Tevye is our narrator. He's funny ("We have here a new philosopher, fresh from the oven!" [6.38]); he's talkative ("but now I think I've gone on too long" [2.116]); and he's a small-time dairy delivery man from a Russian shtetl with big problems: his precarious business, his daughters' dim marriage prospects, and the fact that God really seems to have it in for him.
The way this series of short stories is set up, Tevye's personal problems tend to be pretty much directly related to the larger problems of Jews living in Russia at the turn of the 20th century. The main theme for both? In the words of that one song everyone knows from Fiddler on the Roof, "Tradition!"
Okay, to be clearer about it: should we hang on to tradition, even when it doesn't seem to fit changing times? Should we keep obeying the oppressive powers that be, or should we overthrow them and start fresh? Should we stick to our cassette tapes, or buy one of these new-fangled iGadgets that everyone is so worked up about?
For Tevye, these questions are local and familial. Is it a big deal that the system of arranged marriage that seemed good enough for Tevye and Golde is considered way lame by his daughters? Should Tevye keep up the old-timey idea that girls don't need to be literate, or is it a good thing that he's being all progressive and getting them a tutor?
The questions are bigger for the country as a whole, but they are also about a shift in authority. Should everyone keep accepting the monarchy's power and just stop with the revolutionary talk already? Or should everyone get behind the socialist and democratic movements who say that the tsar's promise of universal suffrage is just a last ditch effort to hang on to power?
The stories don't really offer answers, but they do highlight the fact that such drastic changes usually come with violence and a lot of misery. But you know, in a funny way!
Before we talk too much longer about Tevye's ideas about Jews and their sense of belonging, it would probably help to mention Sholem Aleichem didn't just believe in, but was actually actively involved in lobbying for the creation of a Jewish state (though he wouldn't live to see it happen, since he died in 1916, 31 years too early).
All right, but so what? Well, the whole saga of Tevye's daughters' marriages is basically a long allegory for whether it's possible for Jews to become an acceptably assimilated part of the society where they are living. And, if we know right away that Sholem Aleichem thinks the answer is "No way," then the depressing downward spiral of the stories makes a lot more sense.
It's not hard to see the pattern. Basically, any time one of the Jewish characters tries to make it in the Gentile world, she's either punished by the non-Jews who never really accept them or has to give up so much of her identity that assimilation just ends up meaning eradication. Check out Tevye trying to verbalize this when talking about why Chava marrying a Gentile was the ultimate betrayal:
Where was her pity when I was stretched out like a dog before the priest, cursed be his name, kissed his feet, while she was in the next room […]? And where was her pity when her mother, may she rest in peace, was lying right here on the ground covered in black? […] And the heartache that gnaws at me to this very day when I remember what she did to me and for whom she forsook us? (9.66)
By marrying into a Christian family, Tevye is saying, Chava gave up the things that made her a part of a family. She stopped being a daughter when she failed him in not leaving the priest's house, and how she failed her mom by not being there for her death.
But even more than that, Tevye is personally wounded by the fact that Chava married into the same oppressive culture that's trying to ethnically cleanse the Jews out of Russia, just like before.
What we learn from this is that Tevye is a man who loves his culture and his tradition. He might be willing to forsake some tradition, like having matchmakers come up with his daughters' marriages, but he's not about to discard the really important parts of it. In that way, you could say that Tevye stands for the part of Jewish culture that is willing to adapt—but not assimilate.
At the very end, Tevye points out that Jews have never found a sense of belonging anywhere. Wouldn't it be nice, he thinks, if they could find a place of their own?
There's a funny paradox in Tevye's character. Okay, there are a whole bunch, actually, but let's just focus on one for now. He can talk endlessly about money—how much he has, how much he wishes he had, how he compares to his wealthy neighbors, how he compares to his poor neighbors, and so on and so forth.
Just a few examples: when Perchik is pouring out his heart about the world's injustice, all Tevye can say is "That's all well and good […] but will that get you any money" (5.42). Or after he sees his dead daughter: "The world remains a world. And you must also think of earning money" (7.140). Or when he decides to accept Podhotsur's hush money: "I […] gathered up the bills—oh, the power of money—and stuck them deep in my pocket" (8.100).
Okay, so, dude's got money on the brain. For him, money is pretty much synonymous with respect and prestige, too, which is why when he describes all the fancy people whose dairy he delivers in Boiberik and Yehupetz, he's got a dairyman-to-the-stars vibe about him.
And yet? And yet, whenever he is faced with the choice to either make a bunch of money or soothe the feelings of someone close to him, he never goes for the money. For example, here's how excited he is about the rich match Hodl is about to make:
Matchmakers can talk you into anything […] All sorts of good, sweet thoughts came to my mind, and I was picturing [Hodl] riding in a carriage pulled by a pair of spirited horses […] and the favors I would be doing for everybody through my daughter, the rich man's wife. (5.67)
But when he learns that Hodl and Pershik are totes in love, he jumps on that bandwagon pretty quickly:
Well, it was bad enough that they were engaged—he wants her, she wants him. […] I said, "It's time to talk about practical matters […] about the dowry," I said, "clothes, wedding expenses, this, that, and the other." (5.93)
Tevye immediately switches from daydreaming about his new-found riches to a pragmatic, if somewhat resigned, acceptance. He can see that "he wants her, she wants him" and his daughter's happiness is more important to him than her being "the rich man's wife."
Sounds like his daughters aren't the only ones breaking tradition.
It doesn't matter that his culture gives him ultimate authority over his wife and his daughters. First and foremost, he's concerned about their feelings and desires. He only stresses about money problems after making decisions to keep the people around him happy.
In a way, even his most patronizing nonsense—like say, making up dreams about Golde's grandma to get on her board with Tzeitl's marriage—is a way of dealing with his wife's fears for her daughter's wellbeing.