**Lazarus Fuchs** was a Prussian mathematician who worked on differential equations and the theory of functions.

- Mathematics became the subject which, even at this early stage, Fuchs knew was going to dominate the rest of his life.
- In addition to his school studies, Fuchs had to earn money by giving private tutoring and his abilities for developing hidden skills and talents in his pupils were quickly appreciated so that he became a much sought-after teacher.
- One of his friends was Leo Königsberger who was four years younger that Fuchs and was also a pupil at the Friedrich Wilhelm Gymnasium in Posen.
- After eighteen months, Fuchs had completed the Middle School and, missing out a year in the Upper School, he was able to take his maturity examination at Easter 1853 which he passed with grade "excellent".
- They offered to employ Fuchs as a private tutor to Leo for a year, to give him accommodation in their home, and to pay him a modest fee.
- The rector of the university at this time was the famous astronomer Johann Franz Encke and Fuchs was enrolled into the Faculty of Philosophy whose dean was the philosopher Friedrich Adolf Trendelenburg (1802-1872).
- From Easter 1857 to Easter 1864 Fuchs and Königsberger shared accommodation in Berlin.
- They lived in a great number of different houses, forced to live a very simple and modest life-style since, especially in the first few years, they lived off the income that Fuchs made through giving private lessons.
- At the University of Berlin, Fuchs attended lectures by a number of famous mathematicians including Eduard Kummer and Karl Weierstrass.
- As well as attending lectures by the people listed above, Fuchs read Gauss's Disquisitiones arithmeticae and works by Fourier, Laplace and Cauchy.
- The professors who had the greatest influence on Fuchs were Karl Weierstrass, who introduced him to function theory, and Eduard Kummer who went on to supervise his doctorate.
- Fuchs was awarded the degree by the University of Berlin 1858.
- Before the award of his doctorate, Fuchs began to worry about whether he should convert from Judaism to Christianity.
- Although Jews had been officially discriminated against during the early years of Fuchs' life, a new constitution in Prussia in 1850 gave all citizens equal rights irrespective of their religion.
- Fuchs spent three years deeply worried about whether he should convert to Christianity.
- Both Kummer and Weierstrass were well aware of Fuchs' painful suffering on the issue and encouraged him to take the step.
- In 1860, Fuchs converted to Evangelical-Lutheran Christianity.
- Before obtaining his doctorate, Fuchs was appointed to a teaching post at a Gymnasium in Berlin on 19 March 1859.
- Fuchs also held a second post in Berlin from 23 May 1867 when he was appointed as professor of mathematics at the Artillery and Engineering School.
- We note that Richard Fuchs and Ludwig Schlesinger jointly edited Lazarus Fuchs' complete works: Gesammelte mathematische Werke von L Fuchs which was published by Mayer & Müller, Berlin in three volumes in 1904, 1906 and 1909.
- Fuchs took up the professorship in Greifswald on 3 February 1869, the position becoming vacant since Leo Königsberger, who had taught at Greifswald for five years, had been appointed to a chair of mathematics at Heidelberg.
- After spending five years in Greifswald, Fuchs moved again, this time to Göttingen where he took up an appointment as an ordinary professor on 23 January 1874.
- He loved the natural environment around the city, something that was important to Fuchs who had deep feelings for nature.
- Fuchs held this post for the rest of his life.
- Ernest Julius Wilczynski attended Fuchs' lectures in Berlin.
- Fuchs was not a brilliant lecturer.
- For Fuchs worked when he lectured.
- In 1865 Fuchs studied nth order linear ordinary differential equations with complex functions as coefficients.
- This led him (1865, 1866) to introduce an important class of linear differential equations (and systems) in the complex domain with analytic coefficients, a class which today bears his name (Fuchsian equations, equations of the Fuchsian class).
- Fuchs later also studied non-linear differential equations and moveable singularities.
- Fuchs' study (1876 with Hermite) of elliptic integrals as a function of a parameter marks an important step towards the theory of modular functions (Klein, Dedekind).
- In a series of papers (1880-81) Fuchs studied functions obtained by inverting the integrals of solutions to a second-order linear differential equation in a manner generalising Jacobi's inversion problem.
- It was Fuchs' work on this inverse function which led Poincaré to introduce what he called a Fuchsian group, and use this as a fundamental concept in the development of the theory of automorphic functions.
- Fuchs also investigated how to find the matrix connecting two systems of solutions of differential equations near two different points.
- In this interesting paper Gray also discusses the relationships between Fuchs' ideas and his mathematical tools, and illustrates how solutions of certain problems led Fuchs to the study of further problems.
- Rather, Fuchs' career remains of interest because it shows clearly and dramatically how mathematical ideas are many-sided, and how many new ideas may be needed to solve a problem.
- There is an ironic truth in the assessment that Fuchs opened up a new province: repeatedly Fuchs pointed to problems in analysis that could best be solved by group theory.
- Denying himself this tool, which belonged to the younger generation, one might say that Fuchs could only stand like Moses and gaze upon the promised land.
- Fuchs is a representative of both Berlin's classical and its post-classical era.

Born 5 May 1833, Moschin (near Posen), Prussia (now Poznań, Poland). Died 26 April 1902, Berlin, Germany.

View full biography at MacTutor

Origin Poland

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