Editing Josiah Willard Gibbs (section)

=== Career, 1880–1903 ===
[[File:SloaneLab.jpg|thumb|upright|alt=Yale University's old Sloane Physical Laboratory|Yale's Sloane Physical Laboratory, as it stood between 1882 and 1931 at the current location of [[Jonathan Edwards College]]. Gibbs's office was on the second floor, to the right of the tower in the picture.<ref>Wheeler 1998, p. 86</ref>]]

From 1880 to 1884, Gibbs worked on developing the [[exterior algebra]] of [[Hermann Grassmann]] into a [[vector calculus]] well-suited to the needs of physicists. With this object in mind, Gibbs distinguished between the [[Dot product|dot]] and [[cross product]]s of two vectors and introduced the concept of [[dyadics]]. Similar work was carried out independently, and at around the same time, by the British mathematical physicist and engineer [[Oliver Heaviside]]. Gibbs sought to convince other physicists of the convenience of the vectorial approach over the [[quaternion]]ic calculus of [[William Rowan Hamilton]], which was then widely used by British scientists. This led him, in the early 1890s, to a controversy with [[Peter Guthrie Tait]] and others in the pages of ''[[Nature (journal)|Nature]]''.<ref name="Bumstead" />

Gibbs's lecture notes on vector calculus were privately printed in 1881 and 1884 for the use of his students, and were later adapted by [[Edwin Bidwell Wilson]] into a textbook, ''[[Vector Analysis]]'', published in 1901.<ref name="Bumstead" /> That book helped to popularize the "[[del]]" notation that is widely used today in [[Classical electromagnetism|electrodynamics]] and [[fluid mechanics]]. In other mathematical work, he re-discovered the "[[Gibbs phenomenon]]" in the theory of [[Fourier series]]<ref>{{Cite journal |last=Gibbs |first=J. Willard |date=1899 |title=Fourier's Series |url=https://www.nature.com/articles/059606a0 |journal=Nature |volume=59 |issue=606 |page=606 |doi=10.1038/059606a0|bibcode=1899Natur..59..606G }}</ref> (which, unbeknownst to him and to later scholars, had been described fifty years before by an obscure English mathematician, [[Henry Wilbraham]]).<ref>{{Cite journal |doi=10.1007/BF00330404 |title=The Gibbs-Wilbraham phenomenon: An episode in fourier analysis |journal=Archive for History of Exact Sciences |volume=21 |issue=2 |pages=129–160 |year=1979 |last1=Hewitt |first1=Edwin |last2=Hewitt |first2=Robert E. |s2cid=119355426 }}</ref>

[[File:Sine integral.svg|thumb|left|alt=Plot of the sine integral|The [[sine integral]] function, which gives the overshoot associated with the [[Gibbs phenomenon]] for the Fourier series of a [[Heaviside step function|step function]] on the real line]]

From 1882 to 1889, Gibbs wrote five papers on [[physical optics]], in which he investigated [[birefringence]] and other optical phenomena and defended Maxwell's electromagnetic theory of light against the mechanical theories of [[William Thomson, 1st Baron Kelvin|Lord Kelvin]] and others.<ref name="Bumstead" /> In his work on optics, just as much as in his work on thermodynamics,<ref name=Klein1990>{{cite journal |doi=10.1063/1.881258 |title=The Physics of J. Willard Gibbs in his Time |journal=Physics Today |volume=43 |issue=9 |pages=40–48 |year=1990 |last1=Klein |first1=Martin J. |bibcode=1990PhT....43i..40K }}</ref> Gibbs deliberately avoided speculating about the microscopic structure of matter and purposefully confined his research problems to those that can be solved from broad general principles and experimentally confirmed facts. The methods that he used were highly original and the obtained results showed decisively the correctness of Maxwell's electromagnetic theory.<ref>Wheeler 1998, p. 121, 124–125</ref>

Gibbs coined the term ''statistical mechanics'' and introduced key concepts in the corresponding mathematical description of physical systems, including the notions of [[chemical potential]] (1876),<ref name="Klein-proceedings" /> and [[Statistical ensemble (mathematical physics)|statistical ensemble]] (1902).<ref name="Caldi">{{cite book | editor1= Caldi, D. G. | editor2 = Mostow, G. D.  | title = Proceedings of the Gibbs Symposium | year = 1990 |pages = 143–144}}</ref> Gibbs's derivation of the laws of thermodynamics from the statistical properties of systems consisting of many particles was presented in his highly influential textbook ''Elementary Principles in Statistical Mechanics'', published in 1902, a year before his death.<ref name=Klein1990 />

Gibbs's retiring personality and intense focus on his work limited his accessibility to students. His principal protégé was Edwin Bidwell Wilson, who nonetheless explained that "except in the classroom I saw very little of Gibbs. He had a way, toward the end of the afternoon, of taking a stroll about the streets between his study in the old Sloane Laboratory and his home—a little exercise between work and dinner—and one might occasionally come across him at that time."<ref name="Wilson-reminiscences ">Wilson 1931</ref> Gibbs did supervise the doctoral thesis on mathematical economics written by [[Irving Fisher]] in 1891.<ref name="Fisher">{{cite journal |doi=10.1090/S0002-9904-1930-04919-8 |title=The application of mathematics to the social sciences |journal=Bulletin of the American Mathematical Society |volume=36 |issue=4 |pages=225–244 |year=1930 |last1=Fisher |first1=Irving |doi-access=free }}</ref> After Gibbs's death, Fisher financed the publication of his ''Collected Works''.<ref name="Celebrating-Fisher">{{cite book|last=Fisher |first=George W. |chapter=Foreword |title=Celebrating Irving Fisher: The Legacy of a Great Economist |publisher=Wiley-Blackwell |year=2005 |chapter-url=http://cowles.econ.yale.edu/books/gean/fisher.htm |url-status=dead |archive-url=https://web.archive.org/web/20060616203239/http://cowles.econ.yale.edu/books/gean/fisher.htm |archive-date=June 16, 2006 }}</ref> Another distinguished student was [[Lee De Forest]], later a pioneer of radio technology.<ref name="DeForest">{{cite journal |last=Schiff |first=Judith |title=The man who invented radio |url=http://www.yalealumnimagazine.com/articles/2285 |journal=Yale Alumni Magazine |volume=72 |issue=2 |date=November 2008 |access-date = December 28, 2013}}</ref>

Gibbs died in New Haven on April 28, 1903, at the age of 64, the victim of an acute intestinal obstruction.<ref name="Wilson-reminiscences " /> A funeral was conducted two days later at his home on 121&nbsp;High Street,<ref>Wheeler 1998, p. 197</ref> and his body was buried in the nearby [[Grove Street Cemetery]]. In May, Yale organized a memorial meeting at the Sloane Laboratory. The eminent British physicist [[J. J. Thomson]] was in attendance and delivered a brief address.<ref>Wheeler 1998, pp.&nbsp;197–199</ref>