Peter Ludwig Mejdell Sylow
Who was Peter Ludwig Mejdell Sylow?
Norwegian mathematician (1832-1918)
Biographical data adapted from Wikipedia’s article on Peter Ludwig Mejdell Sylow (CC BY-SA 4.0).
Biography
Peter Ludvig Meidell Sylow was born on December 12, 1832, in Oslo, Norway, and died there on September 7, 1918. He is best known for proving important theorems in group theory, published in 1872 in Mathematische Annalen. These results, known as the Sylow theorems, set conditions for when a finite group must have subgroups of certain orders, called Sylow subgroups or p-groups. The theorems are still key to studying finite groups and are taught in abstract algebra courses worldwide.
Sylow went to Oslo Cathedral School and studied at the University of Oslo and the University of Copenhagen. Although he showed great mathematical talent early on, he spent most of his career teaching at the Fredrikshald Latin School in Frederikshald, from 1858 to 1898. Even though he was not at a university, this did not stop him from producing scholarly work or connecting with the international mathematical community. He kept up correspondence with leading mathematicians of his time and contributed to mathematical discussions while at the school.
Much of Sylow's work involved exploring and expanding on the ideas of Niels Henrik Abel and Évariste Galois in algebra. He edited and helped publish Abel's collected works, working with Sophus Lie on a new edition that came out in 1881. This editorial work made sure Abel's important work on the theory of equations reached more readers. Sylow’s research built on the algebraic structures that Galois and Abel developed, translating their ideas about polynomial equations into group theory.
In 1898, after retiring from Fredrikshald, Sylow became a professor at the University of Oslo, a post he held until his death in 1918. Although this role came late in his life, it was an acknowledgment of his importance in mathematics. He also co-edited Acta Mathematica from the journal’s start in 1882, shaping a major mathematical publication in Europe. Throughout his career, he wrote about twenty-five mathematical and biographical works.
Sylow's work earned him significant recognition. He was elected to the Norwegian Academy of Science and Letters in 1868 and became a corresponding member of the Academy of Sciences in Göttingen. The University of Copenhagen gave him an honorary doctorate in 1894, and he received the Pour le Mérite for Sciences and Arts, a prestigious Prussian award for contributions to science and culture. These honors, given over many years, show how much the international scientific community valued his work.
Before Fame
Sylow was born in Oslo in 1832, during a time when Norway was still a young constitutional monarchy, having adopted its constitution in 1814. He went to Oslo Cathedral School, one of Norway’s oldest and most demanding schools, before attending the University of Oslo and the University of Copenhagen. Norway didn't have as many mathematical institutions as Germany or France, so scholars looking for advanced study often had to go abroad.
While at university, Sylow became familiar with the groundbreaking algebraic ideas of Niels Henrik Abel, a fellow Norwegian who died just three years before Sylow was born. Galois theory, created by French mathematician Évariste Galois, was still being widely understood during Sylow’s early years. These developments in abstract algebra influenced his research, directing him to explore questions about group structure and subgroup existence, which he eventually addressed in his notable 1872 paper.
Key Achievements
- Proved the Sylow theorems in 1872, establishing fundamental results on the existence and structure of subgroups in finite groups
- Introduced the concept of Sylow subgroups, which became a core tool in the study of finite group theory
- Co-edited the complete works of Niels Henrik Abel with Sophus Lie, preserving and disseminating foundational work in algebra
- Served as co-editor of Acta Mathematica from its founding in 1882, contributing to international mathematical publishing
- Elected to the Norwegian Academy of Science and Letters and recognized with an honorary doctorate from the University of Copenhagen and the Pour le Mérite order
Did You Know?
- 01.Sylow spent forty years as a schoolteacher in the provincial town of Frederikshald before finally receiving a university professorship at the age of sixty-five.
- 02.His celebrated theorems on finite groups were all published in a single paper in 1872 in Mathematische Annalen, yet they remain a cornerstone of modern algebra more than 150 years later.
- 03.Sylow collaborated with the Norwegian mathematician Sophus Lie to produce a new critical edition of Niels Henrik Abel's collected works, published in 1881.
- 04.He served as a co-editor of Acta Mathematica from its very first issue in 1882, helping to establish one of the leading European mathematics journals during an era of rapid growth in the field.
- 05.The Pour le Mérite for Sciences and Arts, one of the highest honors Sylow received, was originally a Prussian military order that was repurposed in 1842 to recognize achievements in science and the arts.
Family & Personal Life
Awards & Honors
| Award | Year | Details |
|---|---|---|
| Pour le Mérite for Sciences and Arts order | — | — |
| honorary doctorate of the University of Copenhagen | — | — |