Petra Šarmanová, Pavel Šišma

                           One of the greatest Czech mathematicians and the first professor of mathematics at Masaryk University in Brno, Matyáš Lerch, was born on 20 February, 1860 at Milínov near Sušice in south Bohemia. At the age of six he had a serious accident of his left leg whose consequence was difficult walking with a crutch and later with a stick. That is why he started attending elementary school only at the age of nine. Then he finished council school, studied at a secondary technical school at Plzeň and at Rakovník, where he passed his matriculation examination with honours in 1880. Then he entered the Czech Technical University in Prague to study civil engineering. His teachers of mathematics were among others E. Weyr. G. Blažek and F. Tilšer. In the academic year 1882/83 he attended lectures of F. J. Studnička at the Czech University and Gruenwald's lectures at the German Technical University.

    He drew the attention to his exceptional mathematical talent already at that time by publishing his first six papers in the Časopis pro pěstování matematiky a fyziky (Journal for pursuing mathematics and physics) and in the Zprávy Královské‚ České Společnosti nauk (Reports of the Roval Czech Society of sciences). Due to this fact he obtained a year's scholarship which enabled him to study at Humboldt University in Berlin. At that time there were outstanding mathematicians of world renown there - K. Weierstrass, L. Kronecker and J. L. Fuchs, the greatest influence on Lerch's
further scientific work having L. Kronecker. They confirmed the exceptional character of his talent and the depth of his scientific breadth of views. In Berlin he also made acquaintance of a number of young German mathematicians, such as L. Heffter, K. Runge and the Russian mathematician S. Kowalewska.

    After returning to Prague Lerch became a private Associate Professor at the Czech Technical University, where up to 1892 he substituted Prof. G. Blažek. As the job of private Associate Professor was unpaid at that time, Lerch worked at the same time as assistant of E. Weyr and later of Prof. G. Blažek. At that time, before 1896 he published more than 110 scientific papers in domestic as well as prominent foreign journals, which secured him his prestige in the world. At the same time he maintained friendly contacts with many foreign mathematicians, particularly with the French mathematician Ch. Hermite. He esteemed Lerch very much and appreciated his results concerning the differentiation of Kummer's series for log Gamma(x) or the calculation of Raabe's integral, which he took over in his lectures.

    Despite this success, Lerch did not succeed to find a corresponding job at Czech universities. Therefore he accepted the job of professor at the university in the Swiss Friburg which he was offered thanks to the recommendation of
Ch. Hermite. There his scientifc work culminated. Not only did he publish 75 papers in that period, but in 1900 he became the laureate of the Grand Prix of the Paris Academy of Sciences. Thus, M. Lerch is the second Czech scientist, after the biologist J. E. Purkyně, to obtain that prize.

Despite that outstanding success M. Lerch did not feel happy abroad, and when in 1906 his contract with Friburg University finished, he left for his mother country to take up the job of professor of mathematics at the Czech Technical University in Brno. Together with him also his niece Růžena Sejpková  returned who kept his household for 9 years in Switzerland and who created conditions for his undisturbed pedagogical and scientific work also in Brno. In 1921, at the end of his life, M. Lerch married her.

    Only now was Lerch also recognized at home. In 1907 he was elected honorary member of the Union of Czech Mathematicians and Physicists and in 1909 he was declared honorary doctor of Prague University. In the academic year 1908/09 he was dean of the Faculty of Mechanical Engineering at Brno Technical University. But due to his state of health he refuses the function of rector of that school for the vear 1910/11. He suffered from diabetes which deteriorated and at that time could not be cured successfully. Despite that, during his work at Brno Technical University he published further 31 scientific papers, often very extensive.

    In 1920 M. Lerch came to the newly established Masaryk University in Brno. And when soon afterwards, in 1921, the Czech Academy of Sciences appointed him its full member, he finally felt satisfied, despite his serious disease. With a great fervour he plunged into building the Mathematical Institute and its library, greatly helped by his young assistant
0. Borůvka. But he did not implement all his plans. During the holiday stay at Sušice he dies on 3 August,1922 of rapid pneumonia.

    During his lifetime Matyáš Lerch published altogether 238 papers in 32 different journals and proceedings. Out of them 118 are written in Czech and the others in French, German, Croatian, Polish and Portugese. Besides those papers he is also author of a number of small articles and solutions of different problems and tasks.

    The centre of Lerch's work consists in mathematical analysis, to which he devoted 150 papers. They concern mainly the following topics: the theory of infinite series, the general theory of functions, the theory of the gamma function, the theory of elliptic functions and the integral calculus. This part of his scientific work was systematically studied during the 1940s and 1950s at the Faculty of Science, Masaryk University in Brno, under the management of O. Borůvka. More exactly, M. Lerch dealt with the theory of infinite series for the whole of his life, devoting to it 50 papers, the most significant of them being papers on the so-called Malmstene series. He also applied his perfect knowledge of infinite series in further spheres of mathematics. Lerch dealt with the general theory of functions in twenty papers, most of which were written between 1886 and 1896. In this sphere the most significant is the theory of constituting functions and construction of continuous functions having no derivative. The papers concerning the sphere of elliptic functions and the integral calculus have mostly only methodological importance.

    The most important part of the whole analytical work of Lerch are evidently papers devoted to the gamma function. His contribution consists in the discovery of many properties of this function and particularly connections between the gamma function and the Malmstene series whose theory Lerch established and built.

    M. Lerch dealt with problems of geometry in 15 publications, some of which arose at the beginning, but most at the conclusion of his scientific career in 1911 to 1918.

    It is necessary to mention the fact that M. Lerch liked very much dealing with factual problems and avoided general proofs. He considered the solution of the given problem finished if he could present its numerical calculation. For this purpose he even bought a 20-digit calculator for his institute at Brno Technical University. He did not like formulas inaccessible for numerical calculation. That is why among his papers there are a lot of those dealing with new methods of calculation of problems solved before by other mathematicians. This is also linked up with his preference of the theory of numbers where he achieved eminent success. In this very sphere, for the paper Essai sur le calcul du nombre des classes de formes quadratiques binaires aux coefficients entires he was appreciated by the French Academy in 1900. It concerns the number of classes of binary quadratic forms with entire coefficients. Besides the sphere of quadratic forms Lerch dealt with Gaussian sums, Fermat quotients and quadratic remainders.

    The work of M. Lerch, one of the greatest Czech mathematicians, is great not only by its extent, but mainly by its content. It enriched mathematics by many eminent results, thus contributing to the good reputation of our science abroad.