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{{Short description|English mathematician and physicist (1850–1925)}}
{{Redirect|Heaviside}}
{{Use dmy dates|date=May 2020}}
{{Use British English|date=March 2012}}
{{Infobox scientist
| honorific_suffix  = {{post-nominals|size=100%|FRS}}
| image             = Oheaviside.jpg
| caption           = Heaviside, {{circa|1900}}
| birth_date        = {{birth date|df=y|1850|5|18}}
| birth_place       = [[Camden Town]], [[Middlesex]], England
| death_date        = {{death date and age|df=y|1925|2|3|1850|5|18}}
| death_place       = [[Torquay]], [[Devon]], England
| known_for         = {{plainlist|
* Formulating [[telegrapher's equations]] (1876)
* Patenting a [[coaxial cable]] (1880)
* Reformulating [[Maxwell's equations]] (1884)
* Coining the term ''[[Electrical impedance|impedance]]'' (1886)
* Inventing [[operational calculus]] (1893)
* Postulating the [[Kennelly–Heaviside layer]] (1902)
}}
| relatives         = [[Charles Wheatstone]] (uncle-in-law)
| awards            = [[Fellow of the Royal Society|FRS]] (1891)<ref name="frs">{{Cite journal | author = Anon| doi = 10.1098/rspa.1926.0036 | title = Obituary Notices of Fellows Deceased: Rudolph Messel, Frederick Thomas Trouton, John Venn, John Young Buchanan, Oliver Heaviside, Andrew Gray| journal = Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | volume = 110 | issue = 756 | pages = i–v | year = 1926 |bibcode = 1926RSPSA.110D...1. | doi-access = free}}</ref><br>[[Faraday Medal]] (1922)
| fields            = {{tree list}}
*[[Mathematics]]
*[[Physics]]
**[[Electromagnetism]]
{{tree list/end}}
| work_institutions = 
}}

'''Oliver Heaviside''' ({{IPAc-en|ˈ|h|ɛ|v|i|s|aɪ|d}} {{respell|HEH|vee|syde}}; 18 May 1850 – 3 February 1925) was an English [[mathematician]] and [[physicist]] who invented a new technique for solving [[differential equation]]s (equivalent to the [[Laplace transform]]), independently developed [[vector calculus]], and rewrote [[Maxwell's equations]] in the form commonly used today. He significantly shaped the way Maxwell's equations are understood and applied in the decades following Maxwell's death. His formulation of the [[telegrapher's equations]] became commercially important during his own lifetime, after their significance went unremarked for a long while, as few others were versed at the time in his novel methodology.<ref name=oddity>{{Cite journal | last1 = Hunt | first1 = B. J. | title = Oliver Heaviside: A first-rate oddity | doi = 10.1063/PT.3.1788 | journal = Physics Today | volume = 65 | issue = 11 | pages = 48–54 | year = 2012 | bibcode = 2012PhT....65k..48H | doi-access = free}}</ref> Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science.<ref name=oddity/>

==Early life==
Heaviside was born in [[Camden Town]], London, at 55 Kings Street<ref name = Nahin>{{cite book| ref=Nahin|author = Nahin, Paul J. |author-link=Paul J. Nahin| title = Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age| url = https://books.google.com/books?id=e9wEntQmA0IC&pg=PA13| date = 9 October 2002| publisher = JHU Press| isbn = 978-0-8018-6909-9}}</ref>{{rp|13}} (now Plender Street), the youngest of three children of Thomas, a draughtsman and wood engraver, and Rachel Elizabeth (née West). He was a short and red-headed child, and suffered from [[scarlet fever]] when young, which left him with a hearing impairment. A small legacy enabled the family to move to a better part of Camden when he was thirteen and he was sent to Camden House Grammar School. He was a good student, placing fifth out of five hundred students in 1865, but his parents could not keep him at school after he was 16, so he continued studying for a year by himself and had no further formal education.<ref name=Hunt91>Bruce J. Hunt (1991) [[The Maxwellians]], [[Cornell University Press]] {{ISBN|978-0-8014-8234-2}}</ref>{{rp|51}}

Heaviside's uncle by marriage was Sir [[Charles Wheatstone]] (1802–1875), an internationally celebrated expert in telegraphy and electromagnetism, and the original co-inventor of the first commercially successful telegraph in the mid-1830s. Wheatstone took a strong interest in his nephew's education<ref name=wheatstone>{{cite book| last1= Sarkar|first1= T. K. | last2= Mailloux|first2= Robert|last3= Oliner|first3= Arthur A.|last4= Salazar-Palma|first4= M. |author4-link=Magdalena Salazar Palma|last5= Sengupta|first5= Dipak L.| title = History of Wireless| url = https://books.google.com/books?id=NBLEAA6QKYkC&pg=PA230| date = 2006| publisher = John Wiley & Sons| isbn = 978-0-471-78301-5| page = 230 |author-link1=Tapan Sarkar|author-link3=Arthur A. Oliner}}</ref> and in 1867 sent him north to work with his older brother Arthur Wheatstone, who was managing one of Charles' telegraph companies in [[Newcastle-upon-Tyne]].<ref name=Hunt91/>{{rp|53}}

