It seems to me that "so" is seldom used in math proofs. Instead, "hence" and "therefore" are used very often, even repeatedly appearing in several sentences in a row. So I wonder if my feeling is correct? What do you think is proper use of these words or similar ones in math proofs? Thanks!
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The computer scientist Donald Knuth, who is essentially a mathematician, has written quite a lot about how to write mathematics in a clear and intelligible style. In his book, "Mathematical Writing", co-authored with Tracy Larrabee and Paul Roberts, Knuth uses the word "so" quite a lot. In 118 pages of text, "So ..." (i.e., as the opening word of a sentence) appears 26 times. I think that one of his best pieces of advice is, "Don't get hung up on one or two styles of sentences." At other places in the book he seems to press the idea that good mathematical writing has both consistency (so that the same concept does not appear, ambiguously, as if it were some other concept) and variety of expression.
Of course, none of this specifically addresses your comment about the appearance of the word "so" in proofs, but it does give an idea of the way a person who is a clear expositor of mathematics uses it.
There is a school of thought that a sentence may not begin with So. Therefore, it is seldom so in formal writing.
Hence and therefore may be considered synonyms, or at least interchangeable.
I suspect that hence is preferred where the inference derives from the immediately preceding statement, though not necessarily.
Therefore shows a broader scope and appears after a long descriptive 'method' leading to the proof.