Murmuration Conjectures in Number Theory

Establish the validity of the murmuration conjectures in number theory introduced in Murmurations of elliptic curves (He–Lee–Oliver–Pozdnyakov), resolving whether the predicted murmuratory phenomena indeed occur as conjectured.

Background

In surveying AI-assisted discovery within mathematics, the author cites the emergence of conjectures identified via machine learning, emphasizing that some remain unresolved.

Among these, the paper explicitly singles out the murmuration conjectures, noting that despite their discovery through ML-driven exploration, they are still open, thereby highlighting a concrete target for further mathematical proof or disproof.

References

Hundreds of papers emerged, with notable successes including the Ramanujan machine in finding identities for famous constants , the finding of new formulae in topology and representation theory , as well as the ML discovery of the still-open murmuration conjectures in number theory .

— Mathematics: the Rise of the Machines (2511.17203 - He, 21 Nov 2025) in Section 2, Top-Down Mathematics