Mathematics does not have a clearly defined, universally accepted definition. However it is safe to say that anything that studies the interaction between quantities, variables, structure, and change, is mathematics.
Mathematics is not a tangible thing, but actually an abstract concept. There are many ways of expressing mathematics; the one you are probably most familiar with is the base ten Arabic format that permeates science right now.
Other civilizations have made other ways of expressing mathematics, and if we ever run into alien intelligence, it is likely that they will use a different system than we do.
Mathematics is the language with which God wrote the Universe. – Galileo Galilei
To summarize, I would use the words of Jeans, who said that ‘the Great Architect seems to be a mathematician.’ To those who do not know mathematics it is quiet difficult to get across a real feeling as to the beauty, the deepest beauty, of nature.
C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once.
It is too bad that it has to be mathematics, and that mathematics is hard for some people. It is reputed – I do not know if it is true – that when one of the kings was trying to learn geometry from Euclid he complained that it was difficult. And Euclid said, ‘There is no royal road to geometry.’ And there is no royal road.
Physicists cannot make a conversion to any other language. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. She offers her information only in one form; we are not so unhumble as to demand that she change before we pay any attention.
All the intellectual arguments that you can make will not communicate to deaf ears what the experience of music really is. In the same way all the intellectual arguments in the world will not convey an understanding of nature to those of ‘the other culture’.
Philosophers may try to teach you by telling you qualitatively about nature. I am trying to describe her. But it is not getting across because it is impossible. Perhaps it is because their horizons are limited in the way that some people are able to imagine that the center of the universe is man …