Is the following sentence grammatically correct?
I speak of him, whom is one of the best people I've met.
I think that sentence to be grammatically incorrect. I believe it to be as such because you could replace "whom" in that sentence with "and he"; the word "he" in that situation would indicate that you would replace "he" with "who", not "whom". This is why I believe I know the answer to be that it would be "who", not "whom". However, I get confused because of the fact that you could also change the sentence by placing "of" before "whom". In that case, to my knowledge, it would be grammatically correct.
Best Answer
It's wrong but may be about to become correct. There is really no definite answer because this is a point where the English language is changing right now. Currently there are four basic competing styles for choosing between who and whom.
Who is the subject case, whom is the object case. The case of a relative pronoun is determined by its function in the relative clause.
The word whom is obsolete. It has been replaced by who in all contexts.
The word whom is nothing more than a substitute for who that can be used wherever who can be used, to indicate formality.
Who is the subject case, whom is the object case. The case of a relative pronoun is determined by the function of the referent in the main clause.
Style 1 is the oldest and in some sense the most 'correct' rule. It comes naturally to older people, to people who have read a lot of classical literature, and to native speakers of other languages that make similar case distinctions. (E.g. in German, who is wer and whom is wen or wem depending on which object case it is - accusative or dative.)
Style 2 is a logical and straightforward consequence of natural language change. After already merging dative and accusative into a common object case, English has almost completely lost the distinction between subject case and object case. The role that was once played by cases has mostly been taken over by prepositions - especially to and of. As the who/whom distinction is no longer needed, the m in whom has been fading for centuries. Nowadays many younger speakers no longer make it. This is so common and so logical that by now it is generally considered just as correct as style 1.
Style 3 arises naturally in an environment in which speakers who grew up with style 2 are confronted with the word whom. Normally this happens only in formal text and speech, and for many there is not enough input to understand that who cannot always be replaced by whom. (This is similar to the extremely jarring abuse of thou and thee often encountered in computer games, where these obsolete singular pronouns tend to be used as if they were full synonyms for you.)
Style 4 arises in a way similar to style 3. The speaker understands that the who/whom distinction is the same as the he/him distinction, but since who[m] is the only relative pronoun still allowing this distinction, for some speakers there is not enough correct input (and some misleading input from followers of styles 2 and 3) to form the correct hypothesis on which case wins if the cases in the main clause and in the relative clause don't agree. So they make the wrong choice and stick to it.
Styles 3 and 4 are not generally considered correct, but they seem to be getting more and more popular and so I am somewhat reluctant to call them completely wrong. (Though I do hate them. I sympathise with James Thurber, who wrote a great little piece ridiculing them. Unfortunately, many younger people probably can't even understand its humour fully any more.)
The sentence in question is correct according to styles 3 (any sentence involving him who[m] is clearly meant to be formal) and 4 (the referent him in the main clause is clearly in the object case) but not according to style 1 (who is the subject of the relative clause) or 2.