I wanted to ask you knowledgeable people about an idea that has been going around in my head for years. I'm nowhere near a compression expert, so please don't jump on me if this is ridiculous for reasons I can't grasp.

My math teacher once told me that it is assumed that the number Pi would contain any kind of combinations of numbers thinkable. So, wouldn't it be possible to transform Pi (or any other endless mathematical constant or combination of a multitude of them) into a binary format and then trying to find matches between the file that needs to be compressed? All that would need to be stored in an archive would be coordinates of the corresponding digits to the chunks that match, not the data itself. Restoring the file would be computationally intense on a massive scale, but shouldn't it be possible to even "extract" huge files from tiny archives this way? Has someone ever thought about this?