ArticleslgStudy

mathematics

Paul Stäckel

Paul Stäckel 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 Paul Stäckel rather than just read about it. In short: Paul Gustav Samuel Stäckel (20 August 1862, Berlin – 12 December 1919, Heidelberg) was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term twin prime (in its German form, "Primzahlzwilling") for the first time.

Paul Stäckel — main illustration
Paul Stäckel — illustration

Key takeaways

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

Reference excerpt

Paul Gustav Samuel Stäckel (20 August 1862, Berlin – 12 December 1919, Heidelberg) was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term twin prime (in its German form, "Primzahlzwilling") for the first time. After passing his Abitur in 1880 he studied mathematics and physics at the University of Berlin, but also listened to lectures on philosophy, psychology, education, and history. A year later he qualified for teaching in higher education and then taught at Gymnasien in Berlin. In 1885 he wrote his doctoral dissertation under Leopold Kronecker and Karl Weierstraß. In 1891 he completed his Habilitation at the University of Halle. Later he worked as a professor at the University of Königsberg (außerordentlicher Professor from 1895 to 1897), the University of Kiel (ordentlicher Professor, 1897 to 1905), University of Hannover (1905 to 1908), the Karlsruhe Institute of Technology (1908 to 1913), and the University of Heidelberg (1913 to 1919). Stäckel worked on both mathematics and the history of mathematics. He edited the letters exchanged between Carl Friedrich Gauss and Wolfgang Bolyai, made contributions to editions of the collected works of Euler and Gauss (for whose works he wrote Gauss als Geometer), and edited the Geometrischen Untersuchungen by Wolfgang and Johann Bolyai (published in 1913). Additionally he translated works of Jacob Bernoulli, Johann Bernoulli, Augustin Louis Cauchy, Leonhard Euler, Joseph-Louis Lagrange, Adrien-Marie Legendre, Carl Gustav Jacobi from French and Latin into German for the series Ostwalds Klassiker der exakten Wissenschaften. In 1904 he was an invited speaker at the International Congress of Mathematicians in Heidelberg. In 1905 he was the president of the Deutsche Mathematiker-Vereinigung. His doctoral students include Paul Riebesell.

Works Über die Bewegung eines Punktes auf einer Fläche, 1885, Dissertation Die Integration der Hamilton-Jacobischen Differentialgleichung mittelst Separation der Variablen, 1891, Habilitation Elementare Dynamik der mathematischen Wissenschaft in: Encyclopädie der mathematischen Wissenschaft IV,1 (1908) several papers in the Mathematischen Annalen (from 1890 to 1909) numerous papers in "Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse" from 1896 to 1917. with Friedrich Engel: Theorie der Parallellinien von Euklid bis auf Gauss, 1895

References

External links O'Connor, John J.; Robertson, Edmund F., "Paul Stäckel", MacTutor History of Mathematics Archive, University of St Andrews Paul Stäckel at the Mathematics Genealogy Project Literature by and about Paul Stäckel in the German National Library catalogue http://geb.uni-giessen.de/geb/volltexte/2005/2127/ Briefnachlass von Paul Stäckel im Nachlass von Friedrich Engel

Illustrations

Paul Stäckel: Paul Stäckel.
Paul Stäckel.

Worked examples

Example 1 — a first encounter with Paul Stäckel

Start with the simplest possible case. Write down what Paul Stäckel 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 Paul Stäckel 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 Paul Stäckel 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 Paul Stäckel

In research
Paul Stäckel 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 Paul Stäckel 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
Paul Stäckel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1862 births, 1919 deaths, 19th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Paul Stäckel 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.
Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Paul Stäckel” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Paul Stäckel in 20 minutes

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

Frequently asked questions

What is Paul Stäckel in simple terms?

Paul Gustav Samuel Stäckel (20 August 1862, Berlin – 12 December 1919, Heidelberg) was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term twin prime (in its German form, "Primzahlzwill…

Why does Paul Stäckel 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 Paul Stäckel?

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 Paul Stäckel.

Tags

  • 1862 births
  • 1919 deaths
  • 19th-century German mathematicians
  • 20th-century German mathematicians
  • Academic staff of Heidelberg University
  • Academic staff of Leibniz University Hannover
  • Academic staff of the Karlsruhe Institute of Technology
  • Academic staff of the University of Kiel
  • Differential geometers
  • German historians of mathematics
  • German number theorists
  • Presidents of the German Mathematical Society

Keep exploring