|Alma matter||Yale University|
|Students||Henry Bumstead, Edwin Wilson, Irving Fisher, Lynde Wheeler|
|Known for||Gibbs free energy | Gibbs energy|
Gibbs fundamental equation
Gibbs energy flow
Gibbs energy of attraction
Gibbs energy of repulsion
Gibbs free energy change
|Eponyms|| Gibbsian school |
|Influences||Rudolf Clausius, Francois Massieu, James Maxwell|
Through his 1901 work on the statistical mechanic nature of thermodynamics he is considered as one of the central developers of the science of statistical thermodynamics.  Gibbs is also referred to as the “father of chemical thermodynamics”.  This timelessness quote above by Gibbs, to note, might be representative of Csíkszentmihályi flow, a state of timeless associated with frictionless highly productive work output.
The following is an abstract of Gibbs chemical thermodynamic work, as summarized by American equilibrium historian Cynthia Russett: 
“What [Gibbs] did, essentially, was to add to the independent variables, entropy and volume, of the prime [thermodynamic] equation, a specific number of other independent variables or energy terms equal to the number of components in the system. The new concept he introduced in this connection, called the chemical potential, performs the same function in chemical systems as temperature and pressure do in mechanical systems. Here lay the key to the vast field of chemical equilibrium. In an isothermal (constant temperature) complex system, equilibrium exists when the chemical potential is at a minimum … Gibbs had pioneered a new scientific field, that of physical chemistry.”(add)
The few known direct students of Gibbs include: physicist Henry Bumstead (reviewer for Henry Adams), Irving Fisher, noted maker of the first-every human thermodynamics variables table, and mathematician Edwin Wilson (advisor of Paul Samuelson), noted for his efforts in the 1930s to teach a physical chemistry / steam engine (thermodynamics) based course called "mathematical economics" at Harvard.
Two other direct students of Gibbs include Lee De Forest (1873-1961), who earned his PhD degree in 1899 with a dissertation on radio waves, and Lynde Wheeler, noted for his 1951 biography on Gibbs, who received a PhD in physics in 1902, with a thesis on "The Reflection of Polarized Light from Mercury in Water", both dissertations supposedly supervised by Gibbs.
Gibbs also is said to have advised the following thesis's: Eliakim Hastings More (1885), Percey Frankly Smith (1891), George Pratt Starkweather (1898), and Herbert Edward Hawkes (1900), among a few others wherein his help is acknowledged, which seem to included Bumstead and Wheeler. 
|Gibbs collected works, namely: Scientific Papers, Volume One (Thermodynamics), Scientific Papers, Volume Two (Dynamics, Vector Analysis, Multiple Algebra, Electromagnetic Theory of Light, etc.), and Elementary Principles of Statistical Mechanics (1902) (see: power center).|
See also: Hidden treasuresIt might aptly be said that Gibbs' 1876 On the Equilibrium of Heterogeneous Substances, published at age 37, is the most-difficult-to-read and densest work in all of science. This is evidenced, firstly, by the fact that of the supposed 300-scientists that Gibbs mailed his treatise out to (see: Gibbs correspondence list), only Maxwell was able to understand it and thereby after so intrigued by it as to spend an entire winter building a three-dimensional plaster surface of Gibbs coordinates. Other noted quotes on the so-called "difficulty" of Gibbs' work are as follows:
“Your Equilibrium is too difficult and too condensed for most, I might say all, readers.”— John Strutt (1892), "Letter to Gibbs"; Gilbert Lewis (1923) was the first to "uncondense" it; followed by Guggenheim (1933)“There is, probably, no other book [An Outline of the Theory of Thermodynamics (1900)] so well suited as this to the needs of him who is making preparation for an attempt to explore those tremendous abysses of thought, where reigns that condition of supernal calm known as the Equilibrium of Heterogeneous Substances.”— Edwin Hall (1902), “Review of Edgar Buckingham’s Thermodynamics” “Only one man lived who could understand Gibbs' papers. That was Maxwell, and now he is dead.”— Anon (1903), Connecticut Academy member; circa Nov, said in meeting “It was a number of years before its value was generally known; this delay was due largely to the fact that its mathematical form and rigorous deductive processes make it difficulty reading for anyone, and especially so for students of experimental chemistry whom it concerns most.”— Henry Bumstead (1903), “Josiah Willard Gibbs”, American Journal of Science
“Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from that moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics.”— Henri Poincare (1905), The Value of Science (Ѻ)
“I have run my head hard up against a form of mathematics that grinds my brains out. I flounder like a sculpin in the mud. It is called the ‘law of phases’, and was invented at Yale. No one shall persuade me that I am not a phase.”— Henry Adams (1908), “Letter to Elizabeth Cameron” (Sep 29) 
“The works of Willard Gibbs can only be attacked with profit by the expert mathematician.”— William Bayliss (1915), Principles of General Physiology
“Although Gibbs’ treatment of thermodynamics has been accessible in English, French, and German for many years, its highly condensed and abstract form has repulsed the great majority of students, with the result that the science of thermodynamics has been recast in many different moulds during the last fifty years.”— Frededrick Donnan (1932), Irish physical chemist
A 2017 video summary of Gibbs based on Lynde Wheeler’s 1951 Josiah Willard Gibbs: the History of a Great Mind.
