Finally, August 2018 is the release of "A Modern Introduction to Dynamical Systems"! A long and wonderful effort. Thank you, Oxford University Press....
So what is Mathematics??
"Mathematics is the music of reason....
To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion— not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it. Remove this from mathematics and you can have all the conferences you like; it won’t matter. Operate all you want, doctors: your patient is already dead."
"Mathematics is crystalized logic...."
"Mathematics is not about the numbers, really. It is more about the ideas behind those numbers. Mathematics is about ideas. It is about logical structure. Math can be defined as the study of the logical structure of complicated things. One can alter [a well-known definition] about architecture for use in mathematics here:
Mathematics is the thoughtful making of logical structure."
“Real mathematics must be justified as art if it can be justified at all.”
"The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.”