mathematics

József Kürschák

József Kürschák 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 József Kürschák rather than just read about it. In short: József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed.

Key takeaways

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

Reference excerpt

József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed. In 1918 he proved that the sum of reciprocals of consecutive natural numbers is never a natural number. Extending Hilbert's argument, he proved that everything that can be constructed using a ruler and a compass, can be constructed by using a ruler and the ability to copy a fixed segment. He was elected a member of the Hungarian Academy of Sciences in 1897. He was one of the main organisers of mathematics competitions, for example, Eötvös Loránd mathematics competition.

Biography He was born in Buda to András Kürschák and Jozefa Teller. After completing high school, he studied physics and mathematics from 1881 to 1886 at the Royal University of Pest, where he was a pupil of Gyula Kőnig and Jenő Hunyady. At the same time, as a member of the Budapest Secondary School Teacher Training Institute, he also visited philosophical and literary performances at the university. In 1886, he started his career as a deputy teacher at Fazekas Mihály Gimnázium in Debrecen, but in the same year, taking advantage of the opportunity, he was a probationary candidate in the grammar school of the Budapest Secondary School Teacher Training Institute. He taught at the Gimnázium until 1888 and at that time also graduated from the Budapest University of Science with a mathematics-physics degree. He became a teacher at the Primary Grammar School in Rozsnyó (today Rožňava, Slovakia). In 1890 he obtained his doctoral degree and in 1890–1981 he was deputy teacher at the Markó street public high school. In 1891 he obtained a degree in mathematics at the Royal Joseph University of Budapest, where he taught until his death. At first he did not give up on high school education, continuing to teach from 1893 to 1896. In 1891–1892, he worked as an assistant professor of geometry. From 1904 he taught as a public lecturer in mathematics at the university. From 1906 to 1909 he was the Dean of the Department of General and Chemical Engineering, and between 1916 and 1918 he was the rector of the University of Art and Design.

References

Illustrations

Worked examples

Example 1 — a first encounter with József Kürschák

Start with the simplest possible case. Write down what József Kürschák 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 József Kürschák 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 József Kürschák 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 József Kürschák

In research: József Kürschák 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 József Kürschák 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: József Kürschák is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1864 births, 1933 deaths, 19th-century Hungarian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for József Kürschák 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 “József Kürschák” →

Affiliate

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

How to study József Kürschák in 20 minutes

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

Frequently asked questions

What is József Kürschák in simple terms?

Why does József Kürschák 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 József Kürschák?

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 József Kürschák.