Now I know the maths and logic to figure out that every boolean function can be expressed using only AND and NOT gates, which in turn can be expressed using only NAND gate and hence every boolean function can be expressed using only combination of NANDs. I know the math, I can easily work out the how.
But, I am looking for a more intuitive (not necessarily non-mathematical, maybe philosophical) reason as to why this has to be true (if there is such a reason at all). For some reason I think that it is not just a mathematical fact that NAND gate is universal, there must be a more "deeper" reason or something in property of NAND gates that has this, if I am able to explain myself.
So, is there really such a reason? Or is the universal nature of NANDs really just a mathematical artificact just discovered by us somehow?
EDIT : Fixed the basic gates. I messed up that.