MSC 33 · Analysis & probability

Special functions

Bessel, hypergeometric, and elliptic functions — named solutions of specific differential equations.

Founded: 1732 — Daniel Bernoulli's work on the hanging chain (an early Bessel-type equation)

The claim

No credible dismissal found. The Gauss “supreme uselessness” line sometimes attached here is about number theory, a different field, and is itself apocryphal (Hardy says so in the Apology). Bessel functions, hypergeometric series, and elliptic integrals were all motivated by concrete physical problems (pendulums, planetary perturbation, arc length) from the start.

What happened

Elliptic-curve cryptography (1985) — Abel & Jacobi's abstract elliptic-function theory (1827) sat as pure mathematics for 158 years before ECC — the one genuinely delayed pocket in an otherwise immediately-applied field.

158 years — Abel's elliptic functions (1827) to ECC (1985) — the field's one delayed sub-story; Bessel/hypergeometric functions were applied from birth

Verdict: Mixed / doesn't fit cleanly.

Confidence: medium.