"I know you!"
These words are used differently. You cannot use 知道 here.
知道 is to know a piece of fact (not necessarily a simple one)
认识 is to know about sb/sth from several aspects, or to a certain depth.
He knows about archaeology.
He knows how Egyptians built pyramids.
认识 also means to learn but 知道 doesn't.
Let's learn how Egyptians built pyramids.
"他认识考古学"is not a correct sentence. "He knows about archaeology”could be 他了解考古学 “我知道你”can be i ve heard about you
知道 means "to know, to be aware of." So it can't be used in this case.
认识 may also mean "to know, understand, etc." But it also means "to meet (person)." So it should be used in this case.
知道 refers more to 'information based' knowledge, like knowing a phone number or a fact etc.
Also, I found an answer.
Both 4th and 2d tones are used for this, here is an explanation [it is russian]: http://www.zhonga.ru/chinese-russian/%E8%AF%86/a7h1b
Doesn't 认识 also mean 'meet'. As in the earlier example of "nice to meet you?"
认识 does not mean Meet. That sentence as I recall was It is nice to meet you (or It is nice meeting you) vs. 很高兴认识你 , for which Duo preferred the approach of using situational conversation instead of the usual word-by-word literal translation. The words used were not equivalents.