It's use is mandatory. Its intentional abuse is criminal fraud.
Physics math is no different than stock market, banking, economics, or real estate math. It is absolutely necessary, but still subject to both serious error and dishonesty.
Math is not a crystal ball. It does not "see all, know all". More properly, it is used in discovery-physics in an iteration attitude. There are too many unknowns and unforseeables.
Very often, the simple exercise of looking at the mechanics discloses both the correct and the erroneous.
When either the math or the mechanics indicates absurdities, it is time for further research, not acceptance of impossibilities.
To spend time on an absurdity like "I never lie", is not an excercise in logically proving the existence of paradoxes. It is purely and simply a conceptual impossibility, that cannot exist. It is a nonsensical contradiction. The two sides of it are mutually exclusive.
Unfortunately, illegitimate math "proves" such nonsensical contradictions sometimes. And people like me do not have the math power or political power to refute such paradoxes" etc. of the experts, in a fair public forum.