mathematics

Paul Funk

Paul Funk 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 Funk rather than just read about it. In short: Paul Georg Funk (14 April 1886, Vienna – 3 June 1969, Vienna) was an Austrian mathematician who introduced the Funk transform and who worked on the calculus of variations. Biography Born in Vienna in 1886, Paul Funk was the son of a deputy bank manager and went to high school in Baden and Gmunden.

Key takeaways

Paul Funk 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 Funk to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Paul Funk from memory before moving on to harder problems.

Reference excerpt

Paul Georg Funk (14 April 1886, Vienna – 3 June 1969, Vienna) was an Austrian mathematician who introduced the Funk transform and who worked on the calculus of variations.

Biography Born in Vienna in 1886, Paul Funk was the son of a deputy bank manager and went to high school in Baden and Gmunden. Then, studied mathematics in Tübingen, Vienna, and Göttingen, writing his PhD dissertation (Über Flächen mit lauter geschlossenen geodätischen Linien, 'On surfaces with many closed geodesic lines') under the supervision of David Hilbert. He got his PhD in 1911 and spent the interwar years (1915-1939) in Prague as Professor of Mathematics at the Deutsche Technische Hochschule Prag. He became an associate professor in 1921 and a professor in 1927. Suspended from his professorship in 1939 on account of his being Jewish, Funk was deported to the Theresienstadt concentration camp in 1944, where he spent the last months of the war. He was freed in 1945 and became professor at TU Wien. He died in Vienna on 3 June, 1969. He was buried at Neustift Cemetery.

Major publications Funk, Paul (1962), Variationsrechnung und ihre Anwendung in Physik und Technik, Die Grundlehren der mathematischen Wissenschaften (in German), vol. 94, Berlin, New York: Springer-Verlag, ISBN 978-3-540-04830-5, MR 0152914{{citation}}: CS1 maint: ignored ISBN errors (link)

References

Basch, A. (1956). "Paul Funk zum 70. Geburtstag". Österreich Ingenieur-Archiv. 10: 117–119. MR 0080050. Dann, Susanna (2010), On the Minkowski-Funk Transform, arXiv:1003.5565, Bibcode:2010arXiv1003.5565D Hornich, S. H. (1970). "Nachruf auf Paul Funk". Almanach der Akademie der Wissenschaften in Wien. 119: 271–277. Maximilian Pinl: Kollegen in dunkler Zeit. Jahresbericht DMV Bd.75, 1974, S.172.

External links Literature by and about Paul Funk in the German National Library catalogue

Maple Transactions, Vol. 4 No. 3 (2024): Autumn Issue / Student Corner: "An Investigation of the Funk Transform" by Tobias Funk from Claremont McKenna College who is also grand grandson of Paul Funk. DOI: https://doi.org/10.5206/mt.v4i3.21612

Worked examples

Example 1 — a first encounter with Paul Funk

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

In research: Paul Funk 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 Funk 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 Funk is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1886 births, 1969 deaths, 20th-century Austrian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Paul Funk 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.

Affiliate

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

How to study Paul Funk in 20 minutes

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

Frequently asked questions

What is Paul Funk in simple terms?

Paul Georg Funk (14 April 1886, Vienna – 3 June 1969, Vienna) was an Austrian mathematician who introduced the Funk transform and who worked on the calculus of variations. Biography Born in Vienna in 1886, Paul Funk was the son of a deputy bank manager and went to high school in Baden and Gmunden.

Why does Paul Funk 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 Funk?

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 Funk.