This approach breaks down when you go into higher math. You end up working with these abstract objects that have no visual representation. You may be able to find an equivalent object from geometry or graph theory, but it may be so complicated you could never draw it. Heck, even basic shapes like the Platonic solids are difficult to visualize, let alone draw, correctly.

I solved a problem recently requiring me to count the number of vertex colourings of an icosahedron, up to rotational symmetry. Trying to draw one of these things and visualize all of the possible rotations was basically impossible for me. I ended up loading Blender and playing around with one in 3D, using the coordinate planes to see all the axes of symmetry.

If I had been given a higher dimensional object like a tesseract then all bets would have been off. I would have had to find another approach entirely, likely algebraic.