astronomy

Otto Hölder

Otto Hölder is a astronomy 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 Otto Hölder rather than just read about it. In short: Ludwig Otto Hölder (December 22, 1859 – August 29, 1937) was a German mathematician born in Stuttgart. Early life and education Hölder was the youngest of three sons of professor Otto Hölder (1811–1890), and a grandson of professor Christian Gottlieb Hölder (1776–1847); his two brothers also became professors.

Key takeaways

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

Reference excerpt

Ludwig Otto Hölder (December 22, 1859 – August 29, 1937) was a German mathematician born in Stuttgart.

Early life and education Hölder was the youngest of three sons of professor Otto Hölder (1811–1890), and a grandson of professor Christian Gottlieb Hölder (1776–1847); his two brothers also became professors. He first studied at the Polytechnikum (which today is the University of Stuttgart) and then in 1877 went to Berlin where he was a student of Leopold Kronecker, Karl Weierstrass, and Ernst Kummer. In 1877, he entered the University of Berlin and took his doctorate from the University of Tübingen in 1882. The title of his doctoral thesis was "Beiträge zur Potentialtheorie" ("Contributions to potential theory"). Following this, he went to the University of Leipzig but was unable to habilitate there, instead earning a second doctorate and habilitation at the University of Göttingen, both in 1884.

Academic career and later life He was unable to get government approval for a faculty position in Göttingen, and instead was offered a position as extraordinary professor at Tübingen in 1889. Temporary mental incapacitation delayed his acceptance but he began working there in 1890. In 1899, he took the former chair of Sophus Lie as a full professor at the University of Leipzig. There he served as dean from 1912 to 1913, and as rector in 1918. He married Helene, the daughter of a bank director and politician, in 1899. They had two sons and two daughters. His son Ernst Hölder became another mathematician, and his daughter Irmgard married mathematician Aurel Wintner. In 1933, Hölder signed the Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State.

Mathematical contributions Hölder's inequality, named for Hölder, was actually proven earlier by Leonard James Rogers. It is named for a paper in which Hölder, citing Rogers, reproves it; in turn, the same paper includes a proof of what is now called Jensen's inequality, with some side conditions that were later removed by Jensen. Hölder is also noted for many other theorems including the Jordan–Hölder theorem, the theorem stating that every linearly ordered group that satisfies an Archimedean property is isomorphic to a subgroup of the additive group of real numbers, the classification of simple groups of order up to 200, the anomalous outer automorphisms of the symmetric group S6, and Hölder's theorem, which implies that the Gamma function satisfies no algebraic differential equation. Another idea related to his name is the Hölder condition (or Hölder continuity), which is used in many areas of analysis, including the theories of partial differential equations and function spaces.

References

Illustrations

Worked examples

Example 1 — a first encounter with Otto Hölder

Start with the simplest possible case. Write down what Otto Hölder claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Otto Hölder 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 Otto Hölder 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 Otto Hölder

In research: Otto Hölder appears in astronomy 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 Otto Hölder 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: Otto Hölder is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1859 births, 1937 deaths, 19th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Otto Hölder 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 Otto Hölder in 20 minutes

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

Frequently asked questions

What is Otto Hölder in simple terms?

Ludwig Otto Hölder (December 22, 1859 – August 29, 1937) was a German mathematician born in Stuttgart. Early life and education Hölder was the youngest of three sons of professor Otto Hölder (1811–1890), and a grandson of professor Christian Gottlieb Hölder (1776–1847); his two brothers also became…

Why does Otto Hölder matter?

Because it connects several astronomy 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 Otto Hölder?

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 Otto Hölder.