When to use comma with then

Question

I learned English long time ago. The native speaker teacher told me that we always use comma after the word then. However, one proofreader told me that I must not write a comma after then. I am really confuse. Could some one please explain to me when it is correct to use comma with then?

For example,

Then, the next step is estimating the model parameters.

Set x as a first point, then, find the point y given x.

Answer 1

There are some circumstances that a comma should be used after then:

"It is good, then, that you wish to learn more."

But your examples aren't such circumstances. When using then to indicate a sequence of events, either in reporting events or giving instructions, it should not normally have a comma (though there are always exceptions, like there being a parenthetical clause immediately after it). When used in a similar sense to therefore, it may or may not want a comma after it - to the same standards as if you were using the word therefore.

Answer 2

Then can be used as an adverb, conjunction, noun, and an adjective. There is no definitive answer to your question because

• as it frequently introduces a dependent phrase, however, a comma would be placed at the end of the independent phrase or clause which precedes it.
• The use of a comma is more art than science. What’s ‘correct’ varies depending on the sense and composition of a sentence. In general, you should probably place a comma at every point where you would pause if you were reading the words you’re writing out loud. It’s virtually mandatory to use them to separate words or phrases in a list (They were red, white, smooth in texture, and triangular in shape). They’re also very helpful in setting-off clauses that:
• describe separate actions (went to the office; left for the airport)
• communicate descriptive information that’s important but without which the rest of the sentence would still make sense (around noon). Some people use commas a lot more than others. As a ‘rule of thumb’: if your sentence needs too many commas, it needs to be re-written and you probably have clauses in it that should be sentences on their own. Conjunctive adverbs are followed by a comma. Examples:
• I ate, then I started home.( adverb )
• Read the instructions well , then start answering. (conjunction )