To understand why, during the nineteenth century, about 300 scientists, including mathematicians, physicists, biologists, naturalists, chemists and astronomers distinguished themselves, it is necessary to analyse, in addition to historical and political events, also the evolution of the educational system that made the German universities (Fig. 1), at the end of the century, reference points for scientific training throughout Europe and produced more than a 100 Nobel prize winners in the nineteenth and twentieth centuries.

Fig. 1
figure 1

Early 20th-century map showing the foundation year of several German universities, from [2] (SLUB Dresden/digital collections/Acta acad.160-Phil., 24, 2)

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At the end of the eighteenth century the German territory was divided into over 360 states, many of which were part of the Holy Roman Empire. The most important one was Prussia, which had enlarged its borders thanks to the imperialist policies of its king, Frederick II, but which, with the subsequent monarch Frederick William II, who rose to the throne in 1786, was forced to cede to France the territories on the left bank of the river Rhine. Prussia had held a position of neutrality with respect to post-revolutionary France until the beginning of the nineteenth century, when it sided against Napoleon and suffered a defeat in 1806 in Jena, which deprived it of some territories and subjected it, in addition to foreign occupation, to a huge war reparation.

After the Congress of Vienna in 1815, Prussia regained some territories lost during Napoleonic occupation, promoted a customs union leading to the creation of an extensive common market (Zollverein) and, over the course of the nineteenth century, thanks to treaties and war campaigns, implemented an expansionist policy that allowed it to annex many German states and become the greatest power of continental Europe [7].

On 18 January 1871, with the coronation of William I as German Emperor, the Deutsches Reich (the “Second Reich”) was born. The political action of the Prussian monarchs and governments was accompanied by important economic and social changes. Educational reforms played a central role; at the beginning of the nineteenth century, the influence of neo-humanism was felt in all Germanic states. This movement, which had originated at the end of the eighteenth century as a cultural revolt and looked to ancient Greece and Rome as models for aesthetics and for a philosophical and moral regeneration of the present, was dominant at the time. All classical schools, intended to prepare students for University, were called Gymnasien and, thanks to the action of Wilhelm von Humboldt, a man of broad culture and an official of the Prussian state, who in 1808 was appointed to the Section für Cultus und öffentlichen Unterricht (Prussian Public Education Office), a new curriculum of studies was prepared. The curriculum included 8 h of Latin, seven of Greek, six of mathematics and four of German language to be taught in high schools. Only 2 h were devoted to science. There were no classes of philosophy, modern languages such as French, or any discipline with a practical utility: the guiding principle of the reforms was “the formal development of good culture and virtuous judgement”. For more about this, see [6].

In the opinion of more orthodox neo-humanists, classical education would prepare students from both an intellectual and an ethical point of view and the study of natural sciences was not consistent with these requirements. The best education that could be aspired to was philological, in order to develop universally applicable intellectual skills. The habit of an abstract, ordered and formal thought (formale Bildung) was the central aspect, and learning Latin and Greek would allow students to get in touch with a system of consistent rules, not present in modern languages as regards their purity and grammatical logic. Subjects such as languages, modern history and natural sciences had their own places to be learnt in the Realschule or Bürgerschule, secondary schools for students who would not continue their university studies.

Between 1820 and 1840 the nationalisation of the Prussian scholastic system was completed thanks to the work of the new minister of education, Karl Sigmund Franz Freiherr vom Stein zum Altenstein, who implemented a reform that included a new model of school administration, training and certification for teachers and verification of the levels achieved through examinations at the end of the study cycle. The syllabus for the Gymnasium, promulgated in 1837, was the first compulsory one for all schools in the kingdom. Latin and Greek remained the central disciplines, followed by mathematics and German.

The opinions on mathematics were conflicting: although it was commonly accepted as formal, abstract and self-consistent enough to be taught at the Gymnasium, in 1843 the heads of the Faculty of Philosophy of Jena decided not to introduce it into the curriculum of Weimar Gymnasien. The opposition was based on the criticism of the numerical evaluation system; although this motivation may seem peculiar, the issue was actually of a moral nature: mathematics, and in particular its quantitative approach, seemed to be reductive with respect to the complexity of the evaluation criteria.

The trend of renewal at the beginning of the nineteenth century involved the university but did not yet allow research to play an important role, since it was believed that the main function of academic studies was to train the professionals necessary for the German states, such as physicians, lawyers, government officials, clergymen and teachers. For this reason, at least one university was present in most of the German states and by around 1818 German territory had 19 universities. The universities had to have faculties or professional schools of medicine, law, divinity and generally a fourth faculty, which was often philosophy. The latter covered the scope of humanistic, mathematical and some naturalistic studies and was responsible for supporting the other three by providing a general education.

