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This paper is written in honour of the centenary of Emmy Amalie Noether'sfamous article entitled Invariante Variationsprobleme. It firstly aims to givean exposition of what we believe to be the most significant and elegant issuesregarding her theorems, through the lens of classical mechanics. Despite thelimitation to this field, we try to illustrate the key ideas of her work in arather complete and pedagogical manner which, we hope, presents some originalaspects. The notion of symmetry coming naturally with the idea ofsimplification, the last part is devoted to the interplay between Noether pointsymmetries and the reduction procedure introduced by Edward John Routh in 1877.

On the wonderfulness of Noether's theorems, 100 years later, and Routh reduction