The interesting thing here is the similarity with Fermat's Last Theorem (now the Wiles-Taylor Theorem). There it was a completely unexpected connection between

The interesting thing here is the similarity with Fermat's Last Theorem (now the Wiles-Taylor Theorem). There it was a completely unexpected connection between Modular Forms and Elliptic Curves (Taniyama-Suimura Conjecture - now Theorem) that opened the way for the proof. Here there appears to be predictive power in random matrices to talk about the zeros on the critical line of the RZF. And before you ask, I don't know much about this. I've been to a talk and it all looked reasonable and exciting, but there's no way I could reproduce any of it. I can try to interpret stuff if people ask.