How serious/promising is Connes' work on the Riemann Hypothesis? Connes is mostly known for his work in non-commutative geometry, for which he earned a Fields medal. He is a trusted mathematician with deep insights. On the other hand, his [essay](https://arxiv.org/abs/1509.05576) on RH doesn't seem to identify one clear idea on how to approach the problem. At least, none that I can see. I'm wondering if anybody looked into it. After all, he seems to have been working on RH, one way or another, for twenty years, now. >I am mostly curious, specifically, in conceptual reasons (if any) why this approach is, or may be, regarded as "not promising", or "conceptually incorrect", in contrast to the other questions already on MO, that usually inquire about what such approach may or may not be "still missing", or what it already accomplishes.