Two years later he took a job as a telegraph operator with the Danish [[Great Northern Telegraph Company]] laying a cable from Newcastle to [[Denmark]] using British contractors. He soon became an electrician. Heaviside continued to study while working, and by the age of 22 he published an article in the prestigious ''[[Philosophical Magazine]]'' on 'The Best Arrangement of [[Wheatstone's Bridge]] for measuring a Given Resistance with a Given Galvanometer and Battery'{{sfn|Heaviside|1892|pp=3–8}} which received positive comments from physicists who had unsuccessfully tried to solve this algebraic problem, including [[Sir William Thomson]], to whom he gave a copy of the paper, and [[James Clerk Maxwell]]. When he published an article on the [[Duplex (telecommunications)|duplex]] method of using a telegraph cable,{{sfn|Heaviside|1892|pp=18–34}} he poked fun at R. S. Culley, the engineer in chief of the [[General Post Office#Telegraph|Post Office telegraph]] system, who had been dismissing duplex as impractical. Later in 1873 his application to join the [[Society of Telegraph Engineers]] was turned down with the comment that "they didn't want telegraph clerks". This riled Heaviside, who asked Thomson to sponsor him, and along with support of the society's president he was admitted "despite the P.O. snobs".<ref name=Hunt91/>{{rp|60}}

In 1873, Heaviside had encountered Maxwell's newly published, and later famous, two-volume ''[[Treatise on Electricity and Magnetism]]''. In his old age Heaviside recalled:
{{blockquote|
I remember my first look at the great treatise of Maxwell's when I was a young man... I saw that it was great, greater and greatest, with prodigious possibilities in its power... I was determined to master the book and set to work. I was very ignorant. I had no knowledge of mathematical analysis (having learned only school algebra and trigonometry which I had largely forgotten) and thus my work was laid out for me. It took me several years before I could understand as much as I possibly could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly... It will be understood that I preach the gospel according to my interpretation of Maxwell.<ref>{{cite book| last1= Sarkar|first1= T. K. | last2= Mailloux|first2= Robert|last3= Oliner|first3= Arthur A.|last4= Salazar-Palma|first4= M.|author4-link=Magdalena Salazar Palma |last5= Sengupta|first5= Dipak L. | title = History of Wireless| url = https://books.google.com/books?id=NBLEAA6QKYkC&pg=PA232| date = 30 January 2006| publisher = John Wiley & Sons| isbn = 978-0-471-78301-5| page = 232}}</ref>
}}

Undertaking research from home, he helped develop [[transmission line]] theory (also known as the "''[[telegrapher's equations]]''"). Heaviside showed [[Heaviside condition|mathematically]] that uniformly distributed [[inductance]] in a telegraph line would diminish both [[attenuation]] and [[distortion]], and that, if the inductance were great enough and the [[Electrical insulation|insulation]] [[Electrical resistance|resistance]] not too high, the [[Digital circuit|circuit]] would be distortionless in that [[Current (electricity)|currents]] of all [[Frequency|frequencies]] would have equal speeds of propagation.<ref>{{EB1911 |wstitle=Telephone |volume=26 |page=554 |first=Harry Robert |last=Kempe |inline=1}}</ref> Heaviside's equations helped further the implementation of the telegraph.

==Middle years==
From 1882 to 1902, except for three years, Heaviside contributed regular articles to the trade paper ''[[The Electrician]]'', which wished to improve its standing, for which he was paid £40 per year. This was hardly enough to live on, but his demands were very small and he was doing what he most wanted to. Between 1883 and 1887 he averaged 2–3 articles per month and these articles later formed the bulk of his ''Electromagnetic Theory'' and ''Electrical Papers''.<ref name=Hunt91/>{{rp|71}}

In 1880, Heaviside researched the [[skin effect]] in telegraph transmission lines. That same year he patented, in England, the [[coaxial cable]]. In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form (they had already been recast as [[quaternion]]s) to its modern [[Vector (geometric)|vector]] terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four [[differential equation]]s in two unknowns we now know as [[Maxwell's equations]]. The four re-formulated Maxwell's equations describe the nature of electric charges (both static and moving), magnetic fields, and the relationship between the two, namely electromagnetic fields.

Between 1880 and 1887, Heaviside developed the [[operational calculus]] using <math>p</math> for the [[differential operator]], (which Boole had previously denoted by <math>D</math>''<ref>"A Treatise on Differential Equations", 1859</ref>''), giving a method of solving differential equations by direct solution as [[algebraic equation]]s. This later caused a great deal of controversy, owing to its lack of [[rigour]]. He famously said, "Mathematics is an experimental science, and definitions do not come first, but later on. They make themselves, when the nature of the subject has developed itself."<ref>{{Cite journal |doi = 10.1098/rspl.1893.0059|title = VIII. On operations in physical mathematics. Part II|journal = Proceedings of the Royal Society of London|volume = 54|issue = 326–330|pages = 105–143|year = 1894|s2cid = 121790063}}</ref> On another occasion he asked, "Shall I refuse my dinner because I do not fully understand the process of digestion?"<ref>Heaviside, "Mathematics and the Age of the Earth" in ''Electromagnetic Theory'' vol. 2</ref>

