Kevin Hartnett in Quanta:
It’s not that anyone ever said sophisticated math problems can’t be solved by teenagers who haven’t finished high school. But the odds of such a result would have seemed long.
Yet a paper posted on February 10(opens a new tab) left the math world by turns stunned, delighted and ready to welcome a bold new talent into its midst. Its author was Hannah Cairo(opens a new tab), just 17 at the time. She had solved a 40-year-old mystery about how functions behave, called the Mizohata-Takeuchi conjecture.
“We were all shocked, absolutely. I don’t remember ever seeing anything like that,” said Itamar Oliveira(opens a new tab) of the University of Birmingham, who has spent the past two years trying to prove that the conjecture was true. In her paper, Cairo showed that it’s false. The result defies mathematicians’ usual intuitions about what functions can and cannot do.
So does Cairo herself, who found her way to a proof after years of homeschooling in isolation and an unorthodox path through the math world.
More here.
Enjoying the content on 3QD? Help keep us going by donating now.

I have had early access to GPT-5
Governments, social scientists, public health officials, and others have grown concerned about a possible “loneliness epidemic.” They paint a picture that looks a bit like this: old people staring wistfully out the window, young men growing radicalized online, teenagers glued to their phones, missing real-life connections. It’s a worrying portrait. But what we’re facing isn’t a loneliness epidemic. It’s something much worse.
Will Storr, author and fellow Substacker,
Severe allergic reactions can be swift and deadly. Two new studies of mice, published August 7 in Science, reveal a key step in this terrifying cascade. What’s more, these findings hint at a drug to prevent it. Anaphylaxis
What makes Gibson’s portrait of great cities thought-provoking is that, despite all this change, he imagines them persisting at all, in some ways operating no worse than the worst that can be found today. This situation becomes all the more thought-provoking when we see how he links the fate of his cities to the fate of the modern project itself, whose deep impact on making cities what they are today will persist into the future.
For many months, the only place in New York City still showing Pedro Almodóvar’s most recent film—his first English-language feature,
For the last two and a half years, since the release of ChatGPT, I’ve been suffering from fits of dread. It’s not every minute, or even every day, but maybe once a week, I’m hit by it—slackjawed, staring into the middle distance—frozen by the prospect that someday, maybe pretty soon, everyone will lose their job.
In November, James Lindsay—an independent scholar, author, and sometime
Zadie Smith, Michael Rosen, Irvine Welsh and Jeanette Winterson are among more than 200 writers who have 
The effect of a gene can vary greatly — and sometimes be the complete opposite — depending on whether it is inherited from the mother or the father. Some genetic variants can, for instance, increase a person’s risk of developing type 2 diabetes when inherited from the father, but lower it when inherited from the mother. But such effects have been challenging to unpick owing to gaps in genomic data. A study published in Nature this week describes a
Two moments in Graham Greene’s published life have often returned to me in the past twenty years. This may sound strange: an ideal reader should refrain from crossing the boundary between a writer’s work and his life. And yet it is inevitable: rarely does an author have the luxury of having no known biography. Greene, having written about his life and having had his life extensively written about by others, remains near when one reads his work—not insistently dominating or distracting, as some writers may prove to be, but as a presence often felt and at times caught by a side glance.