Heinrich's formal education began at the age of six when he was enrolled in a private school run by Richard Lange :-
... a taskmaster who had no patience with error. [Heinrich's] mother watched closely over his lessons, determined that he should be - as he was - first in his class.For ten years Hertz studied at Richard Lange's school. He showed a whole host of talents: he had considerable practical skills which he used in doing woodwork with tools he had been given, and later he used a lathe to make apparatus with which he carried out experiments. He also had great language skills, both with modern and classical languages. In 1872 he entered the Johanneum Gymnasium in Hamburg and there he continued to excel at a wide range of subjects. He even took additional subjects with a private tutor, such as Arabic and technical drawing, which were outside the range offered at the school. Not only was he good at many subjects but he also liked these topics and struggled to make decisions about which he should specialise in at university. Should he take engineering and use his practical skills, or should he study the natural sciences which he also loved? He took his Abitur examinations in the spring of 1875 and, having decided to make a career in engineering, he went to Frankfurt to gain practical experience. He had made the wrong decision.
Hertz spent the year 1875-76 in Frankfurt where he gained practical experience in the building industry and also studied for the state examinations in engineering. Already at this stage he began to feel that engineering might not be the right topic for him. He did not enjoy the work environment, he was too isolated and this he felt was due to working in the private sector. He was now struggling to come to terms with having made the wrong decision; should he waste the time spent on this false start and begin again or should he make to best of a bad job and persevere? He decided to continue to follow the engineering route, going to Dresden Polytechnic for a short while in 1876 before leaving to do military service for a year in Berlin. After completing this year in the railway regiment, he went to Munich with the intention of continuing his engineering course at the Technische Hochschule there. That he was on the wrong road was by now so clear to him. There were several new factors in the equation which affected the issue such as, on the negative side, his unhappiness with the working environment of engineering firms, and on the positive side, his enjoyment of the mathematics he had learnt as part of his engineering studies. Hertz's father was supplying the financial support to allow him to undertake higher education so if he were to change direction he would certainly need his father's approval. He explained his soul searching problems to his father and asked if he would continue to support him if he entered the University of Munich and aimed at a research career. McCormmach writes :-
To him engineering meant business, data, formulas - an ordinary life on a par with bookbinding or wood working - and he was uninterested. Although the Technische Hochschule had a good physics laboratory, a course of study there led to state examinations and usually a practical career. The university by contrast promised a life of never-ending study and research, one that suited Hertz's scholarly, idealistic tastes; he knew above all he wanted to be a great investigator.The arguments convinced his father that he should support his son's change of direction. Hertz matriculated at the University of Munich in 1877 and spent the first semester gaining the necessary background in mathematics. He was advised by von Jolly to read works of Lagrange, Laplace and Poisson :-
Although Hertz thought that, when properly grasped, everything in nature is mathematical, he was in his student days - as throughout his career - interested primarily in physical and only indirectly in mathematical problems.He took courses on physics, zoology and astronomy as well as on mathematics taking courses in the second semester both at the University and at the Technische Hochschule. After a year at Munich he moved to Berlin, not due to any unhappiness with what he was now doing but rather because it was the standard practice at the time for German students to move between institutions. At Berlin he studied under Helmholtz and Kirchhoff. Immediately, despite only one year of university study behind him, Hertz wanted to start research. A prize had been announced by the Philosophy Faculty for the solution of an experimental problem concerning electrical inertia and Hertz was very keen to enter. The prize had been proposed by Helmholtz and, despite Hertz's lack of experience, he realised his great potential and offered Hertz a room in his Physical Institute and considerable support in directing Hertz to the background literature.
Now Hertz knew he was on the right road :-
He wrote home that his great satisfaction lay in seeking and communicating new truths about nature. Occupied any other way he felt a useless member of society; private study as opposed to research seemed selfish and indulgent.He was awarded the Philosophy Faculty prize and gold medal in 1879. Helmholtz now suggested that Hertz work on the prize topic proposed by him for the Berlin Academy of Sciences. This asked for experimental evidence for or against the assumptions that underlied Maxwell's theory. This sounded interesting to Hertz yet wanted to progress rapidly in his chosen area and felt that he could not embark on a project likely to take around three years. He declined to follow Helmholtz's proposal, and instead wrote a theoretical work Über die Induction in rotirenden Kugeln Ⓣ on electromagnetic induction and submitted it for his doctorate in January 1880; it had only taken him three months to complete. Hertz's work on the electromagnetic fields associated with a circular disk turning about its axis of symmetry in a magnetic field parallel to the axis of the disk is considered in . He took the necessary oral examination in the following month and was awarded his doctorate with distinction by the University of Berlin. He was then employed as an assistant to Helmholtz at the Berlin Physical Institute.
