If 'telepathy' means intentional communication from one brain to another of complex messages without means of speech, then reading and telegraphy constitute valid definitions of telepathy.

If one goes beyond that and requires the communication to be some sort of 'radio' communication between brains without the requirements of energy or the limitations of time or distance, I think it is possible to prove that such communications do not exist. One can set up a scientific experiment with controls and proceed as with any other experiment. I'm pretty sure there are no documented scientific experiments that have been recognized by respectable scientific institutions.

If one is convinced by personal experience of having intuitive knowledge or hunches, that is human. I've experienced them and witnessed others experience them. But it ain't science and it ain't telepathy unless you personally define them as such, and then how far can you take it? Can you convince others, repeat the performance, investigate the phenomena in a rational matter?

How many times are the words "I'm NOT a mind reader" uttered compared to the words "I AM a mind reader."?

I'm tempted to utter the vainglorious words: "Case Closed" but I know damn well it ain't.