The politicians are interesting people is not accepted? But it has "a" in front of politikusok!
But that is Hungarian, while the other sentence is in English. Different language, different rules. :) Nevertheless, the English sentence should be accepted both with and without a definite article.
Persons is more specific than people in a way which doesn't work here. Teachers are nice people! My teachers are nice persons.
Also, you have to be careful how you say persons, because even if you use it correctly, you might sound like a lawyer.
Btw, "person" is "személy" in Hungarian.
For example, a "four person tent" is "négyszemélyes sátor".
That's interesting. Eye-szem, maybe "that with eyes"? Szemmély would be deep eye :-))
:) No idea if it has anything to do with the eye.
But "szem" also carries the meaning of "one piece", "single", probably when indicating a very small amount:
"Nem akarom, hogy az egy szem fiam politikus legyen." - "I do not want my only son to be a politician."
"Ma csak két szem almát ettem" - "I ate only two apples today."
Maybe "személy" comes from this meaning of "szem". An individual. I am not sure.
The "-ély" in "személy" is one way of creating new words in Hungarian. You might notice it in several common words.
Variations on "személy":
"személyes" - personal
"személyzet" - personnel
"személyszállító" - (a vehicle) carrying people, as opposed to cargo
"személytelen" - impersonal
"személyre szabott" - personalized
"személyi igazolvány" - personal ID
"személyiség" - personality
"személyvonat" - regular train (as opposed to an express train)
"személyi kölcsön" - personal loan
"természetes személy" - natural person (legal)
"jogi személy" - legal person (legal)
"egyesszám első személy" - singular first person - first person singular