**Heinrich Weber** was a German mathematician whose main work was in algebra, number theory, analysis and applications of analysis to mathematical physics.

- Georg Weber had been born in the Rhine Palatinate town of Bergzabern, which was at this time under French rule, and studied at Speyer and the University of Erlangen before being awarded a doctorate from the University of Heidelberg in 1832 for his dissertation De Gytheo et rebus navalibus Lacedaemoniorum Ⓣ(On Gytheio and the Spartan navy).
- Heinrich's love of mathematics began while he was at the Lyceum in Heidelberg.
- After graduating from the Lyceum, Weber entered the University of Heidelberg in 1860 to study mathematics and physics.
- At this time Heidelberg had some outstanding physicists and mathematicians on the staff who gave courses that Weber attended.
- As was the common practice of German students at this time, Weber spent part of his time studying at a different university.
- In order to become a university teacher, Weber needed to write a further thesis, his habilitation thesis.
- Although Jacobi had died over ten years before Weber began his studies at Königsberg, his influence was still strongly felt and it would not be unreasonable to say that Weber, through his teachers at Königsberg, was strongly influenced by Jacobi's style of mathematics.
- So it seems natural that young Weber, when he asked his academic teachers where he should go for his postdoctoral studies, was advised to move to Königsberg.
- There were other students at Königsberg at this time who would become important in the development of mathematics, in particular Albert Wangerin, who studied for his doctorate around the same time as Weber worked for his habilitation, and former students such as Albert Clebsch whose influence was still being felt.
- Weber mentions the names of nine of his fellow students at Königsberg who went on to high profile careers as scientists.
- On 11 August 1866 Weber's habilitation thesis Singuläre Auflösungen partieller Differentialgleichungen erster Ordnung Ⓣ(Singular resolutions of partial differential equations of first order) was accepted and he became a privatdozent at Heidelberg in that year.
- A son, Rudolph Heinrich Georg Weber, born 16 August 1874 in Zürich, went on to study mathematics and physics.
- Over the next twenty-five years, Heinrich Weber taught at a surprising number of different institutions.
- Together with Richard Dedekind, Weber had been editing Riemann's Collected works and this important book was published in 1876.
- At this time Weber was lecturing on number theory, also gave a course on elliptic functions, and ran a seminar on the theory of invariants.
- In addition Weber was quite explicit in making use of modern notions, for instance the abstract notion of a group is to be found, as well as what we now call the "main theorem on finite abelian groups", i.e., decomposition of finite abelian groups into cyclic factors (in the context of description of characters).
- After leaving Königsberg in 1883, Weber was appointed to the Technische Hochschule in Charlottenburg where he spent only one year before he moved again to the Philipps University of Marburg where he was rector of the university during session 1890-91.
- Weber's final post was to Strasbourg where he was appointed in 1895.
- It is reasonable to consider why Weber left Göttingen, perhaps the leading mathematical centre in the world at this time, to move to Strasbourg.
- However, Weber did not move to Strasbourg for mathematical reasons, but rather for personal ones.
- Again Weber served as rector of the university in which he was working, taking on this role at Strasbourg during session 1900-01.
- Note that Weber served as rector three times during his career at three different universities.
- Of course, the reader of this biography will have noted the large number of different universities at which Weber worked.
- Weber's main work was in algebra, number theory, analysis and applications of analysis to mathematical physics.
- This seems a contradiction in terms, for we have now almost said that Weber's main work spans the whole spectrum of mathematics.
- Weber's work was characterised by its breadth across a wide range of topics.
- To a certain extent this breadth can be attributed to the various influences on Weber from colleagues around him.
- But in Königsberg there was also the Jacobi influence, particularly coming through one of his other teachers Friedrich Richelot, which saw Weber doing important work on algebraic functions.
- Perhaps Weber is today remembered for his outstanding text Lehrbuch der Algebra Ⓣ(Textbook of algebra) published in 1895 and it is for his work in algebra and number theory that he is best known.
- If he was influenced by his colleagues to work in different areas of mathematics then it is a very fair question to ask where the influence came from which prompted Weber to work on algebra and number theory.
- Weber's Lehrbuch der Algebra Ⓣ(Textbook of algebra) is an outstanding work but, although he tried hard to connect the various algebraic theories, even fundamental concepts such as a field and a group are only seen as tools and not properly developed as theories in their own right.
- Among other books by Weber we mention Die Partiellen Differentialgleichungen der Mathematischen Physik Ⓣ(The partial differential equations of mathematical physics) and (with Josef Wellstein) Encyklopädie der Elementar-Mathematik Ⓣ(Encyclopedia of elementary mathematics).
- Towards the end of Weber's life a number of tragedies affected him deeply.
- Weber received many honours including the publication of a Festschrift compiled by his friends and colleagues to celebrate his 70th birthday on 5 March 1912.

Born 5 March 1842, Heidelberg, Germany. Died 17 May 1913, Strasbourg, Germany (now France).

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Algebra, Group Theory, Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive