18-year-old expands a 1997 quantum idea, wins $100,000 for maths breakthrough

Rachel Chen, an 18-year-old student from Los Angeles, won $100,000 at the 2026 Regeneron Science Talent Search for expanding a 1997 mathematical idea. Her research uses simple diagrams to represent complex quantum particle systems, while her interests include chess, volleyball, mathematics and Taylor Swift.Rachel Chen, an 18-year-old student from Los Angeles, won $100,000 at the 2026 Regeneron Science Talent Search for expanding a 1997 mathematical idea. (Photo: societyforscience.org)At 18, Rachel Chen has taken a complex problem in quantum mathematics and found a way to make it easier to visualise.The Los Angeles student won fourth place and $100,000 at the 2026 Regeneron Science Talent Search, one of the United States’ leading science competitions for high school students.Her project expanded on a mathematical finding from 1997 and used simple point-and-curve diagrams to represent the behaviour of entire quantum particle systems.FROM SIMPLE DIAGRAMS TO QUANTUM SYSTEMSChen’s project, titled The Dual Canonical Basis in the Spin Representation via the Temperley-Lieb Algebra, focuses on the mathematical description of particles and their spin states. An electron, for example, can have one of two basic spin states, often described as “up” and “down”. When several particles interact with one another or respond to a magnetic field, however, the mathematics becomes much more difficult to represent.Chen’s work builds on Temperley-Lieb diagrams, which use points and curves to encode complex mathematical relationships. These diagrams are already used in areas such as mathematical knots, phase transitions and quantum physics. Her research extends their use to describe how an entire system of quantum particles behaves under the influence of a magnetic field. According to the Society for Science, the approach could offer researchers a more intuitive way to understand the links between different quantum-mechanical states.A NEW WAY TO REPRESENT COMPLEX MATHEMATICSA major part of Chen’s project involved Lusztig’s dual canonical basis, an important structure in the mathematics of quantum systems.Her presentation describes an explicit formula for this basis within the spin representation. She also used the diagrammatic approach to revisit existing mathematical results and examine related structures, including the Hecke algebra.The research does not mean quantum mechanics has suddenly become simple. Rather, it provides a visual framework that may help mathematicians and physicists study complicated systems through more manageable representations.CHESS, VOLLEYBALL AND TAYLOR SWIFTChen studies at Marlborough School in Los Angeles, where she founded the school’s mathematics club. The club has grown to more than 100 members.Away from advanced mathematics, she plays volleyball and is an internationally ranked chess player. She won her age group at the 2022 Pan-American Chess Festival and serves as Contests Director for Athemath, a nonprofit supporting girls interested in mathematics.She is also a Taylor Swift fan who knows the lyrics to more than 200 of the singer’s songs.Chen was among 40 finalists selected from more than 2,600 entrants across the 2026 Regeneron Science Talent Search. The competition awarded more than $1.8 million, with first place going to Connor Hill.- EndsPublished On: Sep 12, 2026 14:44 IST