Dr Oliver Heaviside, Fellow of the Royal Society, was a self-taught mathematician, scientist and engineer, who was awarded the first Faraday Medal, and almost gained a Nobel Prize for physics. He postulated the existence of the ionosphere^{1}, which makes long distance radio communications possible, and simplified and improved Maxwell's electromagnetic field equations. He patented coaxial cable and made high-speed cable telegraphy and telephony a possibility, through his analysis of electromagnetic theory. He was a recluse almost all his life, later becoming an eccentric, signing himself WORM. He lived and died in poverty, but was an intellectual giant of his day. Electrical engineers and physicists still use his terminology and mathematical techniques over 100 years later. Without him the Victorian internet would not have been perfected.

**The Wheatstone Years**

Oliver Heaviside was born in Camden, London in 1850, the youngest of four brothers, and lived near Charles Dickens' former home for a time^{2}. One of Oliver's uncles, Sir Charles Wheatstone, patented the first commercial use of the electric telegraph in the 1830s for use on the railways along with his partner Sir William Fothergill Cooke.

Although Oliver left school at 16, he only had one period of paid employment during the rest of his life. This lasted for 6 years, until the age of 24, after which he became a virtual recluse. He used the rest of his time building his understanding of electrical science and developing new ideas, and mathematics, in this subject. During his brief period of employment he worked in Denmark and Newcastle for a telegraph company, later part of the General Post Office. Telegraphy was to be a lasting interest and motivation throughout his subsequent career as a physicist, mathematician and engineer.

Heaviside was partially deaf because of a bout of scarlet fever as a child, which made him something of a loner. His mother, being an educated woman, opened a school for girls in Camden, which Oliver attended until he was eight. His parents then sent him to a local boy's school 'for intermediate classes'. Eventually his formal education culminated in being awarded the fifth highest marks (out of 538 candidates), despite being the youngest, in the 1865 College of Preceptors Examination, scoring the first place in natural sciences.

After completing his formal schooling, Heaviside, on the advice of his Uncle Charles, entered the telegraph industry at the age of eighteen. In the intervening two years Wheatstone further influenced Oliver to learn to play several musical instruments, as well as learning to speak German and Danish.

While working as a telegraph operator, Heaviside noticed that the speed of transmission between Denmark and England was faster, by around 40%, than between England and Denmark. Although these transmissions eventually degenerated towards the same, lower speed, no one could explain why^{3}. Telegraphic theory had not advanced since 1855, following the initial work of Lord Kelvin.

In 1870, the Government granted the General Post Office monopoly over telegraphic (and later telephone) services in the UK^{4}. The GPO took over the company for which Heaviside worked. He was moved to Newcastle, and was promoted to chief telegraph operator. In 1872 he published his first paper, on comparing electromotive forces. In his second paper, the following year, he used differential calculus for the first time in a description of the Wheatstone Bridge. Heaviside sent a copy of his paper to James Clerk Maxwell, who received it well. This shows that he was already pushing the frontiers of electrical science forward and was known within scientific circles, presumably because of his Wheatstone connections (no pun intended). In the same year, Maxwell published his treatise^{5}, which was to become a cornerstone of physics and electrical engineering in the 19th century and, indeed, to this day.

**Telegraphy**

In 1874, Heaviside left his first and only employment. He joined The Society of Telegraph Engineers, and moved back to Camden to live with his parents. He also spent time reading, understanding and building on Maxwell's treatise, which turned out to be the second great motivator for the rest of his career.

Meanwhile, there was a huge upsurge in interest in telegraphy as a way of communicating between Britain and its dominions. Up to this point ships were the only means of carrying mail between London and the outposts of Empire, sometimes taking months to complete a journey. A telegraph cable was laid the 4,200km (2,600 miles) between Ireland and Newfoundland, Canada. It was the first of many transatlantic cables that Britain would lay, between 1858 and 1865 (latterly using Brunel's SS Great Eastern). The first was ruined almost immediately by using very high voltages in an attempt to speed up communications. Early transcontinental telegraphy subsequently had to use much lower voltages at higher 'carrier' frequencies, along with very sensitive receivers, to work at all. Despite this they were very slow, at eight words a minute, and consequently could not handle voice communications. Nevertheless, the network spanned the world by 1895 with 160,000 nautical miles (250,000km) of submarine cable, at an average cost of £600 per mile (around £50,000 in today's money, costing approximately £8 billion).

In 1874, Heaviside, aware of these problems, applied himself to their solution. He then published, over a number of years, what were then, three remarkable papers about telegraphy^{6}. He used partial differential equations to model the behaviour of a submarine cable of the day, describing how voltage and current would propagate along the cable in the presence of inductance in it, due to the cable's own properties. He also explained how asymmetric transmission speeds could be eliminated, prompted by his experience in Denmark. Finally, he analysed how an artificial cable fault (now called a loading coil) could be used to speed up the rate of transmission of signals. However, little note was taken of his work, at this stage, mainly because few people understood the mathematics, and Heaviside was not interested in explaining it. Consequently, his theories were not put into practical use for almost twenty years. However, eventually others did put his theories into practice to speed up communications on submarine cables, including adding speech via telephony.

