Noncommutative geometry

Noncommutative geometry is a branch of mathematics that extends the traditional concept of geometry, where points and spaces can be described using numbers and functions. In noncommutative geometry, the fundamental objects are not necessarily commutative, meaning the order of operations matters. This theory is particularly useful in physics, especially in quantum mechanics, where particles and their interactions cannot be fully understood through classical geometrical frameworks. It allows researchers to explore complex structures and phenomena, providing insights into the nature of space, time, and the universe at a fundamental level.