While many 17-year-olds last spring were preoccupied with planning for prom, studying for AP exams or booking houses for beach week, Hannah Cairo was shocking the not very teen-coded world of theoretical math. 

In February, she disproved the Mizohata-Takeuchi conjecture, a math assumption that had stumped experts around the world for 40 years (and is impossible to summarize in lay terms). And she did it as a side project to her classes. 

“Once I start working on a problem, it’s kind of addictive,” she said. “I can’t stop thinking about it. For every question I answer, I just have more questions.”

Now the remarkable teen will pursue those answers as she starts her doctoral studies at the University of Maryland this fall. 

“She stands out head and shoulders above her peers,” said math Professor Wojciech Czaja, comparing her to prodigies like alums Charles Fefferman ’66, who won the Fields Medal, math’s highest honor, and George Dantzig ’36, who famously solved two open problems in statistical theory after mistaking them for homework. Cairo didn’t just tackle “a niche question that a small group of people were interested in. This is a well-known problem, spanning various areas of math.” 

Growing up in the Bahamas, Cairo was homeschooled. Her affinity for math became apparent early as she raced through the Khan Academy’s online curriculum, learning calculus by 11. She pored over math textbooks on topics like analytic number theory under the guidance of tutors, finding beauty in the numbers and ideas. It was sometimes a lonely experience, but she found like-minded people when she joined her first math circle, extracurricular gatherings of mathematicians and students. 

“They bring math puzzles and everybody collaborates, and it’s a really nice way to make friends,” she said. 

That led her to apply at age 14 to the Berkeley Math Circle online summer program, where she found both challenge and camaraderie. A few years later, her family moved to California, and she joined Berkeley’s concurrent enrollment program to take graduate-level math courses. 

One of those was on Fourier restriction theory, a branch of harmonic analysis, an area that has wide-ranging applications from telecommunications to music analysis and even image processing. 

A few months in, Professor Ruixiang Zhang assigned a simplified version of the Mizohata-Takeuchi conjecture in homework. Cairo quickly completed the assignment—but couldn’t stop thinking about the problem. She spent months on proofs, consulting Zhang along the way, before coming up with her construction to disprove the conjecture. 

She posted it to arXiv.org in February, and within a few months, she gave a talk at a prestigious math conference in Spain. Since then, she has gotten media coverage in Scientific American, Quanta Magazine and international new outlets. 

It could be overwhelming, but Cairo, despite being soft-spoken, is eager to share her work. 

In person, “it’s funny when people try to guess my age,” said Cairo, now 18. With her quiet poise, she’s often mistaken for a postdoc or a grad student when she’s among fellow mathematicians—but when she volunteered at a summer program, was mistaken for a camper. “I don’t hide my age, but I don’t want to brag about it.” 

Maryland was eager to recruit Cairo, led by math graduate program director Leonid Koralov. Now, he and Czaja are eager to help her maximize her potential at UMD. She’ll continue to research Fourier restriction theory, but they also hope she can examine “other questions of importance to modern science,” said Czaja. 

Cairo also hopes to explore additional opportunities on and off campus. 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.”

Written by Karen Shih

AMSC Ph.D. candidate Mengting Chao’s step-by-step teaching method and commitment to student success earned her recognition from both students and faculty.

When Mengting Chao started her Ph.D. in applied mathematics & statistics, and scientific computation (AMSC) at the University of Maryland in 2020, she never imagined she would win three major campus-level teaching awards in the next five years—or that teaching would become so central to her academic identity. 

“It was the first year of the pandemic, and I felt a lot of anxiety about my future and what it would look like,” Chao recalled. “I felt very disconnected from my instructors and my peers, and there was a great deal of uncertainty at the time. I wasn’t sure how things would work out.” 

Since that rough beginning, Chao accomplished more than she ever expected. In her second year, Chao received a serendipitous email from Bruce Golden, a professor of management science at the Robert H. Smith School of Business and an AMSC faculty member. Golden was recruiting new students for his research, and Chao quickly connected with him over their shared interest in operations research and joined his team.

