Comments on: Hannah "17yo" Cairo stuffs Mizohata-Takeuchi Conjecture

Hannah "17yo" Cairo stuffs Mizohata-Takeuchi Conjecture

BobTheScientist — Sun, 14 Sep 2025 13:34:56 -0800

Mizohata-Takeuchi Conjecture dates from the 1980s something something Fourier something something harmonic analysis something something partial differential equations. Earlier this year autodidact Hannah Cairo found a counterexample; then simplified her proof to make it more generally applicable and send more mathematicians back to their chalkboards. The Fourier restriction conjecture of Elias Stein (1931-2018) is wobbly for example.

Full metal Arxiv (Feb/Mar 2025) "In particular, multilinear restriction estimates at the endpoint cannot be sharpened directly by the Mizohata-Takeuchi conjecture." It may be easier to follow with audiovisual aids [22minYT]. Interview with Sci.Am. "Being trans has forced me to see things about the world that I maybe otherwise wouldn't have seen. It's made me see the world differently and made me see people differently and made me see myself differently." Being home educated might have helped keep her mental math channels open also?

By: chromecow

chromecow — Sun, 14 Sep 2025 14:02:42 -0800

What an amazing achievement! I have the barest glimmer of comprehension of what it's about, but I appreciate the folks out their doing this cutting edge work. Excited to see what else she accomplishes.

By: jamjam

jamjam — Sun, 14 Sep 2025 14:47:50 -0800

Quanta had a very nice article about Cairo and the proof back in early August. That article did not mention that Cairo is trans, and says that Stein's conjecture is now overturned. Cairo is amazingly direct and modest about her ability to a degree I don't think I've seen before:

Growing up, I didn't really know if I was talented," she said. "I like to play piano, and people around me would tell me that I was really talented at math and at piano. And in retrospect, now that I look at it, I can see, sure, my piano was above average. But it was by no means exceptional. While on the other hand, it looks like mathematically I'm, like, whatever."

No one really knows what to do with Cairo, but a number of institutions have seriously embarrassed themselves when they faced the choice:

The math world is also adjusting to the fact of Cairo herself. After completing the proof, she decided to apply straight to graduate school, skipping college (and a high school diploma) altogether. As she saw it, she was already living the life of a graduate student. Cairo applied to 10 graduate programs. Six rejected her because she didn't have a college degree. Two admitted her, but then higher-ups in those universities' administrations overrode those decisions. Only the University of Maryland and Johns Hopkins University were willing to welcome her straight into a doctoral program. She'll start at Maryland in the fall. When she finishes, it will be her first degree.

By: crazy_yeti

crazy_yeti — Sun, 14 Sep 2025 15:33:03 -0800

I think it's a big mistake to skip college and go straight to a math grad program, because of all the non-math stuff (history, philosophy, literature) that one is exposed to in undergrad education (math grad school survivor here)

By: jamjam

jamjam — Sun, 14 Sep 2025 15:36:20 -0800

Damn it, despite myself I referred to Cairo as 'she'. Mods, please correct that to 'they' or delete my comment, whichevever is more convenient

By: RichardP

RichardP — Sun, 14 Sep 2025 16:13:00 -0800

jamjam, Hannah Cairo's preferred pronouns are "she/her".

By: jim in austin

jim in austin — Sun, 14 Sep 2025 17:14:56 -0800

Joel would be proud...

By: xusifem

xusifem — Sun, 14 Sep 2025 20:42:30 -0800

Solving a long-standing conjecture at 17 may indicate that there's a Fields Medal in her future. Although she's skipping college to go straight into a mathematics Ph.D., according to this article, she has attended university-level lectures by mathematicians, including Ruixiang Zhang, at UC Berkeley.

By: billsaysthis

billsaysthis — Sun, 14 Sep 2025 21:33:33 -0800

Amazing!

By: creatrixtiara

creatrixtiara — Sun, 14 Sep 2025 21:57:10 -0800

think it's a big mistake to skip college and go straight to a math grad program, because of all the non-math stuff (history, philosophy, literature) that one is exposed to in undergrad education (math grad school survivor here) It'll just be in line with how university works outside the US, where you specialise from Day 1

By: kliuless

kliuless — Sun, 14 Sep 2025 22:15:23 -0800

here's cairo's presentation she gave in spain :P nice that maryland is rolling out the welcome mat for her:

As a trans woman, she hopes to increase visibility for LGBTQ+ students, and she's also joined an animal rights student group. Once she's passed her qualifying exams and settled in, she hopes to start a math circle for K-12 students in the local community, using games like Nim and Set to pique their interest. "Mathematics to me is like an art, but in school they don't really teach it that way," she said. "If you're just memorizing steps, you're not learning how to build things with ideas, paint pictures with ideas. I want to try to help people do that."

sounds like she has well-rounded role models, too!

If you could have dinner with the five most interesting people in the world, living or dead, who would they be?
Johann Sebastian Bach

Greta Thunberg

Fred Hampton

Ingrid Newkirk

My friends