In 1887, Heaviside worked with his brother Arthur on a paper entitled "The Bridge System of Telephony". However the paper was blocked by Arthur's superior, [[William Henry Preece]] of the [[General Post Office|Post Office]], because part of the proposal was that [[loading coil]]s ([[inductor]]s) should be added to telephone and telegraph lines to increase their self-induction and correct the distortion which they suffered. Preece had recently declared self-inductance to be the great enemy of clear transmission. Heaviside was also convinced that Preece was behind the sacking of the editor of ''The Electrician'' which brought his long-running series of articles to a halt (until 1891).<ref>{{cite ODNB|chapter=Heaviside, Oliver|title=Oxford Dictionary of National Biography|first=Bruce J.|last=Hunt|year=2004|doi=10.1093/ref:odnb/33796|chapter-url=http://www.oxforddnb.com/view/article/33796|chapter-url-access=subscription}}</ref> There was a long history of animosity between Preece and Heaviside. Heaviside considered Preece to be mathematically incompetent, an assessment supported by the biographer [[Paul J. Nahin]]: "Preece was a powerful government official, enormously ambitious, and in some remarkable ways, an utter blockhead." Preece's motivations in suppressing Heaviside's work were more to do with protecting Preece's own reputation and avoiding having to admit error than any perceived faults in Heaviside's work.<ref name=Nahin/>{{rp| xi–xvii, 162–183}}

The importance of Heaviside's work remained undiscovered for some time after publication in ''The Electrician''. In 1897, [[AT&T Corp.|AT&T]] employed one of its own scientists, [[George Ashley Campbell|George A. Campbell]], and an external investigator [[Mihajlo Idvorski Pupin|Michael I. Pupin]] to find some respect in which Heaviside's work was incomplete or incorrect. Campbell and Pupin extended Heaviside's work, and AT&T filed for patents covering not only their research, but also the technical method of constructing the coils previously invented by Heaviside. AT&T later offered Heaviside money in exchange for his rights; it is possible that the Bell engineers' respect for Heaviside influenced this offer. However, Heaviside refused the offer, declining to accept any money unless the company were to give him full recognition. Heaviside was chronically poor, making his refusal of the offer even more striking. In 1959, Norbert Wiener published his fiction ''The Tempter'' and accused AT&T (named ''Williams Controls Company'') and Michael I. Pupin (named ''Diego Dominguez'') of having usurped Heaviside's inventions.<ref>{{cite book| author = Wiener, Norbert | title = Invention: The Care and Feeding of Ideas| year = 1993| publisher = MIT Press| isbn = 0-262-73111-8| pages = [https://archive.org/details/inventioncarefee0000wien/page/70 70]–75| location = Cambridge, Massachusetts|url=https://archive.org/details/inventioncarefee0000wien | url-access = registration | author-link = Wiener, Norbert}}</ref><ref>{{cite book |author=Wiener, Norbert |title=The Tempter |publisher=Random House |year=1959 |location=New York}}</ref><ref>{{cite book |author=Montagnini, Leone |title=Harmonies of Disorder – Norbert Wiener: A Mathematician-Philosopher of Our Time|publisher=Springer|location=Cham (Switzerland)|year=2017|isbn=978-3-31984455-8|pages=249–252}}</ref>

But this setback had the effect of turning Heaviside's attention towards electromagnetic radiation,{{sfn|Hunt|2004}} and in two papers of 1888 and 1889, he calculated the deformations of electric and magnetic fields surrounding a moving charge, as well as the effects of it entering a denser medium. This included a prediction of what is now known as [[Cherenkov radiation]], and inspired his friend [[George Francis FitzGerald|George FitzGerald]] to suggest what now is known as the [[Lorentz–FitzGerald contraction]].

In 1889, Heaviside first published a correct derivation of the magnetic force on a moving charged particle,<ref>{{Cite journal | doi = 10.1080/14786448908628362| title = XXXIX.On the electromagnetic effects due to the motion of electrification through a dielectric| journal = Philosophical Magazine |series=Series 5| volume = 27| issue = 167| pages = 324–339| year = 1889| last1 = Heaviside | first1 = O. | url = https://zenodo.org/record/1431195}}</ref> which is the magnetic component of what is now called the [[Lorentz force]].

In the late 1880s and early 1890s, Heaviside worked on the [[concept]] of [[electromagnetic mass]]. Heaviside treated this as material [[mass]], capable of producing the same effects. [[Wilhelm Wien]] later verified Heaviside's expression (for low [[Velocity|velocities]]).

In 1891 the British [[Royal Society]] recognized Heaviside's contributions to the mathematical description of electromagnetic phenomena by naming him a [[Fellow of the Royal Society]], and the following year devoting more than fifty pages of the ''Philosophical Transactions'' of the Society to his vector methods and electromagnetic theory. In 1905 Heaviside was given an honorary doctorate by the [[University of Göttingen]].

==Later years and views==
[[File:Heaviside blue plaque.jpg|thumb|[[Blue plaque]] dedicated to Heaviside in Paignton]]
In 1896, FitzGerald and [[John Perry (engineer)|John Perry]] obtained a [[Pensions in the United Kingdom#Civil List pensions|civil list pension]] of £120&nbsp;per year for Heaviside, who was now living in Devon, and persuaded him to accept it, after he had rejected other charitable offers from the Royal Society.{{sfn|Hunt|2004}}

In 1902, Heaviside proposed the existence of what is now known as the [[Kennelly–Heaviside layer]] of the [[ionosphere]]. Heaviside's proposal included means by which radio signals are transmitted around the Earth's curvature. The existence of the ionosphere was confirmed in 1923. The predictions by Heaviside, combined with [[Max Planck|Planck's]] radiation theory, probably discouraged further attempts to detect radio waves from the [[Sun]] and other [[astronomical object]]s. For whatever reason, there seem to have been no attempts for 30&nbsp;years, until [[Karl Guthe Jansky|Jansky's]] development of [[radio astronomy]] in 1932.