“The original source is, of course, Gibbs, but his discussion is difficult reading.”— Edward Guggenheim (1933), Modern Thermodynamics by the Methods of Willard Gibbs
“Reading Gibbs' Equilibrium is something like reading Laplace, who frequently omits but the conclusion, with the optimistic remark ‘it is easy to see’, shorthand for things ‘seen’ following hours—sometimes days—of hard work.”— E.T. Bell (c.1940), Scottish mathematician
“I worked this out in detail—the principle that the maximum value of entropy indicates a state of equilibrium, according to which all the laws of physical and chemical equilibrium follow from a knowledge of entropy—during the following years, in a number of different researches. First, in investigations on the changes in physical state, presented in my probationary paper at Munich in 1880, and later in studies on gas mixtures. All my investigations yielded fruitful results. Unfortunately, however, as I was to learn only subsequently, the very same theorems had been obtained before me, in fact partly in an even more universal form, by the great American theoretical physicist Josiah Willard Gibbs, so that in this particular field no recognition was to be mine.”— Max Planck (1948), “Scientific Autobiography” (pg. 20)
“There is a considerable testimony from eminent men that they found the Equilibrium of Heterogeneous Substances very difficult reading. But that it is obscure or lacking in clarity of style is untrue. It is logical, terse, and requires unrelieved concentration of thought.”— Lynde Wheeler (1951), Josiah Willard Gibbs: the History of a Great Mind
“I have not had the opportunity to discuss this matter with a physical chemist, a person with a good understanding of the great work by J. Willard Gibbs on chemical thermodynamics. I am sure that he or she would agree with me.”— Linus Pauling (1989), “Schrodinger’s Contribution to Chemistry and Biology”
“Very few experts in thermodynamics have the ability to read this from cover-to-cover.”— David Bottomley (1999), Japanese physicist“The intrepid reader who takes on Gibbs’ Equilibrium can expect months of ‘blind work’.”— William Cropper (2001), Greatest Physicists“Gibbs’ thermodynamic papers—difficult, abstract, and buried in an obscure journal on the fringes of European scientific awareness-remained for a time virtually unknown except among a small circle of admirers. Fortunately, the latter included physicist James Maxwell, who advocated effectively for Gibbs’ insights and methods. Major centers of Gibbsian influence began to appear in Germany, Holland, and elsewhere, as many Nobel Prize winning careers were launched from a passing remark or footnote in Gibbs’ monumental masterpiece.”— Frank Weinhold (2009), Classical and Geometrical Theory of Chemical and Phase Thermodynamics
“Gibbs’ work is much deeper than I ever possibly imagined.”— Jeff Tuhtan (2011), PhD “A Modeling Approach for Alpine Rivers Impacted by Hydropeaking Including the Second Law Inequality”“Gibbs is not an easy read. He wrote in a terse, abstract style and provided few examples to illustrate his general conclusions. In addition, he would seldom tell his readers about the specific problems that led to the work on which he was reporting, much less inform them of any larger project he thought results might further.”— Robert Deltete (2011), “Josiah Willard Gibbs” 
|2005 commemorative Gibbs stamp, showing an overlay of one of Scottish physisict James Maxwell's 1875 thermodynamic surfaces, based on Gibbs' two 1873 graphical thermodynamics papers.|
In Gibbs’ second graphical paper of 1873, it is said that he extended his graphical methods to three-dimensional space, the first example of which was the volume-pressure-temperature diagram employed by Scottish engineer James Thomson in 1871. 
Equilibrium of Heterogeneous Substances
Gibbs is best-known for his 1876, 700-equation Equilibrium treatise on the extrapolation of the thermodynamics of Rudolf Clausius to chemical systems, among others.
