MSC 13 · Algebra

Commutative rings & algebras

Ideal theory: rings, ideals, modules — the algebraic foundation of algebraic geometry.

Founded: 1871 — Dedekind's ideal theory

The claim

No credible dismissal found. Krull's ideal theory (1920s–30s) was, per MacTutor, “quickly recognised as a decisive advance.”

What happened

McEliece cryptosystem (1978) — Uses algebraic-geometry (Goppa) codes built on this machinery.
NIST post-quantum standards (2024) — Ring-LWE (2012) underlies CRYSTALS-Kyber/Dilithium, finalized as FIPS 203/204.

107 years — founding (1871) to first cryptographic use (1978)

Verdict: Never dismissed, applied anyway.

Confidence: medium-high.