Do I have to be brilliant at mathematics to study science?
It depends on what field of science you are interested in, what degree you are targeting, and what you mean by brilliant. The physical sciences require an above average knowledge of calculus, differential equations, partial differential equations, and complex analysis for a bachelor’s degree. For a graduate degree in the physical sciences, a very good knowledge of these courses is necessary. In my estimation, one needn’t be brilliant (it sure wouldn’t hurt, though!), but one should be willing to work hard to learn as much mathematics as possible.
For experimental work, statistics is also required. For theoretical work, one must have excellent knowledge of the mathematics mentioned as well as knowledge of more advanced mathematics such as tensor analysis, topology, differential geometry, group theory, and special functions. All of these are not required for all theoretical physical sciences, but at least some of them will be required.
For the social sciences, knowledge of statistics is key. A good understanding of calculus and differential equations is helpful and becomes necessary for advanced degrees – some of the other mathematical subjects mentioned above will be required as well; which of them in particular will depend on the field of social science one chooses and one’s area of specialization in the field.
In summary, being dedicated to your goal and willing to work to learn mathematics is more important than being brilliant.