The central thread of Gibbs logic, supposedly, employs the variation principle of Joseph Lagrange.  More research needs to be done on this topic, however, as Gibbs does not cite Lagrange (nor William Hamilton), but rather bases his work on Clausius; Clausius, in turn, does cite Hamilton, but his derivation seems to be self-standing.
In human thermodynamics, through his theories on the free energy of chemical substances and spontaneity, in relation to human chemical reaction prediction, Gibbs is considered one of central founders. In particular, the most-dominant thermodynamic quantity in chemistry is the the Gibbs free energy, G, named in honor of Gibbs by English physicist Edward Guggenheim in 1933: 
The following 2009 summary by American physical chemist Thomas Wallace outlines the role of Gibbs free energy in the process of society: 
“The thermodynamic parameters enthalpy H and entropy S represent the variables of heat content and probability, respectively, for the physical, chemical, and biological processes of nature and society. The thermodynamic parameter free energy G represents the fundamental driving force in nature and determines whether physical and chemical processes conducted by nature and society will take place.”
In very simple terms, as explained by German polymath Johann Goethe in 1809, the entire process and workings of society can be described as the summation of all human chemical reactions occurring in the boundary of the society, whereby each individual reaction can be quantified as an elective affinity reaction, wherein the chemical affinity A or force of reaction, shown to be equal to the negative of the change in the free energy by German physicist Hermann Helmholtz in 1882, determines what will occur:
Therefore, the affinities between people, are functions of Gibbs free energy changes involved in human interactions. This description, however, is compounded by the 1941 discovery, by Fritz Lipmann, that free energy coupling occurs.
|Lawrence Henderson describes Gibbs’ Statistical Mechanics (1902) as the “greatest example of sustained thought in the history of America.”|
In 1892, Gibbs wrote English physicist John Strutt with characteristic modesty: 
“Just now I am trying to get ready for publication something on thermodynamics from the a priori point of view, or rather on 'statistical mechanics' . . . I do not know that I shall have anything particularly new in substance, but shall be contented if I can so choose my standpoint (as seems to me possible) as to get a simpler view of the subject.”
Supposedly, by the term a priori Gibbs meant related to or derived by reasoning from self-evident propositions. In any event, ten years later this work resulted in a classic book, Elementary Principles in Statistical Mechanics (1902), which has since been called the "bible of statistical physics", which put statistical mechanics on a new and more general basis.
“Gibbs’ last work on Statistical Mechanics (1902), written after long years of meditation, but, as it seems, almost without notes to aid in the task, and completed in a period of less than a year, is perhaps the greatest example of sustained thought in the history of America.”— Lawrence Henderson (1917), The Order of Nature (pg. 131)
As far as terminology goes, the terms: "statistical mechanics" (coined by Maxwell in 1878), "statistical physics", and "statistical thermodynamics", all essentially address the same subject, the use of statistics to explain thermodynamic laws and behaviors of physical systems, although each seems to have a peculiar flavor and direction of presentation. 
German-born American physicist Albert Einstein, unaware of Gibbs’ work, had undertaken a similar generalization of Boltzmann’s theory in theory papers of 1902-1904, but as he later observed: 
“I only wish to add that the road taken by Gibbs in his book [Elementary Principles in Statistical Mechanics], which consists in one’s starting directly from the canonical ensemble, is in my opinion preferable to the road I took. Had I been familiar with Gibbs’ book at that time, I would not have published all those papers at all, but would have limited myself to the discussion of just a few points.”(add discussion)
|Top left: Gibbs (c.1855). Top middle two: Gibbs (c.1860).  Top right: Gibbs as Yale tutor (1863-64). Bottom right: Gibbs (c.1895).|
Gibbs entered Yale University at the age of 15 graduating a salutatorian in 1858 at the age of 18. 
In this period, Gibbs seems to have been mentored by American mathematician Hubert Newton, the so-called "grandfather of American mathematics", who in 1855 had become Yale's only professor of mathematics, after receiving his BA their in 1850.
American mathematics historian Steve Batterson (2008) describes Newton as the "confidant and sounding board for Gibbs."  Newton and Rudolf Clausius seems to have been the only two people Gibbs ever wrote biographies or obituaries on (see: collected works). 
He then entered the new Yale graduate school earning the first PhD in engineering in the United States, completed in 1863. Gibbs' PhD thesis was “On the Form of the Teeth of Wheels in Spur Gearing”.  In 1871, two years after returning from a study abroad at various universities in Europe, Gibbs became Yale's first professor of mathematical physics.