Today, Chao is in the final stretch of her Ph.D. program, completing a dissertation on last-mile delivery logistics—the last leg and most crucial step in the shipping process, which involves moving a package from a local hub (like a distribution center) directly to the customer's doorstep. Chao says her work at UMD helped her find her niche in mathematics, and one of her research projects earned the 2025 Best Student Paper Award from the Decision Sciences Institute. Her research experience also led to internships with Amazon and RouteSmart Technologies (now part of FedEx), where she worked on optimizing logistics and transportation processes. 

“Being able to come to UMD physically helped me feel more connected with the community here and have a better idea of what I wanted to do,” Chao said. “I also realized that I could do more with my math skills than I originally thought.”

While Chao conducted research with Golden’s group, she also began teaching courses like MATH 141: Calculus II and STAT 400: Applied Probability and Statistics. There, she discovered a deep passion for education and especially for helping students succeed. 

“The first semester teaching was difficult, especially as English is my second language, but I really enjoyed it and actually received many positive teaching evaluations from my students. I also took their valuable feedback to heart and adjusted my teaching style accordingly,” Chao explained. “The experience made me think, ‘Oh, maybe I’m good at this!’ and I developed confidence in teaching, so I continued to do it.” 

Chao’s students agreed. At the 2025 College of Computer, Mathematical, and Natural Sciences (CMNS) employee awards ceremony, Chao received the collegewide Dean’s Outstanding Teaching Assistant Award. More than 60 undergraduates nominated Chao, sharing stories about how Chao’s patience and step-by-step approaches to complex concepts made math easier for them. Chao also received the Department of Mathematics’ 2022 Aziz/Osborn Gold Medal in Teaching Excellence and UMD’s Outstanding Graduate Assistant Award, which placed her among the top 2% of more than 4,000 graduate assistants across campus.

“Being recognized for my efforts by this community helped me realize how meaningful I find interacting with and supporting others through teaching and mentorship,” Chao said. “I never would have imagined this for myself before.”

A foundation in patience and perspective

Chao’s talent for teaching mathematics didn’t emerge overnight. Beginning in her sophomore year at Dickinson College in Pennsylvania, she worked as a tutor at the university’s Quantitative Reasoning Center. There, she guided students at various levels in mathematics, computer science and economics—three fields in which she eventually received bachelor’s degrees.

But Chao believes that her personal affinity for teaching and math goes back even farther than that.

“Growing up, I was always comfortable with numbers and enjoyed working with math,” she said. “I took Math Olympiad training classes for younger children while I attended primary school. And then, one day, I simply could not figure out a way to solve the problems—they’re not as simple as ‘one plus one equals two’ types of questions.”

With guidance from her grandfather, an accountant, Chao learned creative approaches that helped her solve problems in mathematics, and her interest in math blossomed. 

“My grandfather really introduced me to the beauty of mathematics. In addition to helping me develop the skills to solve math problems, he also gave me the chance to see a problem from a different perspective,” she said. “When I saw how a problem could be solved in different ways, it really shaped how I saw math and how other people can approach it. Without that experience, I probably would have lost interest in math entirely and my path would look very different.” 

Those childhood memories laid the foundation for the teaching principles Chao uses today and the approaches that help her connect with students in the classroom. 

“I try to be completely transparent with content, creating detailed lecture notes, and uploading materials immediately. Everything is easily accessible and written out step-by-step so students can follow my thought processes,” Chao said. 

Chao also tries to tailor her teaching approach to her students’ experiences and backgrounds.  She often provides quick recaps to make sure everyone in the classroom is on the same page and draws on her interdisciplinary background to help students connect with the content.

“Keeping students engaged is a challenge, but a very important thing to keep in mind. If students feel discouraged, just like I was as a kid getting stuck, they sometimes just lose all confidence and don’t have any motivation to learn anymore,” she said. “I review things that they might have forgotten, even when more advanced students say it’s not needed, and try to provide real-world examples of more abstract concepts.”

