Whatever your preferred term, I’m unaware of any verifiable proof. Demonstrations have been unrepeatable, or hoaxes, or not statistically significant. (Does anyone out there have data to the contrary?)So, unproven. How about plausible? Nope, not that either. Because ...
Signals are weak. Brains do generate electrical energy -- reading electrical fields is how EEGs work. But the signals are very weak (neurons signal electrochemically across synapses). Hence, each EEG pickup only senses the aggregated signal from many neurons. EEG pickups are glued to your scalp to make dependable contact. It’s hard to see how one mind can sense the electrical emissions of a remote mind.
The environment is noisy. Your brain has about 100 billion neurons, many with thousands of synapses. They don’t all fire at once – but at any given time, lots are firing. Suppose remote reception were possible. How would a telepath pluck one person’s higher-level thoughts (versus, for example, real-time raw sensory input) from the din? And from the interference the other several billion of us would generate?
Wouldn't evolution favor telepaths? Telepathy seems valuable. Spot your enemies at a distance. Sense deceit. Avoid misunderstandings. Know exactly how to woo that potential mate (so mysterious to those who can’t read minds ;-) ). If humans ever could read minds, why didn’t the trait become common? So evolution argues against telepathy, too.
Natural telepathy among humans? In my mind, an SF trope. But technologically assisted telepathy? That’s another story (or at least another post). Stay tuned.