All Elementary Functions from a Single Binary Operator¶
arXiv: 2603.21852
Researchers have discovered that all elementary functions can be constructed from a single binary operator. This paper in Symbolic Computation (cs.SC) with connections to Machine Learning (cs.LG) shows a fundamental reduction in mathematical primitives.
Overview¶
The paper presents a significant theoretical contribution to mathematical foundations by demonstrating that the entire edifice of elementary functions — trigonometric, exponential, logarithmic, and all their combinations — can be built from just one binary operator.
Key Details¶
- Subjects: Symbolic Computation (cs.SC), Machine Learning (cs.LG)
- MSC Classification: 26A09 (Primary), 08A40, 68W30 (Secondary)
- ACM Classification: I.1.1, F.1.1
- Code: Available at Zenodo
- Supplementary Information: Included
- Figures: Two figures
Significance¶
While the abstract is brief, this work represents a profound theoretical simplification. By showing that everything can be built from a single binary operator, the paper fundamentally simplifies the set of required mathematical operations, with potential implications for symbolic computation systems, machine learning architectures, and our understanding of mathematical primitives.