What are the major branches of mathematics?

Mathematics is the science of structure, order, and relation, evolving from basic practices like counting and measuring into a field defined by logical reasoning, abstraction, and quantitative calculation.1

The substantive branches of mathematics include:

• Arithmetic: The study of numbers, their properties, and basic operations.12
• Algebra: The use of symbols to represent numbers and quantities in equations and functions.13
• Geometry: The study of shapes, sizes, and the properties of space.1
• Analysis: A field rooted in the study of limits, continuity, and change, often interacting with geometry and topology.14
• Number Theory: The study of the properties of integers and numerical relationships.12
• Probability Theory and Statistics: The study of uncertainty, data analysis, and random phenomena.1
• Combinatorics: The study of counting, arrangement, and configuration.1
• Set Theory: The study of collections of objects, which serves as a foundational language for much of modern mathematics.1
• Game Theory, Optimization, Numerical Analysis, and Trigonometry: Specialized fields addressing strategic decision-making, efficiency, computational methods, and the relationships between triangle sides and angles.1