Heaviside was an opponent of Albert Einstein's [[theory of relativity]].<ref name="Eves 1988">Eves, Howard. (1988). ''Return to Mathematical Circles: A Fifth Collection of Mathematical Stories and Anecdotes''. PWS-Kent Publishing Company. p. 27. {{ISBN|9780871501059}}</ref> Mathematician [[Howard Eves]] has commented that Heaviside "was the only first-rate physicist at the time to impugn Einstein, and his invectives against relativity theory often bordered on the absurd".<ref name="Eves 1988"/>

In later years his behavior became quite [[Eccentricity (behavior)|eccentric]]. According to associate B.A. Behrend, he became a recluse who was so averse to meeting people that he delivered the manuscripts of his ''[[The Electrician|Electrician]]'' papers to a grocery store, where the editors picked them up.<ref>
{{cite magazine
  | title = Pages with the editor
  | date=June 1925
  | magazine = [[Popular Radio]]
  | volume = 7 | issue = 6 | pages = 6
  | location = New York
  | url = http://www.americanradiohistory.com/Archive-Popular-Radio/Popular-Radio-1925-06.pdf
  | access-date = 14 August 2014
}}
</ref>
Though he had been an active cyclist in his youth, his health seriously declined in his sixth decade. During this time Heaviside would sign letters with the initials "''W.O.R.M.''" after his name. Heaviside also reportedly started painting his fingernails pink and had granite blocks moved into his house for furniture.<ref name=Nahin/>{{rp|page=xx}} In 1922, he became the first recipient of the [[Faraday Medal]], which was established that year.

On Heaviside's religious views, he was a [[Unitarianism|Unitarian]], but not religious. He was even said to have made fun of people who put their faith in a supreme being.<ref>
{{cite book
 |author=Pickover, Clifford A. |author-link=Clifford A. Pickover 
 |year=1998
 |title=Strange Brains and Genius: The secret lives of eccentric scientists and madmen
 |publisher=Plenum Publishing Company Limited
 |isbn=9780306457845
 |chapter=Oliver Heaviside
 |quote=Religion: A Unitarian, but not religious. Poked fun at those who put their faith in a Supreme Being.
}}
</ref>



Heaviside died on 3&nbsp;February 1925, at [[Torquay]] in [[Devon]] after falling from a ladder,<ref>
{{cite journal
 |title=Oliver Heaviside
 |date=March 1925 |type=obituary
 |journal=Journal of the AIEE
 |volume=44 |issue=3 |pages=316–317
 |doi=10.1109/JAIEE.1925.6537168
|s2cid=51663331 }}
</ref> and is buried near the eastern corner of [[Paignton]] cemetery. He is buried with his father, Thomas Heaviside (1813–1896), and his mother, Rachel Elizabeth Heaviside. The gravestone was cleaned thanks to an anonymous donor sometime in 2005.<ref>
{{cite book
 |first=Basil |last=Mahon
 |year=2009
 |title=Oliver Heaviside: Maverick mastermind of electricity
 |publisher=The Institution of Engineering and Technology
 |isbn=9780863419652
}}
</ref> He was always held in high regard by most electrical engineers, particularly after his correction to [[William Thomson, 1st Baron Kelvin|Kelvin]]'s transmission line analysis was vindicated, but most of his wider recognition was gained posthumously.

===Heaviside Memorial Project===
[[File:Comparison of before and after the monument restoration.PNG|thumb|Comparison of before and after the restoration project.]]
In July 2014, academics at [[Newcastle University]], UK and the Newcastle Electromagnetics Interest Group founded the Heaviside Memorial Project<ref>{{Cite journal |url=http://www.heavisidememorialproject.co.uk |title=Heaviside Memorial Project Homepage |journal=Nature |volume=165 |issue=4208 |pages=991–3 |author=<!--Staff writer(s); no by-line.--> |date=27 July 2014 |publisher=Heaviside Memorial Project |access-date=31 July 2014 |archive-url=https://web.archive.org/web/20140718172517/http://heavisidememorialproject.co.uk/ |archive-date=18 July 2014 |url-status=dead}}</ref> in a bid to fully restore the monument through public subscription.<ref>{{cite web |url=http://www.torquayheraldexpress.co.uk/Bid-restore-monument/story-21752656-detail/story.html |archive-url=https://archive.today/20140806033513/http://www.torquayheraldexpress.co.uk/Bid-restore-monument/story-21752656-detail/story.html |url-status=dead |archive-date=6 August 2014 |title=Bid to restore Paignton monument to Oliver Heaviside |author=<!--Staff writer(s); no by-line.--> |date=27 July 2014 |website=www.torquayheraldexpress.co.uk |publisher=Herald Express |access-date=29 July 2014}}</ref><ref>{{cite web |url=http://www.ncl.ac.uk/sage/about/news/item/the-heaviside-memorial-project |title=The Heaviside Memorial Project |author=<!--Staff writer(s); no by-line.--> |date=29 July 2014 |website=www.newcastle.ac.uk |publisher=Newcastle University |access-date=29 July 2014 |url-status=dead |archive-url=https://web.archive.org/web/20140729185150/http://www.ncl.ac.uk/sage/about/news/item/the-heaviside-memorial-project |archive-date=29 July 2014}}</ref> The restored memorial was ceremonially unveiled on 30 August 2014 by Alan Heather, a distant relative of Heaviside. The unveiling was attended by the Mayor of Torbay, the [[Member of Parliament (United Kingdom)|Member of Parliament]] (MP) for Torbay, an ex-curator of the Science Museum (representing the [[Institution of Engineering and Technology]]), the Chairman of the Torbay Civic Society, and delegates from Newcastle University.<ref>{{cite web |url=http://www.torquayheraldexpress.co.uk/Restored-Heaviside-memorial-unveiled-Saturday/story-22858873-detail/story.html |title=Restored Heaviside memorial unveiled on Saturday |author=<!--Staff writer(s); no by-line.--> |date=1 September 2014 |website=www.torquayheraldexpress.co.uk |publisher=Herald Express |access-date=1 September 2014 |url-status=dead |archive-url=https://web.archive.org/web/20140903114836/http://www.torquayheraldexpress.co.uk/Restored-Heaviside-memorial-unveiled-Saturday/story-22858873-detail/story.html |archive-date=3 September 2014}}</ref>

