The enormous usefulness of mathematics borders on the mysterious - the physical world really is completely mathematical.

 The notion that the world is a mathematical structure alters the way we view many core notions in physics. 

Max Tegmark argues (brlliant as he is) 

'...we will now discuss numerous such examples, ranging from standard topics 

like symmetries, 

irreducible representations, 

units,

 free parameters and initial conditions to broader issues like parallel universes, 

Godel incompleteness and the idea of our reality being a computer simulation.

Hmm, I suddenly feel very tired and with this intellectual feast ahead of me ....I wonder why?