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I wonder if there is any difference between:

I have known about calculus.

I'm familiar with calculus.

To me, I assume those are equivalent, but I think there is something different between them that is hard to tell.

To illustrate this problem, I will give an example. Suppose, I had been learning calculus for 2 years when I went to college. Someone in the present time asks me about calculus but I tell them that I didn't finish studying (I hadn't finished the whole lesson, but currently I'm not studying calculus anymore).

In the example above when I want to tell I've ever learnt calculus, which one should I use between (have known) and (familiar with)? I hope you could elaborate your answer. Thanks!

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    "I have known about..." doesn't really sound natural in any context, because it's about experiences in the past leading up to the present. If you said that, I would say, "Huh? You have known about it, but you don't now?"
    – stangdon
    May 6, 2022 at 11:27
  • @stangdon so, in this case familiar with is preferable? Or are there other better phrases?
    – user516076
    May 6, 2022 at 11:31

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I agree with @stangdon that "I have known about" doesn't sound natural in the present context, but not that it doesn't sound natural in any context. Here is an example:

I have known about their true intentions for quite a long time.

Judging by your explanation, calculus is a subject that you did not "finish", which implies that you do not know it very well. If that is the case, then you need to modify the word "familiar" (which means know well) with something like "somewhat":

I am somewhat familiar with...

You can also use the verb "know" in the present tense:

I know (a little, quite a bit) about calculus.
I know (a little, quite a bit) of calculus.

And of course the obvious choices are the verbs "study" or "learn":

I studied/learnt (some) calculus at school.

Or:

I have studied (some) calculus.

This last one focuses on the present result of your past actions. It denotes that you have a background in the subject and are (quite/somewhat) familiar with it.

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    You are correct; I was too general in my comment. I wouldn't say "I have known about <general field of knowledge>", although "have known about <a specific fact>" sounds good.
    – stangdon
    May 6, 2022 at 15:19

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