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**The mathematician Sophus Lie. It was the audacity of my thinking. Transl. from the Norwegian by Richard H. Daly.**
*(English)*
Zbl 0998.01024

Berlin: Springer. xi, 555 p. (2002).

The Norwegian Sophus Lie (1842-1899) was one of the most important mathematicians of the nineteenth century. His work on line-sphere transformation and the creation of the theory of continuous groups and his application of these to other areas of mathematics was ground-breaking and has had a lasting effect on the further development in the field. Indeed, a new discipline of mathematics known as Lie theory today has resulted.

Despite Lie’s outstanding discoveries, no scientifically adequate biography of his life was published. In honor of his 150th birthday, a symposium to commemorate his name was held in Oslo and on that occasion, the Norwegians decided to correct that. In 1996 Arild Stubhaug published the biography of Niels Henrik Abel which received warm acclaim from the Norwegian public. Consequently, he was approached to write the biography of Sophus Lie. Stubhaug received a great deal of professional assistance from a group of specialists which was especially teamed for this purpose. Thanks to the renowned Scandinavian capacity for team work, the book was published in 2000, in Norwegian, by H. Aschehoug & Co., Oslo. Richard H. Daly’s translation into English is the version we are relating to.

Arild Stubhaug has written an extensive, detailed and readable biography that emphasizes Lie’s relevant mathematical studies. This biography includes new sources like Lie’s correspondence with Ernst Motzfeldt (1842-1915) with whom Lie was friendly since 1857, and it is further enhanced by many pictures of scenes and people from Lie’s life. It also contains an appendix to Sophus Lie’s descendants and important information on mathematicians close to Lie.

Lie had spent time abroad (Berlin, Paris, Leipzig) and in his letters of that time he opens up. An authentic picture dating to the controversial years 1886-1898, when Lie was a professor of geometry at the university of Leipzig, is included. This period is crucial in Lie’s life, since it was during that time that he published his important monographies (collaborating with Friedrich Engel and Georg Scheffers). This period is also marked by Lie’s tragic illness and by his numerous controversies with German scientists (Felix Klein, Carl Neumann, Wilhelm Ostwald to mention but a few).

Following his conclusion, Stubhaug included an addendum (pages 455-555) of important supplements (Chronology, Notes and commentaries, Chronological bibliography of Sophus Lie’s published works, List of literature, Index of names) which are illuminating for experts in the field, for mathematics historians and for Lie theoreticians.

Despite Lie’s outstanding discoveries, no scientifically adequate biography of his life was published. In honor of his 150th birthday, a symposium to commemorate his name was held in Oslo and on that occasion, the Norwegians decided to correct that. In 1996 Arild Stubhaug published the biography of Niels Henrik Abel which received warm acclaim from the Norwegian public. Consequently, he was approached to write the biography of Sophus Lie. Stubhaug received a great deal of professional assistance from a group of specialists which was especially teamed for this purpose. Thanks to the renowned Scandinavian capacity for team work, the book was published in 2000, in Norwegian, by H. Aschehoug & Co., Oslo. Richard H. Daly’s translation into English is the version we are relating to.

Arild Stubhaug has written an extensive, detailed and readable biography that emphasizes Lie’s relevant mathematical studies. This biography includes new sources like Lie’s correspondence with Ernst Motzfeldt (1842-1915) with whom Lie was friendly since 1857, and it is further enhanced by many pictures of scenes and people from Lie’s life. It also contains an appendix to Sophus Lie’s descendants and important information on mathematicians close to Lie.

Lie had spent time abroad (Berlin, Paris, Leipzig) and in his letters of that time he opens up. An authentic picture dating to the controversial years 1886-1898, when Lie was a professor of geometry at the university of Leipzig, is included. This period is crucial in Lie’s life, since it was during that time that he published his important monographies (collaborating with Friedrich Engel and Georg Scheffers). This period is also marked by Lie’s tragic illness and by his numerous controversies with German scientists (Felix Klein, Carl Neumann, Wilhelm Ostwald to mention but a few).

Following his conclusion, Stubhaug included an addendum (pages 455-555) of important supplements (Chronology, Notes and commentaries, Chronological bibliography of Sophus Lie’s published works, List of literature, Index of names) which are illuminating for experts in the field, for mathematics historians and for Lie theoreticians.

Reviewer: Bernd Fritzsche (Küssnacht am Rigi)

### MSC:

01A70 | Biographies, obituaries, personalia, bibliographies |

01A55 | History of mathematics in the 19th century |

01-02 | Research exposition (monographs, survey articles) pertaining to history and biography |