solve(x**2 == 1/2) as you might notice, this is fully legal Python syntax. Unfortunately the semantics is such that sympy has no way to determine what is actually going on, this is why they invented all those helper functions shown above.
This is a SymPy special "solution". Nothing in Python prevents from returning a non-boolean from __eq__(): https://docs.python.org/3/reference/datamodel.html#object.__eq__ For example, instead you could use singletons. In fact, every object in symbolic math is a singleton. x**2 is such, (x + 1)**2 - 2*x - 1 - is another, different one. To test structural equality in this approach - you can use "is", instead of "==".