advanced
A complete enumeration of the noble polyhedra
Connor Hill
Grand award · Regeneron STS 2026
Proved two infinite families of noble polyhedra together with 146 isolated examples.
- geometry
- polyhedra
- enumeration
- +1
Winning projects
What strong projects actually look like — the question they asked, the design that survived review, and the one decision that made the difference.
Archive entries are summaries compiled for study. Read them for how a project was structured, argued, and defended — not as a template to reproduce. Copying someone else's project is the one thing that will end yours.
6 projects in Mathematics
advanced
Solvability of Equations in Elementary Functions
Nikola Veselinov
First place · Regeneron ISEF 2026
A new theorem giving conditions under which an equation cannot be solved in elementary functions, developed by combining ideas from topology, symmetry and Galois theory.
- pure-mathematics
- galois-theory
- topology
- +1
advanced
Temperley-Lieb Diagrams for Quantum Systems
Rachel Chen
Third place · Regeneron STS 2026
A diagrammatic representation of interacting quantum particle systems, using point-and-line diagrams to make the influence of magnetic fields visible in the structure itself.
- quantum-mechanics
- diagrammatic-algebra
- temperley-lieb
- +1
advanced
The unrestricted finite factorization property
Jonathan Du
Finalist · Regeneron STS 2026
Work in factorization theory on algebraic systems whose elements may factor in many ways or in none, extending the theory of when factorizations are finite.
- abstract-algebra
- factorization
- ring-theory
- +1
MathematicsPure Mathematics
advanced
A bound on similar structures in 3-uniform hypergraphs
Owen Jianwen Zhang
Second place · Regeneron STS 2025
A proof establishing a maximum for how many 3-uniform hypergraphs can share a structure while differing in their connections, resolving a question that had stood open, with applications in computer science.
- combinatorics
- hypergraphs
- extremal-combinatorics
- +1
advanced
Memory and Selfishness in the Prisoners Dilemma
Cory Seelenfreund
Third place · Regeneron ISEF 2025
Simulation and mathematical modelling of how memory length and degree of self-interest change outcomes in the iterated prisoner's dilemma, framed around implications for AI agent design.
- game-theory
- prisoners-dilemma
- agent-based-modelling
- +1