What does the Greek proverb “nothing done with intelligence is done without speech” emphasize? And how to interpret it culturally?

I don’t have the answer, but this will help narrow it down:

This is not a proverb as such, but is a quotation from a speech by the orator Isocrates. Nicocles, section 9:

οὐδὲν τῶν φρονίμως πραττομένων εὑρήσομεν ἀλόγως γιγνόμενον

The emphasis out of context is not quite as obvious, because the same word logos is used to mean “the faculty of speech”, “a speech”, and “reason”. In fact the word alogōs normally means not “without speech”, but “irrationally”. But in context, Isocrates is extolling speech as the faculty that both distinguishes us from animals, and that lets us pursue social interaction (including oratory). And ultimately, he is saying that  people who speak for a living (like orators) are pursuing a noble profession:

Nicocles or the Cyprians, 6-9:

But, because there has been implanted in us the power to persuade each other and to make clear to each other whatever we desire, not only have we escaped the life of wild beasts, but we have come together and founded cities and made laws and invented arts; and, generally speaking, there is no institution devised by man which the power of speech has not helped us to establish

For this it is which has laid down laws concerning things just and unjust, and things base and honorable; and if it were not for these ordinances we should not be able to live with one another. It is by this also that we confute the bad and extol the good. Through this we educate the ignorant and appraise the wise; for the power to speak well is taken as the surest index of a sound understanding, and discourse which is true and lawful and just is the outward image of a good and faithful soul.

With this faculty we both contend against others on matters which are open to dispute and seek light for ourselves on things which are unknown; for the same arguments which we use in persuading others when we speak in public, we employ also when we deliberate in our own thoughts; and, while we call eloquent those who are able to speak before a crowd, we regard as sage those who most skilfully debate their problems in their own minds.

And, if there is need to speak in brief summary of this power, we shall find that none of the things which are done with intelligence take place without the help of speech, but that in all our actions as well as in all our thoughts speech is our guide, and is most employed by those who have the most wisdom. Therefore, those who dare to speak with disrespect of educators and teachers of philosophy deserve our opprobrium no less than those who profane the sanctuaries of the gods.

How can I learn to individuate ancient Greek verbs?

No substitute for rote, I’m afraid. But there are patterns and regularities, and you’ll need to make them your friend:

  • If anything looks like a preverb (prepositional prefix), strip it off. It’s usually a safe bet that it is in fact a preverb.
  • The endings do have patterns (the final vowels/consonants, the thematic vowels, the verb stem endings). The more comprehensive grammars present the patterns as part of their historical approach, but they aren’t just of historical interest: they help you learn the inflections. (And native speakers use these patterns subconsciously.)
  • The thematic vowels in particular are your friend, because they help you get to the present form: whether it’s -αω -εω -οω , or  just -ω.
  • If it’s athematic, well, that’s a matter of rote memorisation. Good thing there aren’t that many of them, and they tend to be common. Which is after all the story with irregular verbs in language.
  • Be on the lookout for second aorists and liquid verbs, they are an added complication
  • Think in terms of proto-Greek: it will help the patterns become more obvious. So don’t just learn the tables, but where the inflections came from. Uncontracted verbs, after all, are mostly proto-Greek, and certainly not Attic. The tendency  to drop intervocalic /s/, for example will make 2nd person passives look much more plausible.
  • Dialect is indeed harder. It took me three hours to work out what φαῖο means (The tale of φαῖο), and it didn’t help that the form, being dialectal and in a new edition, was not in the standard grammars.
  • Byzantine Greek is even worse, because there is a *lot* of fantasy morphology. Much like the Irish monks, Byzantine writers often just made tenses up.
  • In the olden days, there were dictionaries of verbs. Lexikon ueber die formen der griechischen verba, Traut, Georg  is one instance; and Greek verbs, irregular and defective, Veitch, William is another. Veitch is comprehensive; the advantage of Traut is that you can actually look up individual inflected verbs in the canonical corpus. (Just remember to strip off the preverbs.)
  • There are morphological analysers of Greek, which are hyperlinked in to some online texts. Including Perseus, and the TLG (both the subscription full version, and the free subset). The TLG’s morphological analyser is an ongoing project that I’m working on, and it provides the possible analyses of word forms in texts.