Nezištně pomáhá světoví velikáni.

The main verb is "pomáhá" 3sg. present tense form of pomáhat 'to help.'

The subject is 3sg., supposedly about Cimrman; since světoví velikáni is a nom. plural form, this cannot be the subject, but the object of pomáhat.

Since "pomáhat" takes the dative case as its object, světoví velikáni (sg. světový velikán) should be in the dative case.