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Issai Schur

Issai Schur 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 Issai Schur rather than just read about it. In short: Issai Schur (10 January 1875 – 10 January 1941) was a Russian mathematician who worked in Germany for most of his life. He studied at the University of Berlin.

Issai Schur — main illustration
Issai Schur — illustration

Key takeaways

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

Reference excerpt

Issai Schur (10 January 1875 – 10 January 1941) was a Russian mathematician who worked in Germany for most of his life. He studied at the University of Berlin. He obtained his doctorate in 1901, became lecturer in 1903 and, after a stay at the University of Bonn, professor in 1919. As a student of Ferdinand Georg Frobenius, he worked on group representations (the subject with which he is most closely associated), but also in combinatorics and number theory and even theoretical physics. He is perhaps best known today for his result on the existence of the Schur decomposition and for his work on group representations (Schur's lemma). Schur published under the name of both I. Schur, and J. Schur, the latter especially in Journal für die reine und angewandte Mathematik. This has led to some confusion.

Childhood Issai Schur was born into a Jewish family, the son of the businessman Moses Schur and his wife Golde Schur (née Landau). He was born in Mogilev on the Dnieper River in what was then the Russian Empire. Schur used the name Schaia (Isaiah as the epitaph on his grave) rather than Issai up in his middle twenties. Schur's father may have been a wholesale merchant. In 1888, at the age of 13, Schur went to Liepāja (Courland, now in Latvia), where his married sister and his brother lived, 640 km north-west of Mogilev. Courland was one of the three Baltic governorates of Tsarist Russia, and since the Middle Ages the Baltic Germans were the upper social class. The local Jewish community spoke mostly German and not Yiddish. Schur attended the German-speaking Nicolai Gymnasium in Libau from 1888 to 1894 and reached the top grade in his final examination, and received a gold medal. Here he became fluent in German.

Education In October 1894, Schur attended the University of Berlin, with concentration in mathematics and physics. In 1901, he graduated summa cum laude under Frobenius and Lazarus Immanuel Fuchs with his dissertation On a class of matrices that can be assigned to a given matrix, which contains a general theory of the representation of linear groups. According to Vogt, he began to use the name Issai at this time. Schur thought that his chance of success in the Russian Empire was rather poor, and because he spoke German so perfectly, he remained in Berlin. He graduated in 1903 and was a lecturer at the University of Berlin. Schur held a position as professor at the Berlin University for the ten years from 1903 to 1913. In 1913 he accepted an appointment as associate professor and successor of Felix Hausdorff at the University of Bonn. In the following years Frobenius tried various ways to get Schur back to Berlin. Among other things, Schur's name was mentioned in a letter dated 27 June 1913 from Frobenius to Robert Gnehm (the School Board President of the ETH) as a possible successor to Carl Friedrich Geiser. Frobenius complained that they had never followed his advice before and then said: "That is why I can't even recommend Prof. J. Schur (now in Bonn) to you. He's too good for Zurich, and should be my successor in Berlin". Hermann Weyl got the job in Zurich. The efforts of Frobenius were finally successful in 1916, when Schur succeeded Johannes Knoblauch as adjunct professor. Frobenius died a year later, on 3 August 1917. Schur and Carathéodory were both named as the frontrunners for his successor. But they chose Constantin Carathéodory in the end. In 1919 Schur finally received a personal professorship, and in 1921 he took over the chair of the retired Friedrich Hermann Schottky. In 1922, he was also added to the Prussian Academy of Sciences.

During the time of Nazism After the takeover by the Nazis and the elimination of the parliamentary opposition, the Law for the Restoration of the Professional Civil Service on 7 April 1933, prescribed the release of all distinguished public servants that held unpopular political opinions or who were "Jewish" in origin; a subsequent regulation extended this to professors and therefore also to Schur. Schur was suspended and excluded from the university system. His colleague Erhard Schmidt fought for his reinstatement, and since Schur had been a Prussian official before the First World War, he was allowed to participate in certain special lectures on teaching in the winter semester of 1933/1934 again. Schur withdrew his application for leave from the Science Minister and passed up the offer of a visiting professorship at the University of Wisconsin–Madison for the academic year 1933–34. One element that likely played a role in the rejection of the offer was that Schur no longer felt he could cope with the requirements that would have come with a new beginning in an English-speaking environment. Already in 1932, Schur's daughter Hilde had married the doctor Chaim Abelin in Bern. As a result, Issai Schur visited his daughter in Bern several times. In Zurich he met often with George Pólya, with whom he was on friendly terms since before the First World War. On such a trip to Switzerland in the summer of 1935, a letter reached Schur from Ludwig Bieberbach signed on behalf of the Rector's, stating that Schur should urgently seek him out in the University of Berlin. They needed to discuss an important matter with him. It involved Schur's dismissal on 30 September 1935. Schur remained a member of the Prussian Academy of Sciences after his release as a professor, but a little later he lost this last remnant of his official position. Due to an intervention from Bieberbach in the spring of 1938 he was forced to explain his resignation from the commission of the Academy. His membership in the Advisory Board of Mathematische Zeitschrift was ended in early 1939.

Emigration

… excerpt ends here. Continue reading the full article.

Illustrations

Issai Schur illustration
Issai Schur: Schur's grave at Trumpeldor Cemetery
Schur's grave at Trumpeldor Cemetery

Worked examples

Example 1 — a first encounter with Issai Schur

Start with the simplest possible case. Write down what Issai Schur 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 Issai Schur 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 Issai Schur 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 Issai Schur

In research
Issai Schur 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 Issai Schur 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
Issai Schur is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1875 births, 1941 deaths, 19th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Issai Schur 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 Issai Schur in 20 minutes

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

Frequently asked questions

What is Issai Schur in simple terms?

Issai Schur (10 January 1875 – 10 January 1941) was a Russian mathematician who worked in Germany for most of his life. He studied at the University of Berlin.

Why does Issai Schur 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 Issai Schur?

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 Issai Schur.

Tags

  • 1875 births
  • 1941 deaths
  • 19th-century German mathematicians
  • 20th-century German mathematicians
  • Academic staff of the Humboldt University of Berlin
  • Academic staff of the University of Bonn
  • Belarusian Jews
  • Burials at Trumpeldor Cemetery
  • Combinatorialists
  • Corresponding Members of the USSR Academy of Sciences
  • Deaths from coronary artery disease
  • Emigrants from the Russian Empire to Germany

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