===The Institution of Engineering and Technology===

A collection of Heaviside's papers is held at the [[Institution of Engineering and Technology]] (IET) Archive Centre.<ref>Savoy Hill House 7–10, Savoy Hill, London WC2R 0BU email: archives@theiet.org</ref>  The collection consists of notebooks containing mathematical equations and calculations, annotated pamphlets mainly relating to telegraphy, manuscript notes, drafts of papers, correspondence, drafts of articles for ‘Electromagnetic Theory’.
An audio tribute from 1950 to Oliver Heaviside by Oliver E Buckley, President of Bell Telephone Labs, has been digitised and accessible on the IET Archives biography of Oliver Heaviside.<ref>{{cite web |last1=Heaviside |first1=Oliver |title=Oliver Heaviside 1850-1925 |url=https://www.theiet.org/membership/library-archives/the-iet-archives/biographies/oliver-heaviside-1850-1925/ |website=The IET Archives:biographies  |access-date=21 November 2023}}</ref>

In 1908 Oliver Heaviside was made an Honorary Member of the [[Institution of Electrical Engineers]] (IEE). His entry reads as: “1908 Oliver Heaviside FRS” in the IEE Roll of Honorary Members and Faraday Medallists 1871-1921<ref>{{cite journal |last1=Heaviside |first1=Oliver |title=IEE Roll of Honorary Members and Faraday Medallists 1871-1921 |journal=IET Archives Reference: IET/SPE/4/8/1|date=1908}}</ref><ref>{{cite web |last1=Heaviside |first1=Oliver |title=From under the sea to the edge of space: the work of Oliver Heaviside |url=https://ietarchivesblog.org/2023/04/05/from-under-the-sea-to-the-edge-of-space-the-work-of-oliver-heaviside/ |website=Stories of the Institution of Electrical Engineers |date=5 April 2023 |publisher=The IET Archives Blog: Stories from the Institution of Engineering and Technology |access-date=21 November 2023}}</ref>
In 1922, he became the first recipient of the [[Faraday Medal]], which was established that year. Later on, in 1950 the Institution of Electrical Engineers Council established the Heaviside Premium Award “The Committee have considered the establishment of some form of permanent memorial to Oliver Heaviside and as a result recommend that a Heaviside Premium to the value of £10 be awarded each year for the best mathematical paper accepted.”<ref>{{cite journal |last1=Heaviside Premium Award |title=IEE Council Minutes | date=2 February 1950 | journal=IEE Archive Reference: IET/ORG/2/1/19}}</ref>

==Innovations and discoveries==
{{electromagnetism|Scientists}}
Heaviside did much to develop and advocate [[Vector (geometric)|vector]] methods and [[vector calculus]].<ref>See especially '''Electromagnetic Theory''', 1893 "The Elements of Vectorial Algebra and Analysis," vol.1 chap.3 pp.132–305 where he gave a complete account of the modern system</ref> [[James Clerk Maxwell|Maxwell's]] formulation of [[electromagnetism]] consisted of 20 equations in 20 variables. Heaviside employed the [[curl (mathematics)|curl]] and [[divergence]] operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables (<math>\textbf{B}, \textbf{E}, \textbf{J} ~\text{and} ~\rho</math>), the form by which they have been known ever since (see [[Maxwell's equations]]). Less well known is that Heaviside's equations and Maxwell's are not exactly the same, and in fact it is easier to modify the former to make them compatible with quantum physics.<ref>''Topological Foundations of Electromagnetism'', World Scientific Series in Contemporary Chemical Physics, 13 March 2008, Terence W. Barrett.</ref> The possibility of [[gravitational waves]] was also discussed by Heaviside using the analogy between the inverse-square law in gravitation and electricity.<ref>A gravitational and electromagnetic analogy,''Electromagnetic Theory'', 1893, 455–466 Appendix B. This was 25 years before Einstein's paper on this subject</ref> With [[quaternion]] multiplication, the square of a vector is a negative quantity, much to Heaviside's displeasure. As he advocated abolishing this negativity, he has been credited by [[C. J. Joly]]<ref>{{cite book |last=Hamilton |title=Elements of Quaternions |year=1899 |page=[https://archive.org/details/elementsquatern01hamigoog/page/n200 163] |publisher=Longmans, Green, and co. |isbn=9780828402194 |url=https://archive.org/details/elementsquatern01hamigoog|edition=2nd |editor-first=C.J. |editor-last=Joly}}</ref> with developing [[hyperbolic quaternion]]s, though in fact that mathematical structure was largely the work of [[Alexander Macfarlane]].

