mathematics

Viggo Brun

Viggo Brun 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 Viggo Brun rather than just read about it. In short: Viggo Brun (13 October 1885 – 15 August 1978) was a Norwegian professor, mathematician and number theorist. He is known for his work in the twin prime conjecture.

Key takeaways

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

Reference excerpt

Viggo Brun (13 October 1885 – 15 August 1978) was a Norwegian professor, mathematician and number theorist. He is known for his work in the twin prime conjecture. Brun's theorem shows that sum of the reciprocals of the twin primes converges.

Biography

Brun was born at Lier in Buskerud, Norway. He studied at the University of Oslo and began research at the University of Göttingen in 1910. In 1923, Brun became a professor at the Technical University in Trondheim and in 1946 a professor at the University of Oslo. He retired in 1955 at the age of 70 and died in 1978 (at 92 years-old) at Drøbak in Akershus, Norway.

Contributions In 1915, he introduced a new method, based on Legendre's version of the sieve of Eratosthenes, now known as the Brun sieve, which addresses additive problems such as Goldbach's conjecture and the twin prime conjecture. He used it to prove that there exist infinitely many integers n such that n and n+2 have at most nine prime factors, and that all large even integers are the sum of two numbers with at most nine prime factors. He also showed that the sum of the reciprocals of twin primes converges to a finite value, now called Brun's constant. In contrast, the sum of the reciprocals of all primes is divergent. He developed a multi-dimensional continued fraction algorithm in 1919–1920 and applied this to problems in musical theory. He also served as praeses of the Royal Norwegian Society of Sciences and Letters in 1946.

See also Brun's theorem Brun–Titchmarsh theorem Brun sieve Sieve theory

References

Other sources H. Halberstam and H. E. Richert, Sieve methods, Academic Press (1974) ISBN 0-12-318250-6. Gives an account of Brun's sieve. C.J. Scriba, Viggo Brun, Historia Mathematica 7 (1980) 1–6. C.J. Scriba, Zur Erinnerung an Viggo Brun, Mitt. Math. Ges. Hamburg 11 (1985) 271-290

External links O'Connor, John J.; Robertson, Edmund F., "Viggo Brun", MacTutor History of Mathematics Archive, University of St Andrews Brun's Constant Brun's Pure Sieve Viggo Brun personal archive exists at NTN University Library Dorabiblioteket

Illustrations

Viggo Brun: Viggo Brun (published in 1911) — Viggo Brun (published in 1911)

Worked examples

Example 1 — a first encounter with Viggo Brun

Start with the simplest possible case. Write down what Viggo Brun 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 Viggo Brun 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 Viggo Brun 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 Viggo Brun

In research: Viggo Brun 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 Viggo Brun 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: Viggo Brun is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1885 births, 1978 deaths, 20th-century Norwegian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Viggo Brun 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 Viggo Brun in 20 minutes

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

Frequently asked questions

What is Viggo Brun in simple terms?

Viggo Brun (13 October 1885 – 15 August 1978) was a Norwegian professor, mathematician and number theorist. He is known for his work in the twin prime conjecture.

Why does Viggo Brun 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 Viggo Brun?

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 Viggo Brun.