Mathematics and Its Laws

"The laws of mathematics are not merely human inventions or creations. They simply ‘are’ they exist quite independently of the human intellect. The most that any man with a keen intellect can do is to find out that they are there and to take cognizance of them." (M C Escher)

“In mathematics there is no understanding. In mathematics there are only necessities, laws of existence, invariant relationships. Thus any mathematico-mechanistic outlook must, in the last analysis, waive all understanding. For, we only understand when we know the motives; where there are no motives, all understanding ceases.” (Friedrich Nietzsche)

“People think of axioms as laws you have to follow, or true things you have to assume, and I think neither of these perspectives is correct. It's more accurate to think of axioms as a way to agree that we're talking about the same thing." (Qiaochu Yuan)

“All mathematical laws which we find in Nature are always suspect to me, in spite of their beauty. They give me no pleasure. They are merely auxiliaries. At close range it is all not true." (Georg C Lichtenberg)

"All the mathematical sciences are founded on the relations between physical laws and laws of numbers.” (James C Maxwell)

“Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework.” (Melvin Schwartz, “Principles of Electrodynamics”, 1972)

“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." (Eugene Wigner)

"Mathematics is a way of expressing natural laws, it is the easiest and best way to describe a general law or the flow of a phenomenon, it is the most perfect language in which one can narrate a natural phenomenon." (Gheorghe Ţiţeica)