He invented the [[Heaviside step function]], using it to calculate the [[Electric current|current]] when an [[electric circuit]] is switched on. He was the first to use the unit impulse function now usually known as the [[Dirac delta function]].<ref>'''Electromagnetic Theory''', vol.II, para.271, eqns 54,55</ref> He invented his [[operational calculus]] method for solving [[linear differential equation]]s. This resembles the currently used [[Laplace transform]] method based on the "[[Inverse Laplace transform|Bromwich integral]]" named after [[Thomas John I'Anson Bromwich|Bromwich]] who devised a rigorous mathematical justification for Heaviside's operator method using contour integration.<ref>See the paper of Jeffreys quoted in the Bromwich WP article</ref> Heaviside was familiar with the Laplace transform method but considered his own method more direct.<ref>'''Electromagnetic Theory''' vol 3, section starting on p.324. Available online</ref><ref>A rigorous version of Heaviside's operational calculus has been constructed see Mikusinski J: '''The Operational Calculus''', Pergamon Press 1959</ref>

Heaviside developed the [[transmission line]] theory (also known as the "[[telegrapher's equations]]"), which had the effect of increasing the transmission rate over transatlantic cables by a factor of ten. It originally took ten minutes to transmit each character, and this immediately improved to one character per minute. Closely related to this was his discovery that telephone transmission could be greatly improved by placing [[electrical inductance]] in series with the cable.<ref>{{cite book| last=Wiener |first=Norbert | title = Invention: The Care and 70–75| location = Cambridge, Massachusetts|url=https://books.google.com/books?id=G3Q2qOtOeLYC| year = 1993| publisher = MIT Press| isbn = 0-262-73111-8}}</ref> Heaviside also independently discovered the [[Poynting vector]].<ref name =Nahin/>{{rp|116–118}}

Heaviside advanced the idea that the Earth's uppermost atmosphere contained an ionized layer known as the [[ionosphere]]; in this regard, he predicted the existence of what later was dubbed the [[Kennelly–Heaviside layer]]. In 1947 [[Edward Victor Appleton]] received the Nobel Prize in Physics for proving that this layer really existed.

===Electromagnetic terms===
Heaviside [[neologism|coined]] the following terms of art in [[electromagnetic theory]]:
* [[admittance]] ''(reciprocal of impedance)'' (December 1887);
* [[elastance]] ''(reciprocal of permittance, reciprocal of capacitance)'' (1886);
* [[Electrical conductance|conductance]] ''(real part of admittance, reciprocal of resistance)'' (September 1885);
* [[electret]] for the electric analogue of a permanent magnet, or, in other words, any substance that exhibits a quasi-permanent electric polarization (e.g. [[ferroelectric]]);
* [[Electrical impedance|impedance]] (July 1886);
* [[inductance]] (February 1886);
* [[Permeability (electromagnetism)|permeability]] (September 1885);
* [[permittance]] (now called capacitance) and [[permittivity]] (June 1887);
* [[reluctance]] (May 1888);<ref>Ronald R. Kline, ''Steinmetz: Engineer and Socialist'', p. 337, Johns Hopkins University Press, 1992 {{ISBN|0801842980}}.</ref>
Heaviside is sometimes incorrectly credited with coining ''[[susceptance]]'' (the imaginary part of admittance) and [[electrical reactance|''reactance'']] (the imaginary part of impedance). The former was coined by [[Charles Proteus Steinmetz]] (1894).<ref>Kline, p. 88</ref> The latter was coined by M. Hospitalier (1893).<ref>Steinmetz, Charles Proteus; Bedell, Frederick, [https://babel.hathitrust.org/cgi/pt?id=iau.31858046100776&view=1up&seq=830 "Reactance"], ''Transactions of the American Institute of Electrical Engineers'', vol. 11, pp. 768–776, 1894,<br />cied to, Blondel, A., "A propos de la reactance", ''L'Industrie Electrique'', 10 May 1893.<br />This is confirmed by Heaviside himself, [https://archive.org/details/electromagnetict0001heav/page/439/mode/1up "The term 'reactance' was lately proposed in France, and seems to me to be a practical word."]<br />Heaviside, ''Electromagnetic Theory'', vol. 1, p. 439, 1893.</ref>

