Yes, there are mathematicians who specialize in pure mathematics and may not have an extensive background or knowledge in physics. Pure mathematics is a branch of mathematics that focuses on abstract concepts and theoretical developments rather than direct applications to the physical world. Mathematicians working in pure mathematics often explore mathematical structures, develop new theories, prove theorems, and investigate mathematical principles for their own intrinsic value and beauty.
While mathematics and physics are closely related disciplines, with mathematics providing a fundamental language and toolset for describing and understanding the physical world, not all mathematicians need to have expertise in physics. Many mathematicians choose to focus solely on pure mathematics, dedicating their careers to advancing mathematical theory and solving abstract mathematical problems. Their research and contributions can be independent of specific applications in physics or any other field.
However, it's worth mentioning that some mathematicians may collaborate with physicists or work on problems that have physical applications, leading to interdisciplinary research and collaboration between the two fields. Additionally, mathematical concepts and techniques are often employed in various branches of physics to develop models, analyze data, and solve complex problems. So, while not all mathematicians may know physics, there can be fruitful interactions and cross-pollination between the two disciplines.