During the three years 1880-83 that Hertz worked at the Berlin Physical Institute, he wrote fifteen papers on a variety of topics. Most related to electricity, two were on cathode rays, and several were on instruments such as a new ammeter and new hygrometer. Hertz had to decide on the best way to progress his career. He was already in the best place to undertake research in physics and working with Helmholtz who, Hertz felt, was the best physicist in the world. However to become a privatdozent in Berlin would put him in competition with a large number of scientists who were already in privatdozent positions there. He made a decision to try to take advantage of the expansion of mathematical physics throughout German universities and, although his real love was in experimenting, to seek a privatdozent position in mathematical physics. The University of Kiel was seeking someone in exactly that area so, with strong recommendations from Helmholtz, he habilitated in Kiel.
It was in Kiel that Hertz first showed his strength as a lecturer. He had deliberately taken a position in mathematical physics at a university which had no physical laboratories fitted out for research. As a consequence he undertook theoretical work, writing three papers during the two years he worked there. One paper was on meteorology, one was on electric and magnetic units, while the third was the most important since it represented his first work on Maxwell's theories. After two years he was keen to return to an institution with a strong experimental reputation and the offer of an extraordinary professorship in the Technische Hochschule in Karlsruhe seemed ideal. He accepted the position and gave his inaugural lecture On the energy balance of the Earth on 20 April 1885. (See  where the lecture is published for the first time.) The Technische Hochschule in Karlsruhe is today the Universität Karlsruhe, and it was here that Hertz made his most important discovery, the one with which his name is mostly associated, namely his famous discovery of long-wavelength electromagnetic waves in 1888. However, when he first took up the post it was far from clear that he was on the verge of greatness :-
His stay began inauspiciously; for a time he was lonely and uncertain about what research to begin next.He was then distracted from research for the first time since he first arrived in Berlin in 1878. He met Elizabeth Doll, the daughter of one of his colleagues, soon after arriving in Karlsruhe and they married in July 1886; they had two daughters, Johanna and Mathilde. It was in November 1886 that he began work on the problem which Helmholtz had posed for the Berlin Academy of Sciences and had tried to persuade him to become involved with back in 1879. However, it may have been a wise decision to delay beginning the work as S D'Agostino  suggests that Hertz's derivation of Maxwell's equations in 1884 formed an important part of the structural background to his studies on the propagation of electric waves which he now carried out. Doncel examines Hertz's thinking in . He writes:-
This paper provides new elements for reconstructing Heinrich Hertz's conversion from an electrodynamic concept to a concept of field theory, a process that took place between September 1887 and February 1888. ... It is concluded that Hertz's idea of 'air waves' belongs at the very end of this process, and was mainly attained through experimental hints found within Helmholtz's theoretical framework.Now Hertz saw his discovery as merely a step towards a deeper understanding of Maxwell's theory. He certainly did not foresee the incredible applications which, after Marconi read Hertz's paper and saw its practical application, would transform communication and entertainment. Hertz wrote:-
I do not think that the wireless waves I have discovered will have any practical application.D'Agostino in  adds more to understanding Hertz's research in electromagnetic theory and his development of Maxwell's experiments. Hertz needed new apparatus to prove Maxwell's theory of the existence of electromagnetic waves and he worked his way towards this which was finally achieved in 1888. During four years in Karlsruhe Hertz published nine papers. His fame was now considerable and he was approached by the University of Giessen with a persuasive offer. However he was also asked to go to Berlin as a replacement for Kirchhoff. As always, Hertz thought deeply about the consequences of accepting the positions. Berlin, he mused, would mean a position of high responsibility, considerable administrative duties, and little time for research. He felt that this would be a good research move later in his career, but he was only 31 years old and he wanted to devote most of his time to research. Helmholtz told Hertz that he would make sure he had a top quality laboratory in Berlin but still Hertz did not feel it was the right move. Then he received an offer of an ordinary professorship at the University of Bonn in December 1888 :-
