BOSTON — The college student in Eleanor Burgess’ thoughtful and thought-provoking new play, “The Niceties,” is black. Her professor is white. And that’s the only part of this smart production, headed off-Broadway after its Huntington run, that is black and white.

Everything else is in that tricky territory called gray, as your sympathies ping-pong from young Zoe (Jordan Boatman), who just wants her history professor to help her fine-tune a paper on the American Revolution, to the professor, Janine (Lisa Banes), who just wants her student to yield to her years of experience and knowledge.

But each has either under- or over-estimated the other, depending on your point of view. What starts out on Janine’s part as low-grade condescension (she begins the session pointing out punctuation and grammar errors, then asks if Zoe has ever been to India: “You really must go.”) turns gradually into criticism of Zoe’s paper, scholarly ability and, ultimately into a take-down of her generation.

As for Zoe, what begins as acceptance of Janine’s critique turns gradually both defensive and argumentative as she makes the case for her paper’s thesis: that the Revolution was an ultimate success in part because the group that might otherwise have risen up after the British were tossed out was enslaved.

It’s a thesis a skeptical Janine wants to see backed up by evidence — letters, journals, documents from the era. Except, as Zoe points out, such evidence about and by slaves is understandably scarce. Why, she asks, does history always brush over people “who couldn’t leave evidence behind.”

Good point. And that’s one of the best parts of this play: Sometimes you think, yes, Zoe is right, and sometimes you think, yes, I see Janine’s point of view here. It helps that both performances are nuanced and compelling.

Zoe resents Janine’s preaching from a position of power. She hates it when Janine suggests she knows how Zoe feels about being marginalized. Janine resents Zoe for not listening to her arguments. She hates it when Zoe brings up microaggression and emotional trauma. Zoe tries to explain what it’s like to be a black student in an elite mainly white university, what it’s like to feel racism taints everything, but Janine keeps interpreting what Zoe says through her own lens. When Zoe says she can’t completely rewrite her paper because she is helping to organize a campus protest, Janine suggests she needs to make better time-management choices, talking about a choice she made between taking an internship at the Smithsonian and a bike trip with a friend from Paris to Amsterdam. As the two grow increasingly frustrated with each other, the dialogue heats up. Zoe says Janine should “just shut up and listen” when a woman of color is speaking. Janine says “no one wants to hear any more about racism.”

It all boils over into a very dramatic end to Act 1, where something Zoe has secretly done puts events in motion for the second act, set three weeks later, when the two meet again to discuss the fallout from their first session. Both have suffered in the interim, and they try to see that suffering from each other’s position, but the attempt begins to unravel, and we’re quickly back to square one, with Janine suggesting Zoe needs to be strategic if she wants to see change on the campus and in the world for people of color. She has to be nicer “to get people on your side.” But Zoe is appalled at the idea: “I am tired of you slowing me down,” she says, finally demanding that Janine resign.

“You have to give up some of your power,” she says. “You have too much.”

Happily, “Niceties” does not end with the two women hugging it out. They end as they began, two ships passing each other on a dangerous sea.

When asked if she was closer to Janine or Zoe, playwright Burgess, a former history teacher, said both. Or neither. “I think both women are right in many ways and wrong in others.” The important point: that the audience talks about how to reach across the divide of disagreements. If the conversation on the way out of the theater Saturday was any indication, it was a mission accomplished.