mathematics

Kurt Schütte

Kurt Schütte 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 Kurt Schütte rather than just read about it. In short: Kurt Schütte (14 October 1909 – 18 August 1998) was a German mathematician who worked on proof theory and ordinal analysis. The Feferman–Schütte ordinal, which he showed to be the precise ordinal bound for predicativity, is named after him.

Key takeaways

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

Reference excerpt

Kurt Schütte (14 October 1909 – 18 August 1998) was a German mathematician who worked on proof theory and ordinal analysis. The Feferman–Schütte ordinal, which he showed to be the precise ordinal bound for predicativity, is named after him. He was the doctoral advisor of 16 students, including Wolfgang Bibel, Wolfgang Maaß, Wolfram Pohlers, and Martin Wirsing. He made important contributions to the proof theory of systems with the ω-rule, and made progress towards solving Takeuti's conjecture.

Biography Kurt Wilhelm Schütte was born on 14 October 1909 in Salzwedel, Germany as the son of August Schütte and Martha Schütte (née Schröder). From 1916 to 1919, he attended the preschool of the Francisceum gymnasium in Zerbst, and from 1920 to 1928 attended the König Wilhelms-Gymnasium in Magdeburg. Schütte studied math, physics, chemistry, and philosophy at the University of Göttingen, and got a doctorate degree in math with David Hilbert as his advisor, being Hilbert's last doctoral student. he worked as a meteorologist for the Reichswetterdienst (Reich Weather Service) from 1937 until the end of World War II. In 1937 he married Hanna Lechte, with whom he had two daughters: Sigrid (born 1939) and Gisela (born 1942). Later in life, Schütte became blind and used a tape recording device to write mathematical work. He died of a heart attack in 1998.

Publications Schütte, Kurt (1977), Proof theory, Grundlehren der Mathematischen Wissenschaften, vol. 225, Berlin-New York: Springer-Verlag, pp. xii+299, ISBN 3-540-07911-4, MR 0505313 Beweistheorie, Springer, Grundlehren der mathematischen Wissenschaften, 1960; new edition trans. into English as Proof Theory, Springer-Verlag 1977 Vollständige Systeme modaler und intuitionistischer Logik, Springer 1968 with Wilfried Buchholz: Proof Theory of Impredicative Subsystems of Analysis, Bibliopolis, Naples 1988 with Helmut Schwichtenberg: Mathematische Logik, in Fischer, Hirzebruch et al. (eds.) Ein Jahrhundert Mathematik 1890-1990, Vieweg 1990

References

Pohlers, Wolfram (2000), "In Memoriam: Kurt Schütte, 1909-1998", The Bulletin of Symbolic Logic, 6 (1): 101–102, doi:10.1017/S1079898600008817, JSTOR 421083 Wilfried Buchholz (2007). "Schütte, Kurt". Neue Deutsche Biographie (in German). Vol. 23. Berlin: Duncker & Humblot. pp. 653–654. (full text online).

External links Kurt Schütte at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Kurt Schütte

Start with the simplest possible case. Write down what Kurt Schütte 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 Kurt Schütte 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 Kurt Schütte 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 Kurt Schütte

In research: Kurt Schütte 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 Kurt Schütte 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: Kurt Schütte is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1909 births, 1998 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kurt Schütte 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 Kurt Schütte in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Kurt Schütte 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 Kurt Schütte out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Kurt Schütte in simple terms?

Why does Kurt Schütte 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 Kurt Schütte?

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 Kurt Schütte.