Mathematical reasoning is the process of using logical thinking to solve problems and make conclusions based on mathematical concepts. It involves understanding relationships between numbers, shapes, and patterns, allowing individuals to analyze situations and derive solutions systematically. This reasoning can be categorized into two main types: deductive reasoning, which starts with general principles and applies them to specific cases, and inductive reasoning, which involves observing specific instances to form general conclusions. Both types are essential for developing strong problem-solving skills in mathematics and other related fields.