Is the article the needed in the following sentence and why?
Want to follow [the] evolution of the project?
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Yes, the is required to make the sentence grammatical because a singular common count noun like evolution requires the definite article in this context, which describes a particular process of evolution rather than a general process. In sentences like "Evolution occurs in mammoth leaps as well as incrementally", it's the name of a theory or a word denoting a general process and seems to function as a collective noun or a proper noun rather than a common count noun, e.g., Water flows downhill and The water flows downhill are both grammatically correct, but the first is a general statement and the second is about some specific water.
Normally the article would be required because evolution is a particular kind of evolution: of the project. In grammatical terms, the use of the here is cataphoric. That is, in the words of 'The Longman Student Grammar of Spoken and Written English', 'definite reference is established by something following later in the text, especially some modifier of the noun'.