---
title: "Über den allgemeinen Plankalkül als Mittel zur Formulierung schematisch-kombinativer Aufgaben"
authors:
  - "Konrad Zuse"
year: 1948
venue: "Archiv der Mathematik"
arxiv: null
doi: "10.1007/BF02038459"
source: "https://doi.org/10.1007/BF02038459"
topics:
  - plankalkul
  - zuse
  - high-level-language
  - programming
seed_rank: 573
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "languages"
relevance_score: 9
lineage: foundations-of-computing
cites:
  - title: "The Education of a Computer"
    url: "https://doi.org/10.1145/609784.609798"
    year: 1952
    arxiv: null
    doi: "10.1145/609784.609798"
see:
  - "571-the-education-of-a-computer"
---

# Über den allgemeinen Plankalkül als Mittel zur Formulierung schematisch-kombinativer Aufgaben

## One-sentence takeaway

Zuse publishes Plankalkül as a general calculus for stating combinatorial plans — typed data, predicates, and algorithmic structure before Fortran.

## Why it matters here

High-level languages are not a 1957 invention. ano's typed plans sit in a lineage that already existed in Zuse's 1945 design, printed here in 1948/49.

## Key ideas

- Plankalkül is a notation for algorithms over structured values, not a machine-code assembler.
- Data types include bits, tuples, lists, and arrays; predicates and quantified conditions are first-class.
- Chess, sorting, and graph problems appear as worked "schematic-combinatorial" examples.
- Designed around 1945 in the Z3/Z4 context; war delayed publication until *Archiv der Mathematik* 1(6):441–449.
- The ZIB Zuse archive holds the manuscript scans; the DOI is the citable journal artifact.

## Caveats

## Links

- DOI: [10.1007/BF02038459](https://doi.org/10.1007/BF02038459)
- URL: https://doi.org/10.1007/BF02038459