astronomy

Jürgen Neukirch

Jürgen Neukirch 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 Jürgen Neukirch rather than just read about it. In short: Jürgen Neukirch (24 July 1937 – 5 February 1997) was a German mathematician known for his work on algebraic number theory. Education and career Neukirch received his diploma in mathematics in 1964 from the University of Bonn.

Key takeaways

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

Reference excerpt

Jürgen Neukirch (24 July 1937 – 5 February 1997) was a German mathematician known for his work on algebraic number theory.

Education and career Neukirch received his diploma in mathematics in 1964 from the University of Bonn. For his Ph.D. thesis, written under the direction of Wolfgang Krull, he was awarded in 1965 the Felix-Hausdorff-Gedächtnis-Preis. He completed his habilitation one year later. From 1967 to 1969 he was guest professor at Queen's University in Kingston, Ontario and at the Massachusetts Institute of Technology in Cambridge, Massachusetts, after which he was a professor in Bonn. In 1971 he became a professor at the University of Regensburg.

Contributions He is known for his work on the embedding problem in algebraic number theory, the Báyer–Neukirch theorem on special values of L-functions, arithmetic Riemann existence theorems and the Neukirch–Uchida theorem in birational anabelian geometry. He gave a simple description of the reciprocity maps in local and global class field theory.

Books Neukirch wrote three books on class field theory, algebraic number theory, and the cohomology of number fields:

Neukirch, Jürgen (1986). Class Field Theory. Grundlehren der Mathematischen Wissenschaften. Vol. 280. Berlin: Springer-Verlag. ISBN 3-540-15251-2. Neukirch, Jürgen (1999). Algebraic Number Theory. Grundlehren der Mathematischen Wissenschaften. Vol. 322. Springer-Verlag. ISBN 978-3-540-65399-8. Zbl 0956.11021. Neukirch, Jürgen; Schmidt, Alexander; Wingberg, Kay (2008). Cohomology of Number Fields. Grundlehren der Mathematischen Wissenschaften. Vol. 323 (2nd ed.). Springer-Verlag. ISBN 978-3-540-37888-4. Zbl 1136.11001. Neukirch, Jürgen (2013). Class Field Theory — The Bonn Lectures. Springer. ISBN 978-3-642-35436-6.

Notes

External links Jürgen Neukirch at the Mathematics Genealogy Project On Neukirch's death (in German) Literature by and about Jürgen Neukirch in the German National Library catalogue

Illustrations

Worked examples

Example 1 — a first encounter with Jürgen Neukirch

Start with the simplest possible case. Write down what Jürgen Neukirch 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 Jürgen Neukirch 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 Jürgen Neukirch 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 Jürgen Neukirch

In research: Jürgen Neukirch 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 Jürgen Neukirch 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: Jürgen Neukirch is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1937 births, 1997 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jürgen Neukirch 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 Jürgen Neukirch in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Jürgen Neukirch 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.
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Frequently asked questions

What is Jürgen Neukirch in simple terms?

Jürgen Neukirch (24 July 1937 – 5 February 1997) was a German mathematician known for his work on algebraic number theory. Education and career Neukirch received his diploma in mathematics in 1964 from the University of Bonn.

Why does Jürgen Neukirch 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 Jürgen Neukirch?

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 Jürgen Neukirch.