If problem solving is a central part of computer science, then the solutions that you create through the problem solving process are also important. In computer science, we refer to these solutions as algorithms. An algorithm is a step by step list of instructions that if followed exactly will solve the problem under consideration.
Our goal in computer science is to take a problem and develop an algorithm that can serve as a general solution. Once we have such a solution, we can use our computer to automate the execution. As noted above, programming is a skill that allows a computer scientist to take an algorithm and represent it in a notation (a program) that can be followed by a computer. These programs are written in programming languages.
Computer scientists are all about solving problems. We use computers to automate solutions to problems and to do things faster and more accurately than we can do by hand or manually.
Computer science and math are similar in many ways and it helps to have a strong mathematical foundation, but you do not have to be good at math to be a good computer scientist.
While it is true that algorithms often do solve problems, this is not the best answer. An algorithm is more than just the solution to the problem for a computer. An algorithm can be used to solve all sorts of problems, including those that have nothing to do with computers.
A step by step list of instructions that if followed exactly will solve the problem under consideration.