Ahem. Nobody has ever “seen” a black hole. A number of notable cosmologists doubt their existence. Their “presence” is always inferred from the observed motions of matter adjacent to their supposed positions. A number of other ideas have been put forward to account for these motions.
Just another example of how Big Science now legislates hypotheses and theories into “Laws” when nobody’s looking.
You are half right. It is true, nobody has seen a black hole. The behavior of objects around it tell us it's mass and therefore gravity. All else is down to math. If you are doubting the math then I urge you to stop balancing your checkbook. Yes, the laws of math that say 2+2=4 are the same as the laws of math that describe high energy physics and they are provable.