Andrzej Odrzywolek posted a new arXiv paper that demonstrates how the single elm function together with the constant 1 can generate every elementary function used in calculus. By repeatedly applying the elm construct, the author derives addition, subtraction, multiplication and division without any other primitives. The result offers a compact foundation for building mathematical libraries from a minimal core.

The supplemental material spells out explicit formulas that recover familiar constants such as π and build operations like squaring, square‑root, and the full suite of circular and hyperbolic functions. Because each of those entities emerges from the same two ingredients, developers can bootstrap a full‑featured math engine with dramatically fewer source files, simplifying verification and porting to constrained environments.

Practical implications stretch beyond academic curiosity. Compiler writers can replace hand‑crafted intrinsics with a single generic routine, while cryptographic code that relies on precise arithmetic gains a uniform reference implementation. By anchoring an entire function set to one definitional core, the approach also opens new avenues for formal proofs of correctness in safety‑critical software. It also reduces binary size for embedded targets.