Why 7G Needs New Theorems: A Geodesy-Based Perspective on Beyond-6G Foundations

Every prior generation of cellular wireless was preceded by a foundational theorem: Shannon for the digital transition of 1G–3G, Telatar for the multi-antenna capacity that defined 4G, Arıkan for the polar codes that underpin 5G control signaling. Sixth-generation wireless is deep into its standardization cycle without an analogous defining result, and seventh-generation wireless has not yet been posed as a theoretical problem at all. We argue, from the perspective of a geodetic engineer who has spent two decades working with the original integrated sensing and communication system—the Global Navigation Satellite System—that the most consequential contributions to 7G will not come from faster hardware but from new theorems, and that the geodetic estimation tradition provides the most mature and most immediately applicable toolkit for producing them. We identify five concrete mathematical bridges from geodesy to beyond-6G open problems: Cramér–Rao analysis to ISAC capacity–distortion regions, ambiguity-function design to delay-Doppler channel theory, multi-constellation estimation to Space-Air-Ground Integrated Network capacity, Kalman-filter convergence to AI-native channel tracking with provable guarantees, and antenna phase-center calibration to near-field electromagnetic information theory. We frame the 2026–2030 window—bounded by the ITU-R IMT-2030 evaluation phase, World Radiocommunication Conference 2027 spectrum decisions, and the first 6G releases of 3GPP—as the critical period in which foundational theoretical work can still shape what systems get built, and issue a call to the geodesy and wireless-communications research communities to engage across the boundary that currently separates them.