For Chao, having great teachers was life-changing, and she hopes to make the same kind of difference for her own students, helping them achieve their future goals. 

“My goal is to give students all the tools they need to succeed,” she said. “My philosophy is to always provide patience and perspective to students. They can feel it when you lack these things, and it can really make a difference.” 

Written by Georgia Jiang

Studies show darker-skinned patients suffer greater mortality from skin cancer. A tumor detection model built by a team that includes mathematics and computer science double-degree student Dhruv Dewan could help close the gap.

For a student so interested in technology, Dhruv Dewan finds a surprising level of comfort in being unplugged. When he’s not exploring the inner workings of artificial intelligence (AI) models, he loves hiking through the woods. 

The University of Maryland double-degree senior in mathematics and computer science is an Eagle Scout and avid backpacker—his favorite trek is a weeklong, 50-mile route in Virginia on the High Knoll Trail in the Blue Ridge Mountains. 

Dewan sees a common thread that unites his two passions. Both foster a mindset of exploration and require transferable skills in problem-solving and resourcefulness—whether it’s to solve a mathematical proof or devise a way to keep food safe from bears. 

Now, Dewan brings that skill set to his studies at UMD. For his four-year research project in the Gemstone program in the Honors College, Dewan and his teammates on “Team Artificial Intelligence Diagnosis” (AID) are developing AI models that can more equitably and accurately detect skin cancer through photos. The three-person team consists of Dewan, a computer science major and a bioengineering major working under the supervision of Heng Huang, Brendan Iribe Endowed Professorship in Computer Science. 

Dewan hopes that doctors can use these models to better diagnose skin cancer in people with darker skin, who have statistically lower survival rates than white patients. 

“I've really seen how exponentially helpful having a deep understanding of math and statistics is for understanding how machine learning and AI work,” Dewan said. “These models just multiply matrices by other matrices. At the end of the day, it’s all truly, purely math.” 

Improving AI for Cancer Detection

Many models can detect skin cancer from images, Dewan said, but they are mostly trained on people with lighter skin tones. 

“That introduces a really big issue in how equitable they are,” he said. “Many models are good at diagnosing skin cancer for whiter and lighter-skinned patients. But when we tested them on a diverse dataset of skin types that included various darker skin tones, we found that they performed extremely poorly.”

Thus, one approach his team takes is to incorporate more diverse data into training sets and ensure that the models pay attention to those data points.

Additionally, the Gemstone team integrates self-supervised learning into the training process. Existing methods train models on photos labeled as cancerous or non-cancerous. By contrast, self-supervised learning provides the model with a larger sample of unlabeled data. Their model learns deeper features of the images using that expansive dataset, which it can later use to identify telltale signs of cancer. This could prevent the model from overfitting on skin tone as its primary diagnostic criterion. 

Dewan finds that his background in mathematics benefits his AI and machine learning research.  

“Many of the techniques that we’re using to improve current methods are pure statistics,” he said. “Having an intuition for statistics and math allows me to understand how the model works and diagnose how to improve it.” 

Dewan expects that the final model, which his team will present at the end of the Spring 2026 semester, will be able to generalize skin cancer beyond only the skin tones it has seen during training. 

"We hope this model helps to provide early diagnosis for darker-skinned patients who have a much lower survival rate for skin cancer because they’re diagnosed too late or because doctors can't diagnose them,” he said. “Hopefully, doctors can use this model as a tool. It feels really fulfilling that this could have an impact.”

Wherever Dewan ends up, he wants to work on robust and scalable software while keeping equity in mind. And, he hopes to quench the thirst for exploration that he developed as an Eagle Scout. 

“Whether I am in academia or in industry,” he said, “I hope to carry that research and exploration mindset going forward.” 

Written by Jason P. Dinh