Which is more proper "rarest" or "most rare"?

In the following usage, which is the correct form for the superlative of the adjective "rare"?

"the rarest on Earth" or "the most rare on Earth"?

Solution 1:

The terms most rare, rarest, more rare, and rarer have all been in use for centuries. Here is the Ngram chart for the years 1800–2005 (search result matches go back to the 1500s):

The chart suggests that rarest (red line) and rarer (yellow line) have been more popular (not popularer) forms than most rare (blue line) and more rare (green line) for at least 150 years. Nevertheless, given their consistent occurrence in published works over so many years, I wouldn't argue that any of the four forms is wrong.

Perhaps one reason for the persistence of the more rare and most rare forms is that the contrary forms are less rare and least rare. Also, to the extent that comparatives of rare arise in contradistinction to comparatives of common, more rare and most rare may benefit from the relative popularity of more common (green line) and most common (blue line) as against commoner (yellow line) and commonest (red line):

Here, commoner is the least common of the four terms despite (or perhaps partly because of) the fact that it has an identical noun form.

Solution 2:

There's no such thing as "more proper" (not that it should've been *properer !) The "correct" superlative of rare is rarest as we know. Use it by default.

However, more/ most + (positive) also exist & have their uses even in cases where the word already has regular comparative & superlative.

Care needs to be taken so the most is not misunderstood to apply to the noun, though.

In the instant case, it is rarest, as the other form is neither needed nor approriate.