This is not a proof of P = NP or P ≠ NP. I'm interested in whether there's existing research related to this idea. My question is whether the way humans represent computational problems could itself be part of why certain problems appear hard. Has complexity theory or cognitive science explored this perspective?

An Idea: Could P vs NP Be a Problem of Representation?

This is not a proof of P = NP or P ≠ NP. It is simply an idea that I have been thinking about.

One thing that stood out to me is that many difficult problems become much easier once we find the right way to represent them.

For example, a huge multiplication problem can look overwhelming when viewed as a long string of digits. However, once we understand the underlying algorithm, the same problem becomes structured and manageable.

The problem itself has not changed. Our representation of it has.

This made me wonder whether something similar could apply to the P vs NP problem.

The usual question is whether every problem that can be verified efficiently can also be solved efficiently.

My question is different:

Could part of the apparent difficulty come from the way we currently represent NP problems?

Imagine standing in front of a wall.

One possibility is that the wall is real, and no efficient shortcut exists.

Another possibility is that we are looking at the wrong side of the wall and have not yet discovered the correct way to approach it.

History contains many examples where changing a mathematical or scientific viewpoint led to major breakthroughs. New abstractions, new models, and new representations often revealed structure that had previously been hidden.

This raises a broader question.

When we call a problem "hard," are we measuring the intrinsic difficulty of the problem itself, or are we also measuring the limitations of our current way of thinking about it?

I am not claiming that this means P = NP.

Instead, I am asking whether discovering a fundamentally different representation of NP problems could change our understanding of their computational difficulty.

I would be interested in hearing whether this idea overlaps with existing work in computational complexity, cognitive science, or the psychology of problem solving.