Is math recursive or iterative?

Question

Is the process of solving a mathematical problem (algebraic equations, limits, derivatives, integrals, EDOs, trigonometric identities proof) recursive or iterative?

For example, for solving $x=1+2+3$ as a first step we can add $1$ and $2$, $1$ and $3$, or $2$ and $3$; and then continue adding the result of that. We can look at it as a recursive search in a tree with a root node with three childs. Or we can just look at it linearly (iterative) as:

$x=1+2+3$

$x=\,\,\,\,3+3$

$x=\,\,\,\,\,\,\,\,6$

At this level it doesn't matter what operation we choose to apply because the problem is too simple. But in problems like integrals what mathematical rule we choose to apply can lead us to a more simple or complicated solution:

For example, for the integral $\displaystyle\int(3x-4)dx$ it could be:

                          initial state

                       /                 \

   integration by substitution    integral of a sum is the sum of integrals of each term
          u = 3x-4, du = dx       int(3x + 4)dx = int(3x)dx + int(4)dx
          int(u)du

              /                               \

   integral of linear function             take constant out of integral

           /                                       \

    re-substitute u                        integral of constant function

                                                     \
                                             integral of linear function

There could be more branches in each step. So my question is, can we program a computer to solve any math problem linearly? So the program would be capable of always choosing the step that leads to the shorter path to the solution, ignoring other branches.