At the age of 18, Rachel Chen has made significant progress in the field of quantum mathematics by simplifying a complex problem. A student from Los Angeles, Chen achieved fourth place and received $100,000 in prize money at the 2026 Regeneron Science Talent Search, a prominent science competition for high school students in the United States. Her award-winning project builds upon a mathematical concept established in 1997 and uses straightforward point-and-curve diagrams to depict the behaviour of quantum particle systems.

Innovative Representation of Quantum Systems

Chen’s project, titled The Dual Canonical Basis in the Spin Representation via the Temperley-Lieb Algebra, delves into the mathematical portrayal of particles and their spin states. For instance, an electron can exist in one of two fundamental spin states, typically labelled as “up” and “down”. However, when multiple particles interact or respond to a magnetic field, the mathematical representation becomes substantially more complex.

Her work leverages Temperley-Lieb diagrams, which represent intricate mathematical relationships using points and curves. These diagrams have applications in diverse areas such as mathematical knots, phase transitions, and quantum physics. Chen extends their application to demonstrate the behaviour of a complete system of quantum particles influenced by a magnetic field. The Society for Science notes that this innovative method could provide researchers with a clearer understanding of the connections between various quantum-mechanical states.

A key component of Chen’s project is Lusztig’s dual canonical basis, a crucial structure in the mathematics involved in quantum systems. Her presentation outlines an explicit formula for this basis within the spin representation, illustrating the potential for diagrammatic methods to revisit established mathematical results while exploring related constructs, including the Hecke algebra. While this research does not simplify quantum mechanics per se, it offers a visual framework intended to aid mathematicians and physicists in analysing complicated systems via more accessible representations.

Beyond Mathematics: A Multifaceted Student

Chen is a student at Marlborough School in Los Angeles, where she took the initiative to establish the school’s mathematics club, which has since expanded to over 100 members. Alongside her academic pursuits, she is an avid volleyball player and has achieved international recognition as a chess player. Notably, she secured first place in her age category at the 2022 Pan-American Chess Festival and currently serves as the Contests Director for Athemath, a nonprofit organisation that encourages girls to engage with mathematics. Additionally, Chen is a dedicated fan of Taylor Swift, reportedly being familiar with the lyrics of over 200 of the singer’s songs.

Among the 40 finalists chosen from a pool of more than 2,600 participants in the 2026 Regeneron Science Talent Search, Chen’s project stood out. The overall competition featured a total prize pool exceeding $1.8 million, with the top award being claimed by Connor Hill. This achievement highlights the remarkable contributions of young scholars in advancing scientific knowledge.

Through her innovative approach to a longstanding mathematical problem, Rachel Chen exemplifies the capabilities of young minds in tackling complex scientific challenges. Her project not only reinforces the importance of visual methodologies in mathematics but also illustrates the potential for future breakthroughs in quantum physics. The recognition she received serves as an inspiration for aspiring scientists and mathematicians worldwide.

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