Anecdote | Touching foreheads to floor
In 1932, American educational theorist Albert Nock gave the following summary about about Gibbs, in the context of eminence: 
“In the last generation, this country produced one of the most eminent men of science in the whole world. His name was quite unknown among us while he lived, and it is still unknown. Yet I may say without too great exaggeration that when I heard it mentioned in a professional assembly in the Netherlands two years ago, everybody got down under the table and touched their foreheads to the floor. His name was Josiah Willard Gibbs.”
The "professional assembly", Nock refers to here, may likely have been some convention or meeting of sorts associated with the Dutch school of thermodynamics, although this is only a reasoned guess.
Anecdote | Maxwell's suggestion
See main: Thermodynamics anecdotesMaxwell: During a visit to Cambridge University, in the years circa 1873-78, the president of Yale (likely Reverend Noah Porter, president from 1871 to 1886) inquired about possible people to promote at Yale.  The famous Scottish physicist, James Maxwell immediately suggested Gibbs. At this time there was also a socially rather prominent individual, named Alan Gibbs, at Yale. Thus, the president replied with pleasure. "Oh, you mean Alan Gibbs." "No! No!" answered Maxwell; "Willard Gibbs." The president's reply was: 
“Well, but he is a nobody. He just sits in his room and writes.”
Anecdote | J.J. Thomson's suggestion
J.J. Thomson: Gibbs had a mailing list of over 300 of the world’s greatest scientists, to which, it has been said, he sent his publications to. Of the bunch, it was Scottish physicist James Maxwell who first took appreciation of Gibbs’ work and began to promote it. One of Gibbs’ biographers, J. G. Crowther, remarked that Maxwell became, in effect, Gibbs’ “intellectual publicity agent”. In the years after Maxwell’s premature death, in 1879, a humorous incident occurred between one of Maxwell’s successors at Cambridge English physicist Joseph Thomson, the discoverer of the electron, and a president of a newly formed American university on a faculty-recruiting mission. As the story went, according to Thomson: 
|When the German physical chemist Walther Nernst visited Yale in 1906 to give the Silliman lecture, he was surprised to discover that there was no tangible memorial for Gibbs, after which he therefore donated his $500 lecture fee to the university to help pay for a suitable monument, which was finally unveiled in 1912 in the form of a bronze bas-relief (above) —with caption: "discoverer and interpreter of the laws of chemical equilibrium"—by sculptor Lee Lawrie, installed in the Sloane Physics Laboratory, now at the entrance to the J. W. Gibbs Laboratories, Yale University. |
“He came to Cambridge, and asked me if I could tell him of anyone who could make a good Professor of Molecular Physics.” Thomson told him that one of the greatest molecular physicists in the world was Willard Gibbs, and he lived in America. The president responded that Thomson probably meant Wolcott Gibbs, a Harvard chemist. Thomson was empathetic that he did mean Willard Gibbs, and tried to convince his visitor that Gibbs was indeed a great scientist. “He sat thinking for a minute or two”, Thomson continues, “and then said, “I’d like you to give me another name. Willard Gibbs can’t be a man of much personal magnetism or I should have heard of him’.”
Anecdote | Mathematics is a language
Gibbs: Gibbs was not talkative and not prone to giving public speeches. Once at the faculty meeting, however, after long wrangling - whether the curriculum should be expanded to make more space for language classes (thus cutting down on time given to mathematics), or whether math should be taught to all freshmen instead - Gibbs stood up and defensively said:
“Mathematics is a language!”
after which he sat down and did not say a word more thereafter. 
Anecdote | Student diagram help
The following, as recounted by Muriel Rukeyser (1942), is a rather telling account of Gibbs attempt to explain one of his geometrical diagrams to a confused student: 
“Gibbs was unknown to the people about him, who were beginning to hear rumors of some achievement, dimly realized, and not, as it seemed, capable of being described. The stories grew in New Haven. One tale was of a student who went into see Gibbs in his office. He asked him about a diagram which had been explained in class; and Gibbs, to explain, began to draw imaginary lines across the floor. The lines grew more complicated. They reached up the walls, to the ceiling, across the door; and, as the student left exhausted, he saw that Gibbs was still standing in the center of the floor, hopelessly enmeshed in his own diagram.”
