Explored here are the Clay Mathematics Institute Millennium Prize problems, namely the Poincaré conjecture, the Hodge conjecture, the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the Yang-Mills existence and mass gap problem, the Navier-Stokes existence and smoothness problem, and the P versus NP problem. Here is identified how the possible solutions to each of these problems can be of use to physical theories. To be charted here therefore for each of these problems is their relevance to dimensional number theory in their application to physical theories, and if indeed a common dimensional number theory basis can solve these problems, and if so how, and if not why. In this charting process, it is found that curved 4d spacetime is an unlikely solution basis given the failure of the currently accepted solution to the Poincaré conjecture to solving the remaining problems. A new dimensional number theory basis is therefore proposed as a solution for the problems, and their solutions identified. By such, new solutions are also formed for Fermat’s conjecture, Goldbach’s conjecture, the twin prime problem, and the Beal conjecture.