==Publications==
{{wikisource author}}
{{Wikiquote}}
* 1885, 1886, and 1887, "Electromagnetic induction and its propagation", ''The Electrician''.
* 1888/89, "[[s:Electromagnetic effects of a moving charge|Electromagnetic waves, the propagation of potential, and the electromagnetic effects of a moving charge]]", ''The Electrician''.
* 1889, "[[s:Motion of Electrification through a Dielectric|On the Electromagnetic Effects due to the Motion of Electrification through a Dielectric]]", ''Phil.Mag.S.5'' 27: 324.
* 1892 "On the Forces, Stresses, and Fluxes of Energy in the Electromagnetic Field" ''Phil.Trans.Royal Soc. A'' 183:423–80.
* 1892 "On Operators in Physical Mathematics" Part I. ''Proc. Roy. Soc.'' 1892 Jan 1. vol.52 pp.&nbsp;504–529
* 1892 {{cite book|first=Oliver|last=Heaviside|title=Electrical Papers|url=https://archive.org/details/electricalpapers01heavuoft|volume=1|year=1892|publisher=Macmillan Co, London and New York|isbn=9780828402354}}
* 1893 "On Operators in Physical Mathematics" Part II ''Proc. Roy. Soc.'' 1893 Jan 1. vol.54 pp.&nbsp;105–143
* 1893 "A gravitational and electromagnetic analogy," ''The Electrician'', vol.31, pp.&nbsp;281–282 (part I), p.&nbsp;359 (part II)
** 1893 reproduced in, ''Electromagnetic Theory'' vol I, Chapter 4 Appendix B [https://books.google.com/books?id=9ukEAAAAYAAJ&pg=PA455 pp. 455-466] 
* 1893 {{cite book |first=Oliver |last=Heaviside |title=Electromagnetic Theory |url=https://archive.org/details/electromagnetict0001heav/mode/2up |volume=1 |year=1893 |publisher=The Electrician Printing and Publishing Co, London|isbn=978-0-8284-0235-4 }}<ref name="Swinburne1894">{{cite journal|last1=Swinburne|first1=J.|author-link=James Swinburne|title=Review of ''Electromagnetic Theory'', Vol. I|journal=Nature|volume=51|issue=1312|year=1894|pages=171–173|url=https://zenodo.org/record/2013208|doi=10.1038/051171a0|s2cid=3940841}}</ref>
* 1894 {{cite book|first=Oliver|last=Heaviside|title=Electrical Papers|url=https://archive.org/details/electricalpapers02heavrich|volume=2|year=1894|publisher=Macmillan Co, London and New York}}
* 1899 {{cite book|first=Oliver|last=Heaviside|title=Electromagnetic Theory|url=https://archive.org/details/electromagnetict02heavrich|volume= 2|year=1899|publisher=The Electrician Printing and Publishing Co, London}}
* 1912 {{cite book|first=Oliver|last=Heaviside|title=Electromagnetic Theory|url=https://archive.org/details/electromagnetict03heavuoft|volume= 3|year=1912|publisher=The Electrician Printing and Publishing Co, London}}
* 1925. ''Electrical Papers''. 2 vols Boston 1925 (Copley)
* 1950 ''Electromagnetic theory: The complete & unabridged edition''. (Spon) reprinted 1950 (Dover)
* 1970 {{cite book|first=Oliver|last=Heaviside| title = Electrical Papers| year = 1970| publisher = Chelsea Publishing Company, Incorporated| isbn = 978-0-8284-0235-4}}
* 1971 "Electromagnetic theory; Including an account of Heaviside's unpublished notes for a fourth volume" Chelsea, {{isbn|0-8284-0237-X}}
* 2001 {{cite book|first=Oliver|last=Heaviside| title = Electrical Papers| date = 1 December 2001|publisher=American Mathematical Society | isbn = 978-0-8218-2840-3}}

==See also==
{{Portal|Mathematics|Physics|Engineering}}
* [[1850 in science]]
* [[Electric displacement field]]
* [[Biot–Savart law]]
* {{section link|Bridge circuit|Heaviside bridge}}

== References ==
{{reflist}}

== Further reading ==
{{div col|colwidth=30em}}
* ''[[Philosophical Transactions of the Royal Society A|Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences]]'', Theme Issue: [https://royalsocietypublishing.org/toc/rsta/2018/376/2134 "Celebrating 125 years of Oliver Heaviside's 'Electromagnetic Theory"], vol. 37, iss. 2134, 13 December 2018.
* {{cite book|title=The Heaviside Centenary Volume|publisher=The Institution of Electrical Engineers, London|year=1950}}
* {{cite book|last=Berg|first= E. J.|title=Heaviside's operational calculus as applied to engineering and physics|series= Electrical engineering texts|publisher=McGraw-Hill|year=1929|url=http://catalog.hathitrust.org/Record/001481657}}
* {{cite book| first = Jed Z.| last = Buchwald| title = From Maxwell to Microphysics: Aspects of Electromagnetic Theory in the Last Quarter of the Nineteenth Century| year = 1985| publisher = [[University of Chicago Press]]| isbn = 978-0-226-07882-3| url-access = registration| url = https://archive.org/details/frommaxwelltomic00jedz}}
* Calvert, James B. (2002) [http://mysite.du.edu/~jcalvert/math/laplace.htm Heaviside, Laplace, and the Inversion Integral], from [[University of Denver]].
* {{cite book| first = Bruce J. |last=Hunt| title = The Maxwellians| year = 1991|edition=paperback 2005| publisher = Cornell University Press| isbn = 978-0-8014-8234-2|title-link=The Maxwellians}}
* {{cite journal
|last=Jackson
|first=W
|publication-date=24 June 1950
|title=Life and work of Oliver Heaviside (May 18, 1850 – February 3, 1925).
|volume=165
|issue=4208
|periodical=[[Nature (journal)|Nature]]
|pages=991–3
|bibcode = 1950Natur.165..991J |year=1950 |doi=10.1038/165991a0 |pmid=15439051 |doi-access=free
}}
* Jeffreys, Harold (1927) ''Operational Methods in Mathematical Physics'', Cambridge University Press, 2nd edition 1931 
* {{cite book|last=Josephs|first= H. J.|title=Oliver Heaviside : a biography|publisher=London|year=1963}}
* Laithwaite, E. R., "''Oliver Heaviside – establishment shaker''". Electrical Review, 12 November 1982.
* {{cite book|last=Lee|first= G.|title=Oliver Heaviside|publisher=London|year=1947}}
* Lŭtzen J: ''Heaviside's Operational Calculus and the attempts to rigorize it'', Arch. Hist. Exact Sci. 21 (1980) 161–200
* {{cite journal|last=Lynch|first= A. C.|title=The Sources for a Biography of Oliver Heaviside|journal=History of Technology, London & New York|volume= 13|editor=G. Hollister-Short|year=1991}}
* {{cite book| first=Basil|last= Mahon| title = Oliver Heaviside: Maverick Mastermind of Electricity| date = 11 May 2009| publisher = Institution of Engineering and Technology| isbn = 978-0-86341-965-2}}
* [http://fmnauka.narod.ru/F-F-Mende-What_is_Not_Taken_into_Account_and_they_.pdf Mende, F.F., "What is Not Taken into Account and they Did Not Notice Ampere, Faraday, Maxwell, Heaviside and Hertz", ''AASCIT Journal of Physics'', Vol.1, No.1, (March 2015), pp.28–52.]
* {{cite book| first1 = Douglas H. |last1=Moore|first2=Edmund Taylor|last2=Whittaker| title = Heaviside operational calculus: an elementary foundation| year = 1928|publisher=American Elsevier Publishing Company | isbn = 0-444-00090-9}}
* {{cite book| first = Paul J.|last= Nahin |authorlink=Paul J. Nahin | title = Oliver Heaviside, sage in solitude: the life, work, and times of an electrical genius of the Victorian age| year = 1987| publisher = IEEE| isbn = 978-0-87942-238-7|url=https://books.google.com/books?id=e9wEntQmA0IC}}
* [https://arxiv.org/pdf/2010.09679.pdf Rocci, Alessio (2020), "Back to the Roots of Vector and Tensor Calculus: Heaviside versus Gibbs", ''Archive for History of Exact Sciences''.] {{doi|10.1007/s00407-020-00264-x}}
* Whittaker E T (1929): ''Oliver Heaviside'', Bull. Calcutta Math Soc vol.20 1928–29 199–220
* {{cite book| first = I. |last=Yavetz| title = From Obscurity to Enigma: The Work of Oliver Heaviside, 1872–1889| year = 1995| publisher = Birkhauser| isbn = 978-3-7643-5180-9|url=https://books.google.com/books?id=JgXZQTeYby8C}}
{{div col end}}

