It is not accurate to compare Sir Isaac Newton's approach to physics with that of Albert Einstein and Stephen Hawking based solely on their mathematical or non-mathematical approaches. Each of these scientists made significant contributions to the field of physics in their respective eras, and their approaches were shaped by the knowledge and tools available to them at the time.
Sir Isaac Newton's work laid the foundation for classical physics and his laws of motion and universal gravitation are still widely applicable in many everyday situations. Newton used a combination of empirical observations, mathematical formulations, and deductive reasoning to develop his theories. His mathematical approach was highly successful in describing the motion of objects on Earth and the motions of celestial bodies, making him one of the most influential scientists in history.
Albert Einstein and Stephen Hawking, on the other hand, lived in a later era when scientific knowledge had advanced significantly. Einstein's theory of relativity and Hawking's work on black holes and cosmology required sophisticated mathematical tools to formulate and understand. Their approaches were heavily mathematical because the phenomena they were investigating demanded it.
The mathematical approach adopted by Einstein and Hawking allowed them to delve into complex and abstract concepts, providing a deeper understanding of the fundamental laws of the universe. Their theories have been extensively tested and have stood up to scrutiny, making them crucial components of modern physics.
It is important to note that both approaches, empirical and mathematical, have their strengths and limitations. While Newton's classical physics is excellent for many practical situations, it fails to accurately describe phenomena at high speeds or in extreme gravitational fields. Einstein's and Hawking's mathematical approaches expanded our understanding of the universe in ways that classical physics couldn't.
In conclusion, it is not a matter of one approach being better than the other. The scientific progress made by each of these scientists was based on the knowledge and tools available in their time, and their contributions, whether empirical or mathematical, have significantly advanced our understanding of the physical world.