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trees and plants
Hello there.Questions I have: what is the value of group theory?I am not trying to say that it is not important I want to know what made mathematicians study these objects and we still study them today.I know there are very interesting for me at least examples of groups like the Lie group but some mathematicians study I think generally groups or some types of them.What are some important or interesting applications of them?I know that R equipped with the operation of addition is an abelian group also other sets of numbers are also groups.Other groups I have read I think have to do with similarity of triangles or with squares and perhaps geometrical applications.Could you provide other applications of groups in mathematics perhaps in fields like riemannian geometry, the differential wave equation, other differential equations like the heat equation, the Schrodinger equation, number theoretical topics like the Riemann zeta function?Thank you.