==External links==
{{div col|colwidth=30em}}
* {{Commons category-inline}}
* The Dibner Library Portrait Collection, "''[http://www.sil.si.edu/digitalcollections/hst/scientific-identity/fullsize/SIL14-H003-03a.jpg Oliver Heaviside]''".
* {{Internet Archive author |sname=Oliver Heaviside}}
* {{cite EB1911 |wstitle=Units, Physical |volume=27 |pages=738–745 |first=John Ambrose |last=Fleming |authorlink=John Ambrose Fleming |short=1}}
* {{cite web | last = Ghigo | first = F. | url = http://www.nrao.edu/whatisra/hist_prehist.shtml#heaviside | title = Pre-History of Radio Astronomy, Oliver Heaviside (1850–1925)| website = National Radio Astronomy Observatory, Green Bank, West Virginia|archive-url = https://web.archive.org/web/20200615213814/https://www.nrao.edu/whatisra/hist_prehist.shtml#heaviside | archive-date = 15 June 2020| url-status=dead}}
* Gustafson, Grant, "''[http://www.math.utah.edu/~gustafso/HeavisideCoverup.pdf Heaviside's Methods]''". math.Utah.edu. ([[Portable Document Format|PDF]])
* Heather, Alan, [http://www.oliverheaviside.com Oliver Heaviside]. Torbay Amateur Radio Society.
* Katz, Eugenii, {{webarchive |url=https://web.archive.org/web/20091027123043/http://geocities.com/neveyaakov/electro_science/heaviside.html |date=27 October 2009 |title="''Oliver Heaviside''"}}. Hebrew University of Jerusalem.
* {{cite episode |credits=Leinhard, John H. |transcript=No 426 Oliver Heaviside |transcript-url=http://www.uh.edu/engines/epi426.htm |number=426 |title=Oliver Heaviside |series=The Engines of Our Ingenuity |series-link=The Engines of Our Ingenuity |network=NPR |station=KUHF-FM Houston |airdate=1990}}
* McGinty, Phil, "''[https://web.archive.org/web/20031129065714/http://www.torbytes.co.uk/op/tm2/lv2/item932-def.htm Oliver Heaviside]''". Devon Life, Torbay Library Services.
* Naughton, Russell, "''[https://webarchive.nla.gov.au/awa/20040302130000/http://pandora.nla.gov.au/pan/13071/20040303-0000/www.acmi.net.au/AIC/HEAVISIDE_BIO.html Oliver W. Heaviside]{{cbignore|bot=medic}}: 1850 – 1925''". Adventures in CyberSound.
* {{MacTutor|id=Heaviside}}
* "Ron D." (2007) [http://myreckonings.com/wordpress/2007/12/07/heavisides-operator-calculus/ Heaviside's Operator Calculus]
* Eric W. Weisstein, "[http://scienceworld.wolfram.com/biography/Heaviside.html Heaviside, Oliver (1850–1925)]". ''Eric Weisstein's World of Scientific Biography.'' Wolfram Media, Inc.
{{div col end}}

=== Archival collections ===

* [https://libserv.aip.org/ipac20/ipac.jsp?session=1680D73IU0570.32021&profile=rev-icos&source=~!horizon&view=subscriptionsummary&uri=full=3100006~!4035~!6&ri=5&aspect=power&menu=search&ipp=20&spp=20&staffonly=&term=OLIVER+HEAVISIDE+&index=.GW&uindex=&aspect=power&menu=search&ri=5&limitbox_1=LO01+=+icos <nowiki>Oliver Heaviside selected papers [microform], 1874-1922, Niels Bohr Library & Archives</nowiki>]
{{Authority control}}

{{DEFAULTSORT:Heaviside, Oliver}}
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