I am not really surprised that there are patterns and connections between seemingly unrelated concepts. Why? Because I think they are way less unrelated than it

I am not really surprised that there are patterns and connections between seemingly unrelated concepts. Why? Because I think they are way less unrelated than it may seem. After all everything is build on top of a pretty small number of axioms. Every result in number theory - proven or yet unproven - is essentially a consequence of the Peano axioms and the definition of the operations on those numbers. The Riemann hypothesis is a statement about prime numbers, which numbers are prime is defined by the Peano axioms and the definition of multiplication. The real numbers are in some sense build on top of the natural numbers by going through the rational numbers. And you can build the natural numbers on top of set theory. So in essence I think we are just exploring the structure of one and the same object - or maybe a few objects - and every branch of mathematics does this by making a few more assumptions and therefore looking only on a part of the whole.