I am currently finishing a project for a module I have in Mathematical Investigations. I have been looking at inequalities and ways to produce true inequalities in homogeneous symmetric form. I have been researching many theorems etc and have been spending quite some time on Muirheads Inequality of which I have found several different proofs. As I am trying to digest this proof and write a paper showing I understand it I would like to ask if you could recommend which proofs you have found to be the most elegant? or most interesting. Thanks in advance.