Mathematical algorithms are step-by-step procedures or formulas used to solve problems or perform calculations. They provide a systematic way to approach tasks, such as sorting numbers, finding the greatest common divisor, or optimizing routes. Algorithms can be expressed in various forms, including natural language, pseudocode, or programming languages. These algorithms are fundamental in fields like computer science, engineering, and data analysis. They help in automating processes and making decisions based on data. Notable examples include the Euclidean algorithm for finding the greatest common divisor and Dijkstra's algorithm for finding the shortest path in a graph.