mathematics

Karl Schröter

Karl Schröter is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Karl Schröter rather than just read about it. In short: Karl Walter Schröter (7 September 1905 in Biebrich near Wiesbaden – 22 August 1977 in Berlin) was a German mathematician and logician. Later on, after the war, he made important contributions concerning semantic consequences (German: semantische Folgerungsrelationen) and provability logic (German: syntaktische Ableitbarkeitsrelationen).

Key takeaways

Karl Schröter belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Karl Schröter to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Karl Schröter from memory before moving on to harder problems.

Reference excerpt

Karl Walter Schröter (7 September 1905 in Biebrich near Wiesbaden – 22 August 1977 in Berlin) was a German mathematician and logician. Later on, after the war, he made important contributions concerning semantic consequences (German: semantische Folgerungsrelationen) and provability logic (German: syntaktische Ableitbarkeitsrelationen). He worked as a mathematical theoretician and cryptanalyst for the civilian Pers Z S, the cipher bureau of the Foreign Office (German: Auswärtiges Amt), from the spring of 1941 to the end of World War II.

Education From 1928 to 1936, Schröter studied mathematics, physics, philosophy, and psychology at the Universities of Göttingen, Heidelberg and Frankfurt am Main. Due to family reasons he had to interrupt his studies several times. He then worked in the mathematical logic group at the University of Münster led by Heinrich Scholz. From 1 April 1939 he was a research assistant at the Department of Philosophy at the University of Münster. On 20 December 1941 he took his examination for promotion of Dr. phil under the logician Heinrich Scholz studying mathematics, logic, and calculus with a thesis titled Ein allgemeiner Kalkülbegriff (English: A General Concept of Calculus). On 1 April 1941 he took a leave of absence to join Pers Z S, the Foreign Office civilian cipher bureau, working as a mathematician. However, even during this time he continued to work on problems of basic mathematical research.

Career On 19 March 1943 he presented the application to the Faculty of Philosophy and Natural Sciences, with the publication Axiomatisierung der Fregeschen Aussagenkalküle (English: Axiomatisation of Frege's Propositional Calculus), to be admitted to his Habilitation. On the basis of the positive opinions of Heinrich Scholz and Adolf Kratzer, the degree of Doctor rerum naturalium habilitatus was awarded to him by certificate of 22 May 1943. On 9 June 1943 the report on the completed Habilitation was given to the Reich Minister. On 1, 2 and 3 July 1943 he held a public trial lecture on the topic Der Nutzen der mathematischen Logik für die Mathematik (English: The Benefits of Mathematical Logic for Mathematics) as a prerequisite for a civil service position as a lecturer. On 18 August 1943 he was appointed lecturer with the authorisation to teach "Mathematical Logic and Fundamental Research", all the while still being employed in Berlin as a "scientific assistant worker" at Pers Z S. Karl Schröter remained at the University of Münster from 31 December 1943 until his contract was up on 31 April 1945, when he was taken prisoner by the Counterintelligence Corps (CIC). From early May to 30 September 1945 he appeared before a joint Anglo-American Commission, first in London, then in Marburg, concerning his work at Pers Z S during the war. After completion, he was dismissed in Marburg after the CIC had determined his political attitude. In the winter semester of 1945/46 he was affiliated as a lecturer in Münster. From May 1946 until his appointment to Berlin, Schröter was working at Münster as a substitute for the Review Committee of the Denazification Main Committee at the Westfälische Landesuniversität. In 1948, Karl Schröter was appointed Professor Extraordinarius for mathematical logic at Humboldt University in Berlin. In 1967, he became director of the Institute for pure mathematics of the German Academy of Sciences at Berlin. He was elected corresponding member in 1962 and two years later ordinary member of the German Academy of Sciences at Berlin. In 1955, Schröter together with Günter Asser founded the Zeitschrift für Mathematische Logik und Grundlagen der Mathematik (English: Journal of mathematical logic and foundations of mathematics) which since 1991 is known as Mathematical Logic Quarterly.

Publications Schröter, Karl (1941). Ein allgemeiner Kalkülbegriff [A General Concept of Calculus]. Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften, Neue Folge. Heft 6 (Dissertation, Philosophische und Naturwissenschaftliche Fakultät, Universität Münster, 1941) (in German). Leipzig: S. Hirzel. Schröter, Karl (1943). Axiomatisierung der Fregeschen Aussagenkalküle [Axiomatisation of Frege's Propositional Calculus]. Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften, Neue Folge. Heft 8 (in German). Leipzig: S. Hirzel.

References

External links Mathematical Logic Quarterly

Worked examples

Example 1 — a first encounter with Karl Schröter

Start with the simplest possible case. Write down what Karl Schröter claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Karl Schröter before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Karl Schröter ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Karl Schröter

In research: Karl Schröter appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Karl Schröter in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Karl Schröter is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1905 births, 1977 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Karl Schröter outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Karl Schröter in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Karl Schröter means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Karl Schröter out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Karl Schröter in simple terms?

Why does Karl Schröter matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Karl Schröter?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Karl Schröter.