Hi, can you suggest me an investigatory project that not yet proven?

Ow... I wonder why you want to know these? Are you trying to do a research work on an experiment, or are you trying to prove it?

You can check this site, of try to Google about them. I'm sure you'll get nice things to learn.

One of the 'hot ones' is about quantum physics and the subatomic particles. Scientists are smashing high speed particles in the hope of discovering new particles in the Large Hadron Collider.