The faculties of philosophy made it possible for German universities to present themselves as institutions of “pure science” and to claim their superiority over mere professional schools or specialised institutions such as the French military and engineering schools that also were spreading throughout the German territory. In this sense, the faculty of philosophy continued, at higher levels, the task of the Gymnasien: providing the younger generations with a Bildung, that is, in addition to an adequate body of knowledge, a method of research and investigation that could develop the students’ intellectual and emotional skills in the best way, ennobling their character and refining their tastes. Including both humanities and natural sciences, the faculty of Philosophy offered students “the opportunity to devote a number of years exclusively to scientific contemplation in order to grasp the unity of knowledge” (Wilhelm von Humboldt).

This ideal of education was not shared by naturalists, to whom the study of ancient languages did not seem the best method to develop the practical and inductive learning typical of sciences. Georg Simon Ohm claimed, in the introduction of his geometry textbook, initially mocked and subsequently ignored, that the teaching of mathematics needed effort and not mere reception. With this new interpretation of Bildung, a “new world formed by men endowed with active reasoning” would be born. For more about this, see [4].

The contribution of physics to Bildung was still marginal: it consisted of a few traditional lessons and the exhibition of measuring instruments in academic museums, but the active involvement of students in the study of this discipline did not fit the traditional idea of education, as Wilhelm Weber noticed when he introduced experimental exercises to the students of medicine, pharmacy, chemistry and to those who were preparing to become secondary school teachers of mathematics. Humanistic education and inadequate instruction in the mathematical and scientific disciplines prepared university students to choose, among the courses held in the faculty of Philosophy, the humanistic ones. Throughout the entire German territory the preparation and interest of the students in mathematics were rather lacking. At the University of Freiburg, for instance, one lecturer, to overcome the difficulties found in physics students, decided to offer a course of differential calculus and analytic geometry: no one attended classes. Physics professors who wrote textbooks regularly had to exclude the most advanced mathematics from the treatment. The main task of physics teachers was to give general introductory lessons, which were simply surveys on the state of the discipline. It was very rare to find students interested in advanced courses in specific areas of physics, to the extent that Gauss refused to give higher classes unless they were attended by at least two or three students. Despite the idea of seeing the university institution as a unique whole, the faculty of Philosophy was not considered at the same level as the other three (Medicine, Law, Divinity); in fact, in some cases it was not even considered superior to secondary education. For this reason, in order to have adequate experimental equipment and arrive at a reasonable salary, the teachers of mathematics and physics, who were not very specialised, moved easily between the two levels of education.

The university courses of physics were divided into experimental and theoretical, but the difference between them consisted only in demonstration by means of devices versus verbal explanations of the fundamental laws. At the beginning of the century, the idea that it was necessary to make use of practical demonstrations to teach of physics was commonly accepted, but the teachers did not have sufficient funding from the universities, so they started to use their own private funds: they built their own devices, they took them to classrooms, sometimes on the other side of the city, set them up and then disassembled them because the classrooms were shared with other teachers. The few professors who had a good collection of experimental devices began to be coveted by the universities, so much so that they could set their own economic conditions, and the few university centres able to purchase the equipment and to take care of their collections became the main centres of study, attracting the best of the new generations of physicists of the middle of the century. The first area of physics for which a support from the German States was granted to universities was the study of terrestrial magnetism (Gauss’s field of study). The motivation lay in the association of this field to astronomy, from which there were good expectations of practical benefits: astronomers were required for military purposes and for the acquisition of territories, due to their ability to create new topographical maps.

One of the most important and innovative aspects of university education since the 1830s were the seminars in mathematics and physics that were born out of the philology seminars of the faculty of Philosophy. The best known ones were those in Königsberg curated by Franz Neumann and Carl Jacobi, in Berlin with Peter Gustav Dirichlet, and in Göttingen with Wilhelm Weber and Johann Benedikt Listing, but Munich, Breslau, Heidelberg and Tübingen also hosted seminars between 1850 and 1860. Initially, these offered to future mathematics and natural sciences teachers the opportunity to learn how to present various topics to their classes, how to use basic instrumentation, how to conduct observations and simple experiments in the most important sciences. While teacher training was the initial justification for setting up the seminars, this alone does not account for their survival and development. For more about this, see [4].

At the beginning of the 1840s, with the accession of Frederick William IV to the throne, specialisation in every area was promoted and encouraged, not least in education.

In this regard, it is very significant that the most eminent German exponent of theoretical physics, Hermann von Helmholtz, was also interested in teaching and research. He had the reputation of bringing together specific knowledge of two areas of science, physics and physiology, and his name first appeared in the list of candidates for a professorship in Physics in the Kingdom of Prussia in 1868. The mathematician Rudolph Lipschitz offered him the chair of Physics of the University of Bonn, vacant after the death of the previous holder, and introduced him to the academics emphasising the qualities that made him a “great mind”. The scientists in Bonn were not particularly impressed by the presentation because they considered him “a specialist who had a dual specialisation” and recommended him for his classical research work in physical physiology and for his outstanding results in “pure physics”, especially for his physical–mathematical contribution. Lipschitz felt that his scientific qualities had not been sufficiently understood and the transfer of Helmholtz to Bonn did not finally take place because of the attitude of the minister of culture Mühler, who made him an unattractive economic offer, despite the fact that Prussia was aiming for a personality that could represent an “element of glory” (as shown by the letters between Beseler and Mühler).

