Something you said reminded me of a math video mentioned a cash prize for anyone who could find a value making the Riemann Zeta function zero. It explains something called 'Analytic continuation' which your comment reminds me of. You have not in anyway used analytical continuation, but I thought the video would be cool.
Consider Math and Physics to be separate things. Math is philosophical while Physics involves measuring physical things. To make any realistic comments about physics you'll need expertise both in Math and in measurement, including an ability to track all changes to whatever object is being studied whether it be temperature, location etc.
Another thing that might interest you is Taoism which first postulates that the universe is composed of opposites, however it comes with no measurement (so no Physics) and no proofs. It is a philosophical system with many political and family ramifications.
That actually had a very nice description of analytic continuation.