**Preece and Electromagnetism**

In 1892, William Preece^{7} became the engineer-in-chief of the General Post Office. He was sixteen years older than Heaviside. Preece, a practical engineer and a one-time assistant to Michael Faraday, thought of electricity as analogous to the flow of an incompressible fluid through a pipe. He did not understand the basic mathematics of electrical science, but nevertheless was a man of tremendous drive and enthusiasm, holding several patents in duplex^{8} telegraphy. Preece eventually came to see Heaviside as an upstart theoretician who dared to challenge his authority as the leading electrical engineer in the land. The ensuing battle between the two men, over the role of induction in telegraph and telephone circuits, would last for decades^{9}. What was the outcome?

Maxwell had died in 1879, at the age of 48. He was a genius in the mould of Newton (famous for his laws of motion) and Einstein (famous for quantum mechanics). Maxwell's treatise postulated that a distributed electrical field could store energy. He used the latest ideas of the day from his contemporaries and pulled them all together and created a theory of electromagnetism that has stood the test of time, unaffected by relativity and quantum theory, because he already factored their effects into his theory. Heaviside, after Maxwell's death, took up the mathematics of his equations, along with others (FitzGerald, Hodge, and Hertz) and simplified them. Maxwell had originally devised twenty equations with twenty unknowns, which Heaviside (and Hertz independently) reduced to four equations with four unknowns. Almost as a by-product, one of the key findings was that the speed of light in a vacuum could not be exceeded. For this work Heaviside was elected a FRS in 1891.

During the intervening ten years he had managed to support himself by publishing many papers in commercial magazines^{10}, as well as in learned society proceedings, which of course was unpaid. He was also the author of a two-volume book on electromagnetic theory. In 1905, he was made an honorary Doctor by the University of Goettingen, which King George II, also Elector of Hanover, had founded in Germany. The University produced many famous students, including Napoleon, and famous professors, such as the brothers Jakob and Wilhelm Grimm, who, amongst other things, wrote the first German dictionary.

**Mathematical Innovation**

Mathematicians, including Hamilton from Ireland, Gibbs in the US, and Tait in England, had been working independently on a new branch of mathematics in the 1870s, known as 'quaternions'. Maxwell had also used this technique in his treatise. Vector analysis subsequently replaced it. Heaviside, in 1882, began using vector analysis, particularly in his work on Maxwell's equations. Gibbs in the US was also an early convert to vector analysis. The Gibbs-Heaviside approach gradually won the day and replaced quarternions as the preferred method of analysing electromagnetism and other physical phenomena.

Within the studies of Vector calculus, Laplace Transforms are 'operators' for reducing complex mathematical relationships to algebraic equations, making them easier to manipulate. Heaviside's contribution to the use of operators in electrical science was to show how to apply these techniques to analyse real physical problems. He began working on these techniques in 1887, using his own version of the Laplace Transform, and another new idea: the step function, which was also to be called the Heaviside Function.

In 1894, shortly after being elected as a FRS, the Society refused to continue to publish Heaviside's work on operators. Part III was rejected, despite earlier publication of Parts I and II. Why? The Society cited a lack of 'rigour'. Heaviside then spent the next ten years harbouring ill feelings towards the Society. Lord Rayleigh, as President, later had Part III published in the Proceedings. He also had a rejected theory from J.J. Waterston, known as The Kinetic Theory of Gases, exhumed from the archive and published.

**Retirement and Eccentricity**

Heaviside's father died in 1896, leaving him to fend for himself for the first time, at the age of forty-six. At about this time his editor on 'The Electrician', his main source of income, moved on. Fortunately Heaviside's friends arranged for a Civil List pension to be paid to him in recognition of his work. He agreed to accept this, unlike an earlier occasion^{11}. When his father retired to Paignton, Heaviside had relocated to Devon, moving to Newton Abbot, close to the River Lemon, after his father died, then finally to Torquay to live in the same house, on the upper floor, as the unmarried sister of a friend's wife.

In 1912, Heaviside, Einstein, Mach, Lorentz and Planck were final contenders for the Physics Nobel Prize. None were successful, the winner being Nils Gustav Dalen who invented a regulator for feeding gas to lighthouse lamps^{12}.

Heaviside was awarded the Faraday Medal in 1922. However he was becoming even more reclusive, signing his correspondence with the initials WORM, due to the way he thought he was perceived by his contemporaries.

He died in 1925 after falling off a ladder, which compounded his poor state of health. Ten years later, in 1935, the first round the world telephone conversation took place, travelling 23,300 miles (37,000km), of which 19,500 miles (31,000km) was by radio. This would not have been possible without the Heaviside layer, which refracts radio waves back to the earth, and without Heaviside's work on electromagnetic theory.

Heaviside is buried in Torbay, in Paignton cemetery, Devon. A blue plaque marks his old house in Newton Abbot by Bradley Manor, put there by The Society of Telegraph Engineers^{13}.