I'm not sure whether it qualifies or not, but I found a link between the golden ratio and the Riemann Hypothesis some years ago: https://math.stackexchange.com/questions/2380532/is-there-a-hidden-connection-between-rh-and-the-golden-ratioIs there a hidden connection between RH and the golden ratio?.
No matter how anecdotic it might be, I nevertheless find this aesthetically pleasant.