They seem essential for a proper foundation, but in my years at the municipality, I saw many capable men keep entire systems running with practical 'jugaad', not formal proofs. Their 'chhata' of common sense often covered more ground than a rigid syllabus. My own son speaks of these subjects with great respect from Bangalore, yet our library's ancient computer, which lets children see the wider world, was repaired by a boy who never went to college. Sometimes, the heart of the work lies outside the theory.
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