A high school student won America’s top science award for solving a centuries-old Geometry problem; how his work on 146 rare shapes can change the future of medicine
US high school student Connor Hill won first place at the 2026 Regeneron Science Talent Search (STS). He has won the award for solving a longstanding problem in geometry involving a class of shapes known as noble polyhedra. His research produced a complete classification of these geometric objects, identifying two infinite families and 146 isolated examples, and earned him the top award from the Society for Science’s competition.The work is rooted in a centuries-old mathematical tradition dating back to Plato and the early study of geometry, but its significance extends beyond the shapes themselves. Hill’s approach involved translating a potentially infinite geometric problem into a finite one using algebra and polynomials. That method of reducing a complex set of possibilities to a manageable number is also used in modern scientific research, including biology, protein structure and drug discovery.
Connor Hill’s geometry research identifies 146 rare shapes
Hill’s research focused on noble polyhedra, geometric objects defined by symmetry in which all faces are identical, and all vertices are identical. A cube is a basic example of a highly symmetrical polyhedron, while noble polyhedra relax some of the restrictions found in classical shapes such as the Platonic solids.Hill said his interest in the subject began through an online mathematics community where he encountered the open question surrounding noble polyhedra. What initially appeared to be a search for additional examples eventually developed into a complete proof and classification.A central part of the research was finding a way to reduce the number of possibilities. Rather than attempting to examine an unlimited number of geometric arrangements directly, Hill connected the problem to algebra, including polynomials, which allowed him to convert it into a finite problem that could be solved.The result was the identification of two infinite families of noble polyhedra along with 146 isolated examples.
How Connor Hill’s math connects to medicine and science
The connection between Hill’s geometry research and medicine lies in the mathematical method rather than in the geometric shapes themselves. Modern biology often involves systems with a large number of possible configurations, making it necessary to identify which possibilities are stable, relevant or biologically meaningful.Henry Wei, MD, Executive Director, Development Innovation at Regeneron, discussed this connection with Hill. Wei is a physician-scientist working at the intersection of biology and medicine.One example is protein structure. Proteins can take on many possible configurations, but only some are stable or relevant to biological processes. Mathematics can help researchers narrow those possibilities and identify structures that may matter for understanding disease or developing medicines.The same principle applies to drug discovery, where researchers need to work through complex biological systems and determine which interactions or structures are most relevant.Hill’s work also demonstrates how a problem can be transformed by moving between different areas of mathematics. His research connected discrete geometry with algebraic geometry to establish a finite framework for a problem that initially involved an effectively unlimited set of possibilities.
Why mathematical proofs matter to medical research
Modern scientific research frequently uses models and approximations to understand complex systems. Mathematical methods can provide another approach by establishing exact relationships and reducing large sets of possibilities to smaller, more defined problems.Hill said the method used in his project could apply beyond noble polyhedra because the same approach can be useful wherever researchers encounter structure, symmetry or a large number of possibilities that need to be narrowed down.Wei similarly pointed to the role of mathematics in making complex biological systems more understandable. Problems involving protein folding, disease progression, and interactions between treatments and the human body all require researchers to identify patterns within large, complex systems.The connection does not mean Hill’s 146 geometric examples directly produce new medicines. Instead, his research illustrates how mathematical techniques for simplifying complex problems can also be relevant to scientific fields where researchers face similarly large sets of possibilities.
Connor Hill’s next step after Regeneron Science Talent Search
Hill is set to attend MIT this fall, with his education supported in part by his winnings from the 2026 Regeneron Science Talent Search.His research also reflects the role of curiosity-driven mathematics in scientific work. Hill said his project did not begin with a planned breakthrough. It developed gradually as he explored an open mathematical question and connected different areas of mathematics to solve it.The broader relevance of the work lies in that process: reducing a problem that appears infinite to a finite set, establishing an exact solution and then applying the underlying method to other fields where complexity needs to be reduced.As Hill puts it, “Math is the language that makes scientific ideas usable.” Science provides concepts, while mathematics formalises them and makes them applicable to specific problems.
