A 17-year-old teen refutes a mathematical conjecture proposed 40 years ago

Mathematical result and context

• The linked paper gives a counterexample to the Mizohata–Takeuchi conjecture in harmonic analysis.
• Commenters connect it to X-ray/Radon transforms and inverse problems used in reconstruction (e.g., imaging from scattered light).
• A quoted line (from the article) notes she used several tools including fractals and careful construction.

What “refuting a conjecture” means

• Several comments explain that the conjecture has “for all x” form, so a single valid counterexample disproves it.
• Multiple posters emphasize that finding such a counterexample counts as “solving” the conjecture, just as much as proving it true.

Significance, skepticism, and exposition

• Many express admiration for doing original, nontrivial math at 17; some call it “insanely hard” at any age.
• One commenter voices doubts about the counterexample, criticizing loose use of asymptotic methods and asking for links to earlier work.
• Others highlight a video where she herself explains the conjecture and her result; her note-taking/presentation style is praised.

PhD, training, and how academia works

• A long subthread debates why someone who solved a decades-old problem should still do a PhD.
• Points in favor:
  • A PhD provides structured research training, breadth, and communication skills.
  • One result doesn’t guarantee a sustainable research agenda or publication track record.
  • It offers mentorship and time to mature, especially important for someone so young.
• Critiques of the system:
  • In some places, PhDs are seen as cheap labor, credentialing for industry, and vehicles for incremental work.
  • “PhD by publication” (especially in parts of Europe) is discussed: bundling several peer‑reviewed papers as a thesis, versus traditional dissertations. There’s disagreement over how common/rigorous this path is and over the term’s usage.
  • A PhD is described as much a test of endurance and bureaucracy as of intelligence.

Youth, creativity, and research careers

• Several note that many famous mathematical breakthroughs historically came from people in their 20s, and see this result as fitting that pattern.
• Others push back, citing major work done in mid‑career or later, arguing that broad experience and framework‑building also matter.
• There’s criticism of modern academic structures that force principal investigators into constant grant‑seeking, reducing sustained deep thinking.
• One detailed comment outlines a typical natural‑science career arc: deep thinking peaking in late PhD/first postdoc, then giving way to survival‑driven publishing and grant pressure.

Teaching, opportunity, and mentorship

• The result emerged from a class where the professor included the full conjecture as an optional homework part.
• Commenters see a lesson: expose students to real open problems and give them chances to exceed expectations.
• Some recall being shown hard unsolved problems early (e.g., Collatz) and valuing being treated seriously.
• Others mention that juniors sometimes succeed because they don’t “know” a problem is impossible and just try.

Article quality and media framing

• Multiple commenters think the newspaper article is poorly written:
  • It initially misspells her name.
  • Some feel the refutation vs. proof isn’t emphasized clearly enough, though others note the first paragraph explicitly describes a counterexample.
  • One critic argues it leans too much on age and venue (Spanish academy) rather than clearly explaining the mathematical consequences, while another responds that naming specific theorems would be meaningless for a general audience.

HN title and moderation meta-discussion

• There is frustration about editorial changes to the Hacker News submission title, seen as violating the guideline to keep the original title unless it’s misleading.
• The title was later adjusted to be closer to the original, which explicitly mentions a 17‑year‑old refuting a 40‑year‑old conjecture.