequence of numbers. [...] And for the kind of automorphic form that appears in the Langlands correspondence, you can compute an infinite list of numbers analogous to quantum energy levels." What on earth does that mean? This might well be the projection of the truth onto the low-dimensional space of ordinary language, but it ends up being word salad.