Anecdote | Uncut books
Sometime between 1899 and 1902, in the years when Edwin Wilson studied under Gibbs at Yale, the following incident occurred, as recounted by Wilson in 1930: 
“Once I desired to consult some books which were not in the library but which I had seen on the shelves in his office during a lecture. I ventured to ask whether I might borrow them. He was entirely willing. As I picked the books off the shelves I noticed that the pages had not been cut and enquired whether I might cut them, to which he replied : Certainly, if you think it worthwhile. Probably I looked abashed, for he added: The author kindly sends me all he writes; there is a great deal of it; I sometimes feel that a person who writes so much must spread his message rather thin.”
Quotes | On
The following are parse and tributes given to Gibbs:
“In a series of remarkable papers read before the Connecticut Academy, Gibbs has proved that the laws of thermodynamics are as applicable to chemical action as to simple changes of state.”— James Dewar (1888), “Presidential Address to the Society of Chemical Industry” 
“The translation of your main work is nearly complete and I cannot resist repeating here my amazement. If you had published this work over a longer period of time in separate essays in an accessible journal, you would now be regarded as by far the greatest thermodynamicist since Clausius—not only in the small circle of those conversant with your work, but universally—and as one who frequently goes far beyond him in the certainty and scope of your physical judgment. The German translation, hopefully, will more secure for it the general recognition it deserves.”— Wilhelm Ostwald (1891), comment after spending entire year translating Gibbs' Equilibrium 
“Gibbs is the greatest synthetic philosopher since Newton.”— Ludwig Boltzmann (c.1900) 
“By the year 2000 Yale will be best known to the world for having produced J. Willard Gibbs.”— William Thomson (c.1902), comment during visit to Yale; as recounted by Irving Fisher 
“Gibbs is the greatest of Americans, judged by his rank in science.”— Henry Adams (1907), The Education of Henry Adams 
“The concept of an independent system is a pure creation of the imagination. For no material system is or can ever be perfectly isolated from the rest of the world. Nevertheless it completes the mathematician’s ‘blank form of a universe’ without which his investigations are impossible. It enables him to introduce into his geometrical space, not only masses and configurations, but also physical structure and chemical composition. Just as Newton first conclusively showed that this is a world of masses, so Willard Gibbs first revealed it as a world of systems.”— Lawrence Henderson (1917) The Order of Nature: An Essay 
“When I studied in Berlin in 1893, and was asked under whom I had studied in America, I enumerated the mathematicians at Yale. To my mortification not one of the names was known to those Berlin professors, until I mentioned Gibbs, whereupon they were loud in his praises. "Geebs, Geebs, jawohl, ausgezeichnetl" [Gibbs, Gibbs, yes, excellent!!] My acquaintance with J. Willard Gibbs was an open sesame with any scientist there (Ѻ)”— Irving Fisher (1929/17), “The Application of Mathematics to the Social Sciences” 
“Gibbs did for statistical mechanics and for thermodynamics what Laplace did for celestial mechanics and Maxwell did for electrodynamics, namely, made his field a well-nigh finished theoretical structure."— Robert Millikan (c.1920) 
“Gibbs ranks with men like Newton, Lagrange and Hamilton, who by the sheer force and power of their minds have produced those generalized statements of scientific law which mark epochs in the advance of exact knowledge.”— Frederick Donnan (1924), “The Influence of J. Willard Gibbs on the Science of Physical Chemistry” 
“Gibbs is the greatest mind in American history.”— Albert Einstein (c.1925), Source; cited by William Phelps (1939), in Autobiography (pg. 425)
“No result of Gibbs’ work has yet been overthrown, and, in this respect, Gibbs seems to stand unique and supreme among the great scientists.”
