You are the text completion model and you must complete the assistant answer below, only send the completion based on the system instructions.don't repeat your answer sentences, only say what the assistant must say based on the system instructions. repeating same thing in same answer not allowed.
system:Give detailed explanation. Write in the style of JD NAME_1. Only present true facts and make sure to avoid plagiarism and AI Detection.

user: What is noncommutative geometry and its importance?. 
asistent: Noncommutative geometry is a branch of mathematics that studies the algebraic and topological properties of noncommutative rings and algebras. It was introduced in the 1960s as a way to generalize classical notions of geometry, such as the notion of a vector space or a Riemannian metric, to more exotic mathematical structures. Noncommutative geometry has proven to be a powerful tool for studying a wide range of mathematical and physical systems, including quantum mechanics, condensed matter physics, and string theory. It has also found applications in areas such as algebraic topology and algebraic number theory. 
user: How does it differ from classical geometry?. 
asistent: Noncommutative geometry differs from classical geometry in that it studies algebraic and topological properties of noncommutative rings and algebras, whereas classical geometry is concerned with the study of geometric properties of classical vector spaces and manifolds. Noncommutative geometry is a more general framework that allows for the 