If you genuinely want the strongest statement of it, read The Emperor's New Mind followed by Shadows of the Mind, both by Roger Penrose.
These books often get shallowly dismissed in terms that imply he made some elementary error in his reasoning, but that's not the case. The dispute is more about the assumptions on which his argument rests, which go beyond mathematical axioms and include statements about the nature of human perception of mathematical truth. That makes it a philosophical debate more than a mathematical one.
Personally, I strongly agree with the non-mathematical assumptions he makes, and am therefore persuaded by his argument. It leads to a very different way of thinking about many aspects of maths, physics and computing than the one I acquired by default from my schooling. It's a perspective that I've become increasingly convinced by over the 30+
years since I first read his books, and one that I think acquires greater urgency as computing becomes an ever larger part of our lives.