MacTutor
The great advances in science usually result from new tools rather than from new doctrines.
I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce.
For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created.
The reason why new concepts in any branch of science are hard to grasp is always the same; contemporary scientists try to picture the new concept in terms of ideas which existed before.
As we look out into the Universe, and identify the many accidents of physics and astronomy that have worked together to our benefit, it almost seems as if the Universe must have known that we were coming.