He gladly accepted, more for Bonn's beautiful and quiet setting on the Rhine than for its scientific prospects.The vacancy at Bonn came about because Rudolf Clausius had died in August 1888. When Hertz moved to Bonn in the spring of 1889 not only did he move into Clausius's chair but he also moved into his house. He undertook more research into Maxwell's theories, publishing two theoretical papers in 1890. He searched for a mechanical basis for electrodynamics starting from Maxwell's equations. As he wrote in the Introduction to Electric waves (an English translation of some of his papers published in 1893):-
Maxwell's theory is Maxwell's system of equations.Hertz was a fervent believer in the aether and during this work proposed identifying electromagnetic fields in free space with polarization of the aether. McCormmach writes :-
Hertz brought an unparalleled clarity to Maxwell's theory, organising its concepts and its formalism so that others were able quickly to go beyond him.Even before moving to Bonn, Hertz suffered the first signs of his serious health problems. He had already complained of toothache and had major dental treatment. In 1889 he had all his teeth removed in an attempt to cure the persistent condition. However, by early 1892 the problem returned, this time in his throat and nose. The pain became to intense that he could no longer work. He was given hay fever treatment and went to health clinics to try to find a cure. Nothing was successful, and this was not too surprising since the condition was caused by a malignant bone condition. Bravely he began teaching again in the spring of 1893, undergoing several operations which at least provided a short spell of respite but one consequence of the illness was that he now suffered from depression. He began his 1893-94 lecture courses in the autumn of 1893 and on 3 December he sent the manuscript of his book Die Prinzipien der Mechanik Ⓣ to the publisher. He gave his final lecture on 7 December. He died less than a month later.
In mechanics Hertz followed Kirchhoff and considered only length, time and mass as the fundamental entities, force being a derived concept. In Die Prinzipien der Mechanik Ⓣ Hertz hoped to explain all electromagnetic phenomena, in terms of a mechanical aether :-
Hertz explained in the Introduction to the 'Principles' that to construct a mechanics capable of accounting for the lawful interaction of perceptible bodies it was necessary to add a hypothesis to the three concepts [length, time and mass]. The hypothesis was that in addition to perceptible masses the universe contained hidden, moving masses bound to one another by rigid constraints.In  Lützen discusses Hertz's introduction of hidden mass. In  he talks about Hertz's approach to mechanics having three novelties: (1) a philosophical introduction, (2) an account of mechanics that does not introduce force as a basic concept, and (3) a geometric form. In fact in  Tougas claims that the philosophical introduction to Die Prinzipien der Mechanik Ⓣ strongly influenced Wittgenstein's Tractatus logico-philosophicus Ⓣ. (See also Barker . Hamilton  and Kjaergaard  where Hertz's philosophy is discussed.) Another interesting approach to the same question is by Wilson in . He writes:-
During the past decade and a half, several scholars have tried to gain a better understanding of Wittgenstein's early thought by examining the philosophical aspects of his scientific education. Those taking this historical approach have focused almost exclusively on the connection between Wittgenstein's picture theory of linguistic meaning and the epistemology of mental pictures developed by the physicist Heinrich Hertz in the introduction to his Die Prinzipien der Mechanik, published in 1894. They have taken their cue, quite naturally, from Wittgenstein, who refers twice to Hertz's work in the Tractatus logico-philosophicus. In addition to Hertz, but to a much lesser extent, they have also discussed the role played by Ludwig Boltzmann's philosophical writings in Wittgenstein's intellectual development. ... While analysing and stressing the importance of Hertz's influence on Wittgenstein, however, they have misconstrued the chronological and substantive relationship between Hertz's philosophy and the philosophical writings and ideas of Boltzmann. This, in turn, has significantly affected the current understanding of the genesis and development of Wittgenstein's early thought.An English translation of Die Prinzipien der Mechanik Ⓣ was published in 1899, and reprinted by Dover Publications in 1956.
After Hertz died, one of his friends gave this eulogy:-
He was a noble man, who had the singular good fortune to find many admirers, but none to hate or envy him; those who came into personal contact with him were struck by his modesty and charmed by his amiability. He was a true friend to his friends, a respected teacher to his students, who had begun to gather around him in large numbers, some of the coming from great distances; and to his family a loving husband and father.
Article by: J J O'Connor and E F Robertson
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