“In view of the statements of Lord Kelvin and others, Gibbs virtually ranks as the Sir Isaac Newton of America.”— Irving Fisher (1929), “The Application of Mathematics to the Social Sciences” 
“Gibbs is almost beyond doubt the greatest mind in theoretical chemistry that ever lived.”— Albert Nock (1933), Journal of These Days 
“Willard Gibbs’ generalized physico-chemical system is possibly the most famous piece of scientific work that has been done by an American.”— Lawrence Henderson (1935), “Physician as Patient and as a Social System” 
“Like Newton’s Principles, the work of Gibbs stands out in the history of man’s intellectual progress as an imperishable monument to the powers of abstract thought and logical reasoning.”— Lynde Wheeler (1952), A History of a Great Mind (pg. 69) (Ѻ)
“Lorentz is the greatest and most powerful thinker I have ever known. I never met Willard Gibbs, but, perhaps, had I done so, I might have placed him beside Lorentz.”— Albert Einstein (1954), response to question about who were the greatest men, and most powerful thinkers he had known
“When I entered Niels Bohr’s institute in Copenhagen in 1924, the first thing Bohr demanded was that I should read the book of Gibbs on thermodynamics. And he added that Gibbs had been the only physicist who really understood statistical thermodynamics.”— Werner Heisenberg (1973), retrospect comment 
“Gibbs is the greatest thermodynamicist of them all.”— John Fenn (1982), Engines, Energy, and Entropy 
“William James was right. Gibbs, who did not particularly care, gets the ‘last laugh’ in that 150-years after his birth we discuss how he drove his sister's buggy to marketing because her husband was the important librarian of Yale.”— Paul Samuelson (1989), “Gibbs in Economics” (pg. 266) 
“Few theoretical scientists have had the talent and assurance to do their work in such isolated fashion. Only Einstein—who wrote some of the most important papers before he even laid eyes on another theoretical physicist—may have outdone Gibbs in this respect.”— William Cropper (2004), Great Physicists 
“Gibbs is perhaps the greatest American scientist, ever.”— Richard Hughes (c.2010), "A Thermodynamic View of Politics" 
|The Gibbs medal in honor of Gibbs who in 1950 was elected to the Hall of Fame for Great Americans, at New York University.  A similar award is the Willard Gibbs Medal a yearly award of the American Chemical Society, founded in 1910 by William A. Converse.|
Quotes | By
The following are noted Gibbs' quotes:
“A mathematician may say anything he pleases—but a physicist must be a least partially sane.”— Willard Gibbs (c.1895)
“The comprehension of the laws which govern ANY material system is greatly facilitated by considering the energy and entropy of the system in the various states of which it is capable. As the difference of the values of the energy for any two states represents the combined amount of work and heat received or yielded by the system when it is brought from one state to the other, and the difference of entropy is the limit of all the possible values of the integral ∫ dQ/T, dQ denoting the element of the heat received from external sources, and T the temperature of the part of the system receiving it, the varying values of the energy and entropy characterize in all that is essential the effects producible by the system in passing from one state to another.”— Willard Gibbs (1876), On the Equilibrium of Heterogeneous Substances (pg. 1)
1. (a) Gibbs, J. Willard. (1873). "Graphical Methods in the Thermodynamics of Fluids", Transactions of the Connecticut Academy, I. pp. 309-342, April-May.
(b) Gibbs, J. Willard. (1873). "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces", Transactions of the Connecticut Academy, II. pp.382-404, Dec.
(c) Gibbs, Willard. (1876). "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy, III. pp. 108-248, Oct., 1875-May, 1876, and pp. 343-524, may, 1877-July, 1878.4. Fenn, John, B. (1982). Engines, Energy, and Entropy (pg. v). San Francisco: W.H. Freeman and Co.
2. Gibbs, J. Willard (1901). Elementary Principles in Statistical Mechanics - Developed with Special Reference to the Rational Foundation of Thermodynamics. New York: Dover.
3. Nock, Albert J. (1934). A Journal of These Days: June 1932-December 1933 (pg. 47). W. Morrow.
2. Gibbs, J. Willard (1901). Elementary Principles in Statistical Mechanics - Developed with Special Reference to the Rational Foundation of Thermodynamics. New York: Dover.
3. Nock, Albert J. (1934). A Journal of These Days: June 1932-December 1933 (pg. 47). W. Morrow.
5. (a) Adams, Henry. (1907). The Education of Henry Adams (pg. 377). Publisher.
(b) Staff writer. (1943). “Scientists’ Scientist”, Time, Monday, Jan 04.
6. (a) Richard D. Hughes – California State University, Sacramento.
(b) A Thermodynamic View of Politics (pdf) – by Richard D. Hughes.
7. Cropper, William H. (2004). Great Physicists: the Life and Times of Leading Physicists from Galileo to Hawking, (section II: Thermodynamics, pgs. 41-134; ch. 9: “The Greatest Simplicity: Willard Gibbs”, pgs 106-23). Oxford University Press.
8. (a) Johnson, Wayne D. (2004). “Hall of Fame at New York University Medal Series”, MedalCollectors.org.
(b) Issue date: 1964; Sculptor: Stanley Martineau.
9. The Willard Gibbs Award – American Chemical Society.
10. Gibbs, Willard. (1863). “On the Form of the Teeth of Wheels in Spur Gearing” in Gibbs, W. and Wheeler, Lynde P. (1947). The Early Work of Willard Gibbs in Applied Mechanics. Schuman.
