[raganwald]

Please forgive my simplistic questions, I do not have any higher education in physics and in my reading of pop science magazines I doubtless remain ignorant of important developments.

What is the proof that there are only three spatial dimensions?

You say "three spatial dimensions and time." Is time a dimension just like the spatial ones but we perceive it differently? Or is time something other than a dimension? And when was this proved or demonstrated?

[glymor]

You can't prove there aren't more dimensions. After all you could be hiding them in your garage with your invisible dragon or you could of rolled them up in a Calabi-Yau manifold.

Time is a unidirectional so it's considered to be a different kind of dimension than the spacial (bidirectional) dimensions.

[gchpaco]

.. Although depending on the particle theory you subscribe to, it may only be unidirectional to us (positrons being electrons moving backwards in time, etc.)