mathematics

Rudolf Fueter

Rudolf Fueter 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 Rudolf Fueter rather than just read about it. In short: Karl Rudolf Fueter (30 June 1880 – 9 August 1950) was a Swiss mathematician, known for his work on number theory. Biography After a year of graduate study of mathematics in Basel, Fueter began study in 1899 at the University of Göttingen and completed his Promotion in 1903 with dissertation Der Klassenkörper der quadratischen Körper und die komplexe Multiplikation under David Hilbert.

Key takeaways

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

Reference excerpt

Karl Rudolf Fueter (30 June 1880 – 9 August 1950) was a Swiss mathematician, known for his work on number theory.

Biography After a year of graduate study of mathematics in Basel, Fueter began study in 1899 at the University of Göttingen and completed his Promotion in 1903 with dissertation Der Klassenkörper der quadratischen Körper und die komplexe Multiplikation under David Hilbert. After his Promotion, Fueter studied for 1 year in Paris, 3 months in Vienna, and 6 months in London. In 1905 he completed his Habilitierung at the University of Marburg. Fueter worked as a docent in 1907/1908 at Marburg and in the winter of 1907/1908 at the Bergakademie Clausthal. He was called to positions as professor ordinarius in 1908 at Basel, in 1913 at the Technische Hochschule Karlsruhe, and in 1916 at the University of Zurich. From 1920 to 1922 he was the rector of the University of Zurich. Fueter did research on algebraic number theory and quaternion analysis proposing a definition of ‘regular’ for quaternionic functions similar to the definition of holomorphic function by means of an analogue of the Cauchy-Riemann equations. He also published a proof of the Fueter–Pólya theorem with George Pólya. In 1910 he was one of the founders of the Swiss Mathematical Society and he became its first president. With Andreas Speiser he was instrumental in the editing and publication of the collected works of Leonhard Euler and from 1927 he was the head of the Euler Commission. He gave plenary lectures at the International Congress of Mathematicians in 1932 at Zurich (Idealtheorie und Funktionentheorie) and in 1936 at Oslo (Die Theorie der regulären Funktionen einer Quaternionenvariablen). During WWII he was a colonel of artillery in the Swiss army, an outspoken opponent of German National Socialism, and an advocate for freedom of the press. Fueter was an editor for the Commentarii Mathematici Helvetici. Fueter married in 1908 and had a daughter.

Selected works Synthetische Zahlentheorie. 3rd edition DeGruyter, Berlin 1930 (1st edition 1917). Vorlesungen über die singulären Moduln und die komplexe Multiplikation der elliptischen Funktionen. Teubner, Leipzig 1924/1927 142 pages 1924. pp. 144–358. 1927. Das mathematische Werkzeug des Chemikers, Biologen, Statistikers und Soziologen. Vorlesung über die höheren mathematischen Begriffe in Verbindung mit ihren Anwendungen (publ. Schweizerische Mathematische Gesellschaft; vol. 3). 3rd edition Orell Füssli, Zürich 1947 (1st edition 1926). Der Klassenkörper der quadratischen Körper und die complexe Multiplication. Dieterich, Göttingen 1903 (Dissertation, Universität Göttingen 1903). Die Theorie der Zahlenstrahlen. Reimer, Berlin 1905 (Habilitationsschrift, University of Marburg 1905).

Sources Johann Jakob Burckhardt (1961). "Fueter, Karl Rudolf". Neue Deutsche Biographie (in German). Vol. 5. Berlin: Duncker & Humblot. p. 707. (full text online). Siegfried Gottwald, Hans-Joachim Ilgauds, Karl-Heinz Schlote (eds.): Lexikon bedeutender Mathematiker. Verlag Deutsch, Thun 1990, ISBN 3-8171-1164-9.

References

External links Works by or about Rudolf Fueter at the Internet Archive Literature by and about Rudolf Fueter in the German National Library catalogue O'Connor, John J.; Robertson, Edmund F., "Rudolf Fueter", MacTutor History of Mathematics Archive, University of St Andrews

Illustrations

Worked examples

Example 1 — a first encounter with Rudolf Fueter

Start with the simplest possible case. Write down what Rudolf Fueter 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 Rudolf Fueter 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 Rudolf Fueter 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 Rudolf Fueter

In research: Rudolf Fueter 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 Rudolf Fueter 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: Rudolf Fueter is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1880 births, 1950 deaths, 20th-century Swiss mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Rudolf Fueter 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 Rudolf Fueter in 20 minutes

Read the reference excerpt below once, without taking notes.
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Frequently asked questions

What is Rudolf Fueter in simple terms?

Karl Rudolf Fueter (30 June 1880 – 9 August 1950) was a Swiss mathematician, known for his work on number theory. Biography After a year of graduate study of mathematics in Basel, Fueter began study in 1899 at the University of Göttingen and completed his Promotion in 1903 with dissertation Der Kla…

Why does Rudolf Fueter 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 Rudolf Fueter?

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 Rudolf Fueter.