It takes similar logical skills like:
- Not knowing end result/solution of an equation
- Performing multiple operations to solve different parts of an equation
- Crafting an equation to match the observation (similar to writing a logical program to achieve a certain end result)
- Dealing with constants that never change
When I'm programming, I often start tackling a complicated function (I do ML and numerics) without knowing the logic 100%. I just let my instinct guide me and I stumble little by little onto the solution with the help of the compiler. You can do the same process with math, but the mental strain required is orders of magnitudes more because you need to actually do the math yourself.
I would however expect similar fundamental brain functions to be at play. For debugging and instinct driven tasks, I would co-relate that with hit-and-trial methods for solving equations or validating equation formulations.