It is certainly no coincidence that, in this period, seminars were developing, places where scholars and researchers could meet and work, under precise regulations: generally teachers demanded, besides a regular attendance, the obligatory presence at all exercises and continuity of participation throughout the course that had, at times, a multi-year duration. Neumann, in his seminars in Königsberg, succeeded in organising courses for both beginners and advanced students, including joint classes. Animated by a strong sense of duty, he said that

a university teacher, conscious of his role, knows that he is required not just to teach his own discipline, but to take part in the development and progress of knowledge. If he were denied such an opportunity, as if he were not provided with an adequate laboratory, then he should take the first opportunity to leave the university.

Although much appreciated, Neumann’s course always remained one in mathematical physics, since in Königsberg there were no adequate spaces and laboratory instruments. In Göttingen, however, Weber was able to offer an excellent course in physics based on observation and measurement. During the lessons, in addition to conducting laboratory exercises, his students had the task of expounding on physical treatises and scientific articles related to the exercises performed. The lessons were great experimental shows, as it was believed that the number of attending students depended on the attractiveness of the proposed activities. Since the preparation of the experimental equipment required too much time from the teacher, in 1866 the figure of the assistant at the Institute of Physics was included for the first time in the payroll of the university. Contemporary with the development of seminars, Heinrich Gustav Magnus established in Berlin a course in experimental physics, having an advantage over his colleagues: money. He acquired, with his possessions, instruments and devices that the university did not have, agreeing to hand them over to that institution, which was to repay him in instalments. For this reason, he taught at his home and allowed the most talented students to do research in his laboratory and to use his library. Once the payment of the equipment was finished, he moved to the university premises but, not having sufficient space there, he continued to maintain the laboratory in his home; this, in 1863, was recognized as a physics laboratory of the University of Berlin. Many promising physicists, including Helmholtz, Wiedemann, Kundt, Warburg, would carry out their first experiments in that laboratory. In 1867 Magnus proposed to found a real Institute of Physics, which the university accepted. As he did for the laboratories, Magnus put teaching and research together in the physikalische Kolloquien that took place weekly and that he had begun to hold at his home in 1843. In this context, more experienced physicists led the younger ones through recent papers and allowed them to practice the art of popularization by encouraging an open criticism of both their works and those which from time to time were “discussed, dismembered and torn to pieces”. This area of confrontation was the cradle of sharing views that led in 1845 to the establishment of the Berlin Physical Society (Physikalische Gesellschaft zu Berlin). Initially the meetings were held every 2 weeks and the issues discussed were mainly introduced by the founding members, but soon, thanks to their constant presence, new members were encouraged to discuss their work too. These included Kirchhoff, Helmholtz and Clausius. This society grew so much that by the end of the century it became the Deutsche Physikalische Gesellschaft.

In the following decades the Prussian policies for secondary education aimed at strengthening the students’ technological and scientific knowledge: the emperor and, later, the new chancellor, Otto von Bismarck, wanted to make of Prussia the first European power not just from a military viewpoint, but also in the commercial and industrial fields.

After the failed revolution of 1848, the reformers promulgated a regulation of the educational system with new norms for the training of teachers and citizens, aimed at countering “the fatal influence of the poisonous spirit of the time” (in the words of Frederick William IV in 1849 [5]).

The non-gymnasium schools were enhanced; from them, technicians were beginning to emerge so prepared as to allow Germany to bridge the industrial disadvantage it had with respect to the other great European nations and to reach cutting-edge levels in the technical-scientific field. The Realschule were widely recognised and openly supported by the new political course: in 1859 a ministerial order was issued that clarified their curriculum and allowed modern languages (English completely replaced Greek), mathematics and natural sciences to assume greater weight, with hours specifically for physics. Later, at the beginning of the 1880s, the Realgymnasium and the Oberrealschule were established, replacing the Realschule and the Bürgerschule. Although they had a partly different timetable, with the latter more oriented towards practical and technical education, they allowed their graduates to have access to scientific faculties, such as mathematics or natural sciences, and—in the first case—also to modern languages, but not to law, medicine and divinity. For more about this, see [6].

By promoting a more specific school orientation, students were encouraged, starting in high school, to specialise in areas that aroused their interest. In the last decades of the century Germany fully entered into the world markets, became a competitive rival for commercial supremacy and completed its transformation from a medieval agricultural country to a highly advanced industrial power. The construction and development of the railway network, already started in 1840 and extremely widespread by the early 1850s, was one of the elements that allowed the growth of heavy industry and simplified transportation of goods and people. The German industrial revolution of the second half of the century made Germany the greatest producer of steel in Europe, and the leading country in the electrical and chemical sectors. This primacy was achieved thanks to a clear inversion of the tendency in scientific research, which, from the 1870s, was promoted by public policies aimed at industrial and technological innovation.

For more about the general problems, see [1, 3]; about the situation in Prussia and Germany, see [8, 9].

Translated from the Italian by Daniele A. Gewurz.