"So" versus "Therefore" and punctuation

Consider the two phrases:

"We know 2 times 3 equals 6. So 6 divided by 2 equals 3."

"We know 2 times 3 equals 6. Therefore, 6 divided by 2 equals 3."

The conventional wisdom I have heard says we should place a comma after "Therefore" but not after "So". This seems quite illogical to me because, as far as I can tell, the two sentences above are effectively the same and "Therefore" and "So" are serving grammatically identical purposes in the sentence. So why should "Therefore" be followed by a comma, but not "So"? It just seems inconsistent.

For context, I am a mathematician and frequently use "Therefore", "Hence", and "So" to connect lines of thought.

That conventional wisdom, wherever it came from, does broadly reflect the data in the Corpus of Contemporary American English, where searching for

. ADV ,

and

. ADV

yields 18,896 hits for Therefore and 114,120 for So with the comma following, with total hits for sentences starting with Therefore at 23,012 and So at 569,266; which indicates that Therefore is mostly used with a comma following (~82% of instances have the comma), while So is much more likely to be used without the comma than with (~20% of instances have the comma).

The the data is mostly comparable if we look for these with a cardinal number following:

• 2787 hits for . So CARDINAL NUMBER
• 572 hits for . So, CARDINAL NUMBER
• 33 hits for . Therefore CARDINAL NUMBER
• 112 hits for . Therefore, CARDINAL NUMBER

indicating that at the start of a sentence, So followed by a cardinal number has the comma in ~17% of instances, while Therefore in that same situation has the comma in ~77% of instances.

Many patterns in language are due to convention, punctuation perhaps more so than other elements, and do not adhere to what should be were we only to consider the logical side of things. There may not even be explicit rules here, as The Cambridge Grammar of the English Language comments on p1727 "many of the rules of punctuation that have been mastered by competent writers are part of tacit linguistic knowledge no less than the rules of spoken language are, and as such are never mentioned in usage manuals or style guides."