That's exactly how a great deal of research level math is done.
In fact all open conjectures can be cast this way: the objective function is just the function that checks whether a written proof is a valid proof of the statement.
Is there a solution to this PDE? Is there a solution to this algebraic equation? Is there an optimal solution (i.e. we add an optimality condition to the objective function). Does there exist a nontrivial zero that is not equal to 1/2, etc.
I can't tell you how many talks I've seen from mathematicians, including Fields Medal winners, that are heavily driven by computations done in Mathematica notebooks which are then cleaned up and formalized. That means that -- even for problems where we don't know the statement in advance -- the actual leg work is done via the evaluation of computable functions against a (explicit or implicit) objective function.
In fact all open conjectures can be cast this way: the objective function is just the function that checks whether a written proof is a valid proof of the statement.
Is there a solution to this PDE? Is there a solution to this algebraic equation? Is there an optimal solution (i.e. we add an optimality condition to the objective function). Does there exist a nontrivial zero that is not equal to 1/2, etc.
I can't tell you how many talks I've seen from mathematicians, including Fields Medal winners, that are heavily driven by computations done in Mathematica notebooks which are then cleaned up and formalized. That means that -- even for problems where we don't know the statement in advance -- the actual leg work is done via the evaluation of computable functions against a (explicit or implicit) objective function.