Learn Finnish: Tämä ei ole maailman kolmanneksi suurin vesiputous. - This is not the world's third largest waterfall.

This is the standard Finnish formula for ranking superlatives, like 'second best' or 'third largest'. You put the ordinal number in the translative case (-ksi) and follow it with the superlative adjective. Here, the base word kolmas changes to its stem kolmanne- before adding the suffix, becoming kolmanneksi.

Why doesn't the adjective suurin match the translative case of kolmanneksi?

In this specific ranking structure, the ordinal number acts as a fixed modifier for the adjective. The translative ending (-ksi) is locked onto the number, so the two words don't need to agree in case. The adjective (suurin) and the noun (vesiputous) simply take their case from their grammatical role in the sentence, which is the nominative here.

Since this is a negative sentence (ei ole), shouldn't vesiputous be in the partitive case?

Not in this situation. With the verb olla (to be), a singular, countable noun acting as a subject complement (identifying what the thing is) typically stays in the nominative case, even if the sentence is negative. You would only use the partitive here if it were an uncountable noun, like saying 'This is not water' (Tämä ei ole vettä).

Instead of the genitive maailman, could I use the inessive case and say maailmassa ('in the world')?