11. Capri, Anton Z. (2007). Quips, Quotes, and Quanta (ch. 1: Thermodynamics: Founders and Flounderers, pgs. 1-10) [PDF]. World Scientific.
12. (a) Wheeler, Lynde, P. (1951). Josiah Willard Gibbs - the History of a Great Mind (pg. 173). Woodbridge, Connecticut: Ox Bow Press.
(b) J.W. Gibbs gives a speech (mathematics quotes) – Cut-the-Knot.org.
(c) Other version: Gibbs was known in Yale as a faculty member who never spoke at the meetings. Once, during a discussion another professor argued that students are better of learning another foreign language instead of taking mathematics classes. Gibbs spoke first time. He said, "Mathematics is a language". (Source: Paul Samuelson's "on being an economist".)
13. Josiah Willard Gibbs (1829-1903) – AIP.org.
14. Ebeling, Werner and Sokolov, Igor M. (2005). Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems (ch. 1.2: On history of fundamentals of statistical thermodynamics, pgs. 3-12). World Scientific.
15. Bergethon, Peter R. (1998). The Physical Basis of Biochemistry: the Foundations of Molecular Biophysics (pg. 229). Springer.
16. Josiah Willard Gibbs – MSU Gallery of Chemists.
17. Deltete, Robert J. (1995). “Gibbs and the Energeticists” (pgs. 135-170), in: No Truth Except in the Details: Essays in honor of Martin J. Klein (quote, pg. 149), by Martin J. Klein, Anne J. Kox, Daniel M Siegel. Springer.
18. Comments of Georgi Gladyshev to Libb Thims, during a Chicago visit (17 Dec 2007).
19. Guggenheim, Edward, A. (1933). Modern Thermodynamics by the Methods of Willard Gibbs (pg. 11). London: Methuen & Co.
20. Wallace, Thomas P. (2009). Wealth, Energy, and Human Values: the Dynamics of Decaying Civilizations from Ancient Greece to America (Appendix A: The Fundamentals of Thermodynamics Applied to Society, pgs. 469-89.). AuthorHouse.
21. Presidents of Yale – Yale University.
22. (a) Thomson, James. (1871). “Article”, Proc. Roy. Soc. Lond., XX: 1.
(b) Garrison, Fielding H. (1909). “Josiah Willard Gibbs and his Relation to Modern Science” (pg. 280), Popular Science, 74(27): 470-84.
(c) Garrison, Fielding H. (1909). “Josiah Willard Gibbs and his Relation to Modern Science II”, Popular Science Monthly (van’t Hoff school, pg. 560), Jun 74:551-61.
23. Nock, Albert J. (1932). The Theory of Education in the United States (pg. 104). Ludwig von Mises Institute.
24. Heisenberg, Werner. (1973). “Tradition in Science”, Smithsonian Institution, Lecture, Apr, 24.
25. Deltete, Robert J. (2011). “Josiah Willard Gibbs (1839-1903)”, in: Philosophy of Chemistry (pgs. 89-95, etc.), eds. Dov M. Gabbay, Paul Thagard, John Woods, Robin Findlay Hendry, Andrea Woody, Paul Needham. Elsevier.
26. Weinhold, Frank. (2009). Classical and Geometrical Theory of Chemical and Phase Thermodynamics (pg. 151). Wiley-Interscience.
27. (a) Gibbs plaque (photos) – Yale University, Physics Department.
(b) Staff. (c.2012). “J. Willard Gibbs”, APS.org.
28. Millikan, Robert A. (1938). "Biographical Memoir of Albert Abraham Michelson, 1852–1931." Biographical Memoirs of the National Academy of Sciences of the United States of America 19 (4): 121–146.
29. Rukeyser, Muriel. (1942). Willard Gibbs: American Genius (Academy member quote, pg. 251; Gibbs' theses advised, pgs. 327-28; diagram anecdote, pgs. 328-29). Garden City, New York: Doubleday, Doran & Co., Inc.
30. Seeger, Raymond J. (1974). Men of Physics: J. Willard Gibbs, American Mathematical Physicist Par Excellence (Lee Lawrie, pg. 21). Pergamon Press.
31. Wilson, Edwin B. (1930). “Reminiscences of Gibbs by a Student and Colleague” (abs) (pdf), Eighth Josiah Willard Gibbs Lecture, delivered, by invitation of the Council of the Society, before the Society and the American Association for the Advancement of Science, Dec 30, in: Bull. Amer. Math. Soc.37(6): 401-16, 1931.
