Nor can I, like that fluent sweet-tongued Greek Who lisp'd at first, in future times speak plain.
One of the things we really like about this poem is how the thoughts are linked together from line to line and stanza to stanza. That also applies from line to line, like in this case, where the sentence carries over across the line break.
Here Bradstreet starts a new stanza by picking up and extending an idea she just talked about (lines 17-18), that nature can't fix flaws. This time, though, she drops in a fancy-pants allusion to classical Greece. The "sweet-tongued Greek" she's talking about is Demosthenes, a famous orator from ancient Athens. The story goes that he had a speech impediment as a boy, but overcame it with hard work and practice. We should point out that "sweet-tongued" is just a figure of speech, a metaphor for being a good talker. His tongue wasn't really sweet—that would be kinda gross.
Of course, you'd only catch the Demosthenes reference if you had a classical education, which Bradstreet did (see our "Best of the Web" section for more on her unusual childhood). So while she's supposedly downplaying her ability, she's also showing off a little, letting the boys know that she belongs in their club, at least in one way.
By Art he gladly found what he did seek, A full requital of his striving pain.
Demosthenes worked hard and got what he wanted. His skill as an orator was the compensation ("requital") for his efforts. In his case, at least, Art overcame nature. Our speaker isn't so sure that this applies to here, and the comparison to Demosthenes comes off as a little negative.
At the same time, we can't help but think of Bradstreet's huge achievement, as a woman and a published poet from the brand-new American colonies (there weren't that many American poets of either gender back then). It's hard to imagine that publishing her work didn't feel at least a little like a reward for her own "striving pain"
Art can do much, but this maxim's most sure: A weak or wounded brain admits no cure.
Even though Demosthenes triumphed, Bradstreet's speaker isn't so sure that she'll be able to do the same. She's impressed by the power of Art, and believes it "can do much." Still, she doesn't think it can fix her problem, which is, apparently, a "weak and wounded brain."
It's maybe kinda tough for all of us open-minded, modern Shmoopers to imagine how seriously people in Bradstreet's day took the difference between men and women. It's not that they all hated women or anything, but they definitely believed in the idea of the "weaker sex." So when Bradstreet describes her brain as "weak or wounded," she might really mean it.
On the other hand, she might be using this poem to push back a little against the idea of female inferiority. We think every reader has to decide that for herself.