Latest news with #BerkeleyMathCircle
News18
3 days ago
- Science
- News18
Homeschooled Student Solves 40-Year-Old Math Theory, Gets Direct PhD Admission
Last Updated: Hannah has been offered a place in the University of Maryland's PhD programme in mathematics, bypassing the need for a high school diploma or college degree. Anyone can earn a PhD if they complete their degree and postgraduate studies, pass difficult entrance exams, and qualify at the top. However, a young woman who studied at home rather than attending school got the chance to pursue a PhD directly after solving a mathematical theory that had been a mystery for 40 years. Seventeen-year-old Hannah Cairo from the Bahamas achieved this remarkable feat. Hannah disproved the Mizohata–Takeuchi conjecture, a longstanding problem in mathematics within the realm of harmonic analysis, which studies how waves behave on curved surfaces. Many mathematicians had attempted to solve it over the years, but Hannah proved it wrong and provided a clear example to demonstrate why. Born in the Bahamas and homeschooled by her parents, who encouraged her to delve deeply into subjects of interest, Hannah chose mathematics. By age 11, she had mastered calculus and went on to study university-level subjects such as linear algebra, differential equations, and topology. She read books, took online classes, and occasionally had tutoring. During the COVID-19 lockdowns, Hannah joined the Chicago Math Circle online, where she engaged with problems more advanced than typical schoolwork. This introduced her to the questions and ideas that professional mathematicians grapple with. At 14, Hannah applied to the Berkeley Math Circle summer programme, stating on her application that she had already covered the advanced undergraduate math curriculum—a true claim. Her application was accepted, allowing her to join Berkeley's concurrent enrolment program and take university-level classes alongside graduate students, all while still officially in school. A professor named Ruixiang Zhang introduced Hannah to the Mizohata-Takeuchi conjecture, which predicted limits on how waves can focus on curved surfaces. While many students might have viewed it as a challenging puzzle, Hannah sought to create examples that defied the conjecture's rules, despite frequently encountering dead ends. Although Zhang doubted some of her ideas, Hannah persisted. Her breakthrough came with a seemingly simple idea: instead of trying to work within the pattern of the conjecture, she thought of creating an entirely different wave pattern. She developed waves that extended rather than intersected. After thorough testing, her example showed that the conjecture's predictions were completely incorrect. In February, Hannah published her research paper on arXiv. Some experts were astonished and congratulated her, while others were sceptical, questioning how someone so young could achieve such a feat. Consequently, Hannah was offered a place in the University of Maryland's PhD programme in mathematics, bypassing the need for a high school diploma or college degree. view comments First Published: August 13, 2025, 14:36 IST Disclaimer: Comments reflect users' views, not News18's. Please keep discussions respectful and constructive. Abusive, defamatory, or illegal comments will be removed. News18 may disable any comment at its discretion. By posting, you agree to our Terms of Use and Privacy Policy.
The Star
03-08-2025
- General
- The Star
Contradictheory: 'Mathmo' for life – how math can be found everywhere
The other day a friend asked me, if I had to do it all over again, would I still choose to study maths at university? In some ways, I didn't really have much of a choice. Maths was the subject I earned a scholarship for, and the only one in which I got top grades across all my exams. I could have applied for an adjacent subject like engineering, or computer science, or even accountancy, but that would be like using a canon in a sword fight. It can work, but it's inelegant. The truth is that maths has been my weapon of choice in school for a very long time. I even learn music by looking at it from a mathematical perspective, finding patterns hidden within notes and chords, especially in Bach's work. For many years, it was also a bit of an obsession for me. It was what I would think of almost as soon as I woke up, as well as in those twilight moments as I was trying and failing to drop off to sleep. Eventually I did maths in university and was and became a 'mathmo' (Cambridge University slang for mathematicians). Law and history undergrads looked on with envy from their foot-long reading lists at us mathematicians whose weekly assignments rarely covered more than a couple of A4 sheets. We could discuss homework while calculating angles at the pool table or think about imaginary numbers while sprawled on the grass in the quad. Those heady days of full-time maths (at least in my head) are now behind me. I simply wasn't good enough to do it full time. Now I browse the odd YouTube video about the Langlands programme (about connections between various areas of mathematics), or solve cute puzzles about liars in green hats choosing doors, and these have become moments in my life rather than the mainstream. Occasionally, I do pay attention to news about mathematicians. For example, Hannah Cairo recently casually disproved a 50-year-old conjecture about the kinds of shapes you get when you combine a lot of very tiny waves. She presented her work in a deceptively whimsical-looking presentation and is due to start on her PhD later this year. She is also currently 17 years old. Another is Kate Wenqi Zhu who won a prestigious prize in numerical analysis, shutting up her haters who thought she was too trendy as a social media influencer to also be fluent in non-convex optimisation and tensors. But aside from these attention-grabbing headlines, what really caught my attention was how they approached maths. Were they more dedicated, more focused at maths than I, which is why they succeeded while I stagnated? Before she turned 17, Hannah was reading university-level textbooks for fun and emailed professors asking to join their classes. During the summer of the Covid-19 pandemic, she joined the Berkeley Math Circle online, and came to the realisation that doing maths was more like 'painting a picture' rather than memorising facts. It was a way to understand things, ask questions, and make friends. According to her, she uses maths to 'help other people, to make them happy'. Meanwhile, Kate was accepted into university at 15, and after graduating, she worked at JPMorgan and then Goldman Sachs. Life was good. She travelled, she ate at nice restaurants, she posted fashion shots online. But when she mentioned on Weibo she was also an Oxford graduate, the post got 1.2 billion views, along with a flood of accusations claiming she was faking it. In this dark period she turned back to maths. Solving problems brought her a sense of peace. This realisation prompted her to resign from her high-paying, high-flying job and return to Oxford to pursue her master's and doctorate degrees. Winning the prize to shut up the critics was probably just a nice bonus. I think these two stories give some insight about what it means to love mathematics. It's not about locking yourself in a room with a large blackboard to unlock the hidden secrets of the universe (or at least, not just about that). It's about finding the right place to share what you get from it with others. Indeed, I say this with the benefit of my own hindsight. While doing maths was fun, thinking about it 24/7 can have consequences. It's one thing lulling yourself to sleep with algebraic equations; it's another to be kept awake to the point of insomnia. But eventually, life coalesces, and I discovered that I also enjoyed teaching others and helping them understand the world around us. I ended up doing things like training people on how to use software, and helping kids prepare for tests – and writing columns about strange and wonderful topics, including maths. Maths is still very much with me, but it's part of a larger picture. It's one pillar among many others that supports the whole house. There is a very human aspect of being thrilled about something, falling in love with it, and then as life unfolds, finding the right places and times so it strengthens rather than consumes you. When this passion helps you better connect with the world at large, rather than isolate and exclude you, then it most definitely becomes something to embrace truly and tightly, even if it's just once in a while. Logic is the antithesis of emotion but mathematician-turned-scriptwriter Dzof Azmi's theory is that people need both to make sense of life's vagaries and contradictions. Write to Dzof at lifestyle@ The views expressed here are entirely the writer's own.
