The River’s New Channels: Reorienting Applied Mathematics and Mechanics

Applied mathematics and mechanics have entered a stage at which their disciplinary direction, research priorities, and journal orientation must be re-examined. The difficulty today does not lie in the lack of directions, but in the excessive abundance of them; not in the absence of new concepts, but in their inflation, to the point that mainstreams and tributaries, riverbeds and waves, are increasingly blurred. Using the metaphor of “the river’s new channels,” this editorial discusses why applied mathematics and mechanics must be reoriented in the intelligent age, where this reorientation should lead, and how it should be organized. It argues that, for Applied Mathematics and Mechanics, the real point of departure must remain mechanical objects, mechanical problems, and mechanical laws. The importance of applied mathematics lies not only in advancing abstract formulations and general methods, but also in providing trustworthy methodological support for real mechanics problems through modeling, analysis, computation, inverse identification, optimization, uncertainty quantification, and data assimilation. Convincing new channels should therefore not be reduced to a catalog of fashionable topics, but must first return to the basic variables, relations, boundaries, and methods of mechanics, and rebuild a general framework of fundamental problems and trustworthy methodologies. On this basis, AI for Mechanics represents a route of methodological reorganization,the transition from metamaterials to intelligent metastructural systems represents a route of structural-object expansion, nonlocal theory and multiphysics coupling represent a route of theoretical reconstruction, and the transition from biomechanics to life mechanics represents a route of life-object and mechanism integration. These four routes are not isolated lines, but interacting channels that converge and are tested in complex engineering problems and extreme mechanics. Real-world needs should not replace free exploration and original innovation. Rather, fundamental problems provide the riverbed, free exploration opens the sources, real-world needs expose the boundaries, and complex systems test the depth and reliability of emerging channels. The journal should therefore remain open to interdisciplinary expansion while making clear that its core orientation lies in mechanics problems—especially fundamental and complex engineering problems—supported by trustworthy mathematical methods. It should act not only as a publication platform, but also as a “hydrological surveyor” of emerging channels by organizing focused themes, supporting problem-chain research, and helping to shape a more coherent scholarly community.