... mathematics is the science of skillful operations with concepts and rules invented just for this purpose.

It's nice the know the computer understands the situation, but I would like to understand it too.

... mathematics is the science of skillful operations with concepts and rules invented just for this purpose.

The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it.

When the province of physical theory was extended to encompass microscopic phenomena through the creation of quantum mechanics, the concept of consciousness came to the fore again. It was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness.

The simplicities of natural laws arise through the complexities of the language we use for their expression.

The unreasonable efficiency of mathematics in science is a gift we neither understand nor deserve.