Do one way function exist?

I was recently going through the Wiki page List of unsolved Problems in Computer Science.

There was a problem which I do not understand

Do one-way functions exist ? [Is public-key cryptography possible ?]

A one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input.

A one-way function that comes to mind is a Cryptographic hash function which is used to create message digests. Where size of the message digest is relatively small as compared to the size of the message and hence it becomes very hard to reconstruct message from the message digest.

So, why does the above problem say that these functions do not exist?

In cryptography there is a very exact definition of one-way functions, which implies, among else, that P$\neq$NP. While there are several specific functions which are conjectured to satisfy the definition, no one knows how to prove this. We don't even know how to prove that one-way functions exist assuming P$\neq$NP.