[uselesswords]

Sure context and audience matters, but even outside of that the article is rather poorly written. This part in particular should really emphasize that she disproved the conjecture, as it stands it almost sounds like she proved it:

> Cairo solved the so-called Mizohata-Takeuchi conjecture, a problem first proposed in the 1980s that had kept the harmonic analysis community had been working on for decades. The conjecture was widely believed to be true — if so, it would have automatically validated several other important results in the field — but the community greeted the new development with both enthusiasm and surprise: the author was a 17-year-old who hadn’t yet finished high school.

[tzs]

From the first paragraph of the article:

> "After months of trying to prove the result, I managed to understand why it was so difficult. I realized that if I used that information correctly, I might be able to refute the claim. Finally, after several failed attempts, I found a way to construct a counterexample [a case that does not satisfy the studied property and therefore proves it is not universally true]."

That makes it quite clear that she refuted it.

[billforsternz]

This excerpt features a terrible typo, so I agree it's poorly written, or at least not properly proof read. I don't agree with your specific criticism of the excerpt though. I think the excerpt makes it perfectly clear she disproved the conjecture by highlighting how that was potentially a disappointing outcome.

The writer introduced and resolved the potential disappointment much more elegantly and in far fewer words than I can manage here by paraphrasing. I admire that and feel it's indicative of good writing, albeit spoiled by an earlier typo.