Comment 4 by AtheistEgbert : I think science needs to be explanatory as well as a body of knowledge. If someone can't explain to me what's going on, but hides behind the esoteric claims of mathematical certainty, then I find that somewhat problematic.

The problem is, that at some level of understanding you just need to do the maths. You won't be able to understand quantum physics without that. And it is possible to logically understand quantum physics. The far too often recycled Feynman quote is better read as a statement that even for us experts - I'm a theoretical physicist - it's very hard or even impossible to get a good intuition for Quantum Physics. The laws are just too counterintuitive.

If you are serious about wanting to understand quantum Physics, I advice Vol. III of the Feynman Lectures on Physics. It requires less math then any other real course in quantum physics and is written by the greatest science teacher of the 20th century. In fact, all three Volumes of this masterpiece will leave you with a pretty good grasp of the fundamental theories of classical and modern Physics, excluding the general theory of relativity. But you are going to need at least some university-level mathematics.

I can understand your frustration and I really sympathise with your desire to understand it all for yourself. But for this you will have to do the maths. Sadly, without it all you can do is trust the authorities. It's similar to what I said in another thread about climatology. It can be understood, but it's a little more complicated then Darwin's theory of evolution, so you are going to have to work long and hard on it, or - like many others - be contend with the fact that it works.