32. Fisher, Irving. (1930). "The Applications of Mathematics to the Social Sciences" (abs) (pdf), Bulletin of the American Mathematical Society, 36(4): 225-243.
33. Arveson, M. H. (1936). “The Greatest Synthetic Philosopher since Newton”, The Chemical Bulletin 23, No. 5.
34. (a) Donnan, Frederick G. (1924). “The Influence of J. Willard Gibbs on the Science of Physical Chemistry” (pg. 4), an address by F. G. Donnan, on the occasion of the centenary celebration of the founding of the Franklin institute and the inauguration exercises of the Bartol research foundation, September 17, 18, 19. Franklin Institute.
(b) Fisher, Irving. (1930). "The Applications of Mathematics to the Social Sciences" (abs) (pdf), Bulletin of the American Mathematical Society, 36(4): 225-243.
35. Cropper, William H. (2004). Great Physicists: the Life and Times of Leading Physicists from Galileo to Hawking. Oxford University Press.
36. (a) Russett, Cynthia. (1966). The Concept of Equilibrium in American Social Thought (quote, pg. 18; Gibbs, 18+ pgs). Yale College.
(b) Weintraub, E. Roy. (1991). Stabilizing Dynamics: Constructing Economic Knowledge (pgs. 59, 63-64). Cambridge University Press.
37. (a) Henderson, Lawrence J. (1917). The Order of Nature: An Essay (pg. 126). Harvard University Press.
(b) Russett, Cynthia. (1966). The Concept of Equilibrium in American Social Thought (pg. 113). Yale College.
(c) Bynum W.F. and Porter, Roy. (2005). Oxford Dictionary of Scientific Quotations (pg. 275:6). Oxford: Oxford University Press.
40. (a) Adams, Henry. (1908). “Letter to Elizabeth Cameron” (Sep 29), in: Letters of Henry Adams, 1892-1918 (editor: Worthington Ford) (pg. 510). Kraus Reprints, 1969.
(b) Schwehn, Mark R. (1978). The Making of Modern Consciousness in America: the Works and Careers of Henry Adams and William James (pg. 109). Stanford University.
(c) Samuels, Ernest. (1989). Henry Adams (pg. 401). Harvard University Press.
41. Batterson, Steve. (2008). “The Father of American Mathematics” (pdf), Notices of the American Mathematical Society, 55(3):352-63, Mar.
42. Gibbs, J. Willard. (1897). “Hubert Anson Newton.” American Journal of Science, 4(3):359–378.
43. Dewar, James. (1888). “Presidential Address to the Society of Chemical Industry”, Journal of the Society of the Chemical Industry, 2: 474-79; in: The Collected Papers of Sir James Dewar (thermodynamics, pgs. 312-14).
44. (a) Henderson, Lawrence. (1935). “Physician as Patient and as a Social System”, New England Journal of Medicine, 212:819-23.
(b) Barber, Bernard. (1970). L.J. Henderson on the Social System (§6:202-13, quote, pg. 205). University of Chicago Press.
55. (a) Buckingham, Edgar. (1900). An Outline of the Theory of Thermodynamics (Ѻ) (pdf) (ice-rubbing, pgs. 13-14). MacMillan Co.
(b) Hall, Edwin. (1902). “Review of Buckingham’s Thermodynamics” (pdf), Bulletin of the American Mathematical Society, 9:173-75.
(b) Edwin Hall – Wikipedia.
56. Samuelson, Paul. (1989). “Gibbs in economics”, in: Proceedings of the Gibbs Symposium, Yale University, May 15-17 (editors: D.G. Caldi and George Mostow) (pgs. 255-68). American Mathematical Society.
● Hastings, Charles S. (1909). Biographical Memoir of Josiah Willard Gibbs, 1839-1903. National Academy of Sciences.
● Donnan, Frederick G., Haas, Arthur. (1936). A Commentary on the Scientific Writings of J. Willard Gibbs. Yale University Press.
● Wheeler, Lynde, P. (1951). Josiah Willard Gibbs - the History of a Great Mind. Woodbridge, Connecticut: Ox Bow Press.
● Seeger, Raymond J. (1974). Men of physics: J. Willard Gibbs, American mathematical physicist par excellence. Pergamon Press.
● Aris, Rutherford, David, Howard T, and Stuewer, Roