Viggo Brun — LLMpedia

Viggo Brun
Peder O. Aune / NTNU UB · CC BY-SA 4.0 · source
Name	Viggo Brun
Birth date	13 October 1885
Birth place	Lillesand
Death date	15 August 1978
Death place	Oslo
Nationality	Norwegian
Fields	Mathematics, Number theory
Alma mater	University of Oslo
Known for	Brun sieve, Brun's theorem

Contents

Viggo Brun was a Norwegian mathematician notable for pioneering sieve methods in number theory and proving results about sums of primes. His work linked analytic techniques from complex analysis and asymptotic analysis to combinatorial approaches used in the study of prime number distribution. Brun influenced later developments in the Twin prime conjecture, the Goldbach conjecture, and sieve theory as advanced by researchers in France, United Kingdom, and the United States.

Early life and education

Brun was born in Lillesand and educated at the University of Oslo where he studied under leading Norwegian scientists associated with the Royal Norwegian Society of Sciences and Letters and scholars connected to the Nordic mathematical community. During his formative years he encountered works by Carl Friedrich Gauss, Adrien-Marie Legendre, Peter Gustav Lejeune Dirichlet, and Sophie Germain through curricula shaped by professors connected to the University of Copenhagen and the University of Göttingen traditions. Brun completed doctoral-level research influenced by analytic methods seen in the work of Bernhard Riemann, Godfrey Harold Hardy, J. E. Littlewood, and G. H. Hardy's collaborations with John Edensor Littlewood.

Brun held positions at Norwegian institutions including faculty roles at the University of Oslo and associations with the Norwegian Academy of Science and Letters. He participated in mathematical exchanges that involved figures from the Mathematical Institute, University of Göttingen, the École Normale Supérieure, and contacts with scholars from the Royal Society and the American Mathematical Society. Brun's interactions connected him indirectly with contemporaries such as Srinivasa Ramanujan, Émile Borel, Jacques Hadamard, G. H. Hardy, J. E. Littlewood, Harald Bohr, Frigyes Riesz, and later generations including Atle Selberg. He contributed to mathematical societies and conferences that brought together members of the International Mathematical Union and participants from the Warsaw School of Mathematics and the Italian school of algebraic geometry.

Brun developed the Brun sieve, an adaptation and refinement of earlier ideas originating with Viggo Brun's predecessors like Legendre and methods influenced by Sieve of Eratosthenes-style combinatorics combined with analytic inputs reminiscent of techniques used by G. H. Hardy and J. E. Littlewood. Brun's theorem established that the sum of reciprocals of twin primes converges, contrasting with the divergence of the sum of reciprocals of all prime numbers as shown by Euclid and refined by Leonhard Euler. Brun's work laid groundwork that influenced later sieve theoreticians such as Atle Selberg, Heinrich Selberg (note: Selberg is Atle Selberg), Alfréd Rényi, Paul Erdős, Ronald Graham, Enrico Bombieri, Harald Cramér, I. M. Vinogradov, Yuri Linnik, Henryk Iwaniec, John Friedlander, D. A. Goldston, and Daniel Goldston. The Brun sieve became a central tool used in later advances by Vaughan and Richert, and framed further progress represented by the Bombieri–Vinogradov theorem and developments culminating in partial results towards the Twin prime conjecture and the Goldbach conjecture.

Beyond the Brun sieve and Brun's theorem, Brun worked on problems linked to additive number theory, interacting conceptually with research themes from Additive number theory pioneers like Ivan Vinogradov, Paul Erdős, Pál Erdős, Paul Turán, J. E. Littlewood, and Harald Helfgott-era trajectories. His methods informed later work on arithmetic progressions explored by Ben Green and Terence Tao, and influenced combinatorial perspectives adopted by researchers in probabilistic number theory such as Andrew Granville and K. Soundararajan. Brun's approaches interfaced with algebraic number theory contributions from Richard Dedekind, Ernst Kummer, Helmut Hasse, and analytic frameworks used by Atle Selberg and Nikolai Korobov. His legacy can be traced in results touching on distribution of primes in short intervals studied by Maier and the study of prime gaps advanced by Yitang Zhang, James Maynard, and collaborators.

Brun received recognition from Norwegian institutions including membership in the Norwegian Academy of Science and Letters and honors from Scandinavian scientific societies linked to the Royal Norwegian Society of Sciences and Letters and the University of Oslo. His influence persists through named concepts such as the Brun sieve and Brun's constant which are central in contemporary discussions by mathematicians at the Institute for Advanced Study, Princeton University, Cambridge University, Oxford University, University of Chicago, Columbia University, Harvard University, and research groups at the Clay Mathematics Institute. Modern computational projects and analytic initiatives by teams at institutions like ETH Zurich, University of Bonn, Max Planck Institute for Mathematics, Institut Henri Poincaré, and the National Institute of Standards and Technology continue to reference Brun's results in the context of twin primes, prime gaps, and sieve refinements. Brun's work remains a cornerstone cited alongside achievements of Euler, Riemann, Hardy, Littlewood, Selberg, Erdős, and recent breakthroughs by Zhang and Maynard.

Category:Norwegian mathematicians Category:Number theorists Category:1885 births Category:1978 deaths