Yes, it is common for high-level theoretical physicists to have a significant amount of knowledge in mathematics. Mathematics is an essential tool for theoretical physicists as they develop and work with mathematical models to describe and understand the fundamental laws of nature. Theoretical physicists often use advanced mathematical techniques, such as calculus, differential equations, linear algebra, group theory, and topology, to formulate and solve physical theories.
Mathematics provides the language and framework through which theoretical physicists can express and manipulate physical concepts and relationships. It allows them to derive equations, make predictions, and analyze the behavior of physical systems. Theoretical physicists rely on mathematics to develop theoretical frameworks, such as quantum field theory, general relativity, or string theory, that describe the fundamental interactions and structure of the universe.
Moreover, mathematical rigor is crucial in theoretical physics to ensure the validity and consistency of the models and theories being developed. Theoretical physicists need to have a solid foundation in mathematics to understand and apply mathematical concepts and techniques effectively. They often engage with advanced mathematical literature, collaborate with mathematicians, and stay updated on the latest mathematical developments relevant to their work.
While the level of mathematical expertise may vary among individual physicists, a strong background in mathematics is generally considered essential for high-level theoretical physicists to make significant contributions to their field.