This theorem is extremely important in physics and yet so little known! thanks for sharing it. Here is an article/answer I really liked, explaining why this theorem is so significant: https://physics.stackexchange.com/questions/21572/whats-the-importance-of-noethers-theorem-in-physics
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Ah.. the brilliant insight that symmetries in mathematics might correspond to conserved quantities in the physical world .. leading to the formulation of the Special theory of Relativity. Still remember the first time I read and understood this, felt a bit like an epiphany :D