Solvability of Equations in Elementary Functions
Nikola Veselinov · Sofia, Bulgaria
Regeneron Young Scientist Award ($75,000) · Regeneron International Science and Engineering Fair · 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.
Impossibility results are unusually strong for a fair project: there is no dataset to argue with and no measurement to challenge. The work is in the proof, and the proof either holds or it does not.
- Galois theory
- Topological argument
- Symmetry analysis
- Theorem construction and proof
- A theorem is judged on whether the argument closes, which is a different kind of rigour from an experiment
- Combining tools from separate branches of mathematics is where new results usually come from
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