# The Forgotten Genius of Oliver Heaviside: A Maverick of Electrical Science

Oliver Heaviside (1850-1925) was a British self-made electrical engineer and mathematician. He is probably best known as an electrical engineer, although his name is not explicitly attached to many terms. There is a Heaviside condition for transmission lines, but maybe less known is that he also coined terms such as conductance, inductance, impedance, and many more. In mathematics, his name is explicitly attached to the Heaviside step function usually denoted as $H(x)$ in his honour, although he himself preferred the notation $\mathbf{1}$ instead. Sometimes his name is also attached to a method to compute the partial fraction expansion of a rational function. However, probably his most important contribution to science is that he reformulated the Maxwell equations in the form as we know them today. As a side product he introduced vector calculus and the associated (force)fields. It also brought complex numbers and complex analysis into electro-technical formulas. He is also the originator of operational calculus. The mathematics community was originally reluctant to accept it because it lacked fundamental rigidity. But it worked so well that it could not be ignored and others provided the necessary rigidity. It allowed to transform a differential equation into an algebraic one, which is much easier to solve. The letter *p* that is often used as the variable in the Laplace domain was his notation. In the time domain, it is a differential operator. The square root of $-1$, which mathematicians usually denote as $i$ is denoted as $j$ in (electrical) engineering because $i$ or $I$ was used for current (although Heaviside preferred to use $C$ for current). He considered $j$ as an operator that had the effect of delaying the signal with a quarter of a cycle, just as mathematicians see a multiplication with $i$ as a rotation over 90 degrees. These are but a few illustrations to show that his field was electrical engineering, and that he is more recognized for his legacy in that domain, it can be said that his influence on mathematics, although less known, is equally important.

Mahon has used the term "maverick" in the subtitle which is most appropriate in the case of Heaviside. Now one can be a maverick in different ways. For example Richard Feynman was really unconventional and did not pander to the customs attached to his status, but it was all in a playful and friendly way. Heaviside on the other hand was a grumpy, stubborn, loner, who did not shy away from aggressive reactions and including insulting remarks in his scientific papers about people he did not agree with. He was for sure not the most likeable person. He had only few friends and admirers who tried to mediate between him and the scientific community. Among them were George FitzGerald, Oliver Lodge, and Heinrich Hertz, who together with Heaviside became known as *The Maxwellians* by the book of Bruce Hunt (1991). No wonder that such an outspoken character has inspired other biographers to write about Heaviside. Fortunately much of his publications, notes and letters are at their disposal to reconstruct his personality. Paul J Nahin's *Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age* (John Hopkins University Press, 2002), is a basic reference, and there is an account of Heaviside's character by his friend G.F.C. Searle described in the booklet *Oliver Heaviside, the Man* (1987). Also the book under review was published earlier in 2009 by a different publisher and with a slightly different title *Oliver Heaviside: Maverick mastermind of electricity*. Not much is changed in this edition except the spelling and the notes at the end which have been extended.

As a child Oliver Heaviside had scarlet fever which left him partially deaf. This may in part explain his tendency to withdraw from crowds and prefer solitude. He suffered of several illnesses throughout his life, some were due to poverty and negligence. His uncle was Charles Wheatstone (from the Wheatstone Bridge known in electricity) and an expert in telegraphy. To understand Heaviside's scientific breakthrough, one should think back mid 19th century. James Maxwell just discovered the relation between electricity and magnetism which he presented as a complex system of 24 equations. Submarine cables for telegraphy were laid with a lot of experimentation and disastrous failures. Wheatstone looked after Heaviside's education, but when his parents could not afford the studies anymore he studied on his own. When working for Wheatstone's telegraph company he trained himself as an electrician and published a paper about the Wheatstone Bridge, that was received well by, among others, William Thomson (Lord Kelvin) and James Maxwell. His next publication earned him his first enemy: R.S. Culley, the engineer-in-chief of the nationalized telegraph company. Heaviside's view on the duplex method was opposed to Culley's and he ridiculed the man for his short-sightedness. His next achievement was a development of a theory for transmission lines (mathematically these are the telegraphers equations) which are of course tremendously important for telegraphy (and telephony) cables. The speed of light popped up in his equations, which pointed already to the electromagnetic interpretation of light.

Heaviside has been poor throughout his whole life. He got a small income form his scientific contributions to *The Electrician* in the period 1882-1902. They also published his 3 volume work *Electromagnetic Theory* (1893-1912) but that didn't earn him much money. He had moved to London in 1882. It was there that he reduced twelve of Maxwell's equations to just four using vector calculus. They are in their simplest form the following relations: $\mathrm{curl}\,\mathbf{E}=−\frac{\partial \mathbf{B}}{\partial t}$, $\mathrm{curl}\,\mathbf{B}=\frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial t}$, $\mathrm{div}\,\mathbf{E}=0$, and $\mathrm{div}\,\mathbf{B}=0$, where $\mathbf{B}$ is the magnetic field and $\mathbf{E}$ the electric field, and $c$ the speed of light. A mathematical beauty by its simplicity and its symmetry. Previously people had tried to deal with them using quaternions, invented by Hamilton in 1843. Together with his brother Arthur, Oliver had worked on the design of a distortion free transmission line. One had to arrange that $G/C=L/R$, which is known as the Heaviside condition ($C=$ capacitance, $R=$ resistance, $L=$ inductance, and $G=$ shunt inductance). This was his gift to society that would make long-distance telephony possible. However Arthur and Oliver had to ask for publishing permission from their employer the Post Office, but that was surprisingly refused. The bad omen was William Preece, who had opposing views on the solution and happened to be the engineer-in-chief of the Post Office then, and this resulted in a lifelong and bitter battle between him and Oliver. Oliver referred to Preece's ideas as the "drain-pipe theory". Oliver's results were eventually published with some delay, which brought him new fame. Unfortunately for Oliver, Preece was well respected and the next year he became president of the IEE and in this position he could thwart Oliver some more. In that period the Maxwellians became friends and collaborators. First FitzGerald and Lodge, and later Hertz from Germany.

Approaching the turn of the century, fate still haunted Oliver. His mother died in 1894, his father in 1896. Poorer than ever and plagued by illness his friends organized a pension for him and he moved to live on his own. Pupin (and AT&T) in the U.S. got rich on a patent for distortion-free transmission lines based on a formula that Heaviside published 3 years earlier. When the Royal Society wanted to award him the Hughes Medal, he refused because they had rejected the last part of his paper on operators in physics saying that the mathematics were not rigorous enough. Nevertheless, later he accepted a pension, just to survive. But recognition started to emerge. At some point he was even shortlisted for the Nobel Prize (like Einstein and Planck, but the 1912 Prize went to Niels Dalen). By then he had published his three volumes of his *Electromagnetic Theory*. He got an honorary membership of the American IEE (1918) and he was awarded the Faraday Medal of the IEE (1921). When he was found unconscious in 1925 he was moved to a home, but he died shortly after.

Mahon goes through the life of Heaviside in twelve chapters, each one corresponding to a place where Heaviside lived and covering successive time periods. However each chapter is also the starting point to discuss one of his achievements. Because that requires to explain what preceded, how he came to his conclusion, and how and by whom the idea was picked up, and what its eventual fate was, the period covered in a chapter is much broader than announced in the title. Hence, the text is not always strictly chronological. Therefore the chronology summarised in the time-line in the beginning of the book comes in handy. There are also, sometimes relatively extensive, biographies of the persons who played a role in Heaviside's life, and then the list of the main characters inserted after the time-line is also useful. It is clear that Mahon, who also authored a book on Maxwell and co-authored another one on Maxwell and Faraday, is an admirer of Heaviside's electrical contributions, but he also gives credit to his significance for mathematics. The book is obviously written for a general public, so the discussions about Heaviside's results are only slightly technical. There are many quotations from texts written by Heaviside, which explains a lot of how his character was, and what he thought and expected from others. The way he wrote about his housekeeper at a later age is hilarious. He must have been a very difficult man to live with. There are also 33 pages with extra notes giving additional explanations. The book gives some insight in his work and the man that is behind it. Heaviside's very peculiar and enigmatic character will forever remain inscrutable, but Mahon does a really good attempt to understand what was driving this lone genius and to give him some of the respect that he rightfully deserves and that he had to miss during most of his life.

**Submitted by Adhemar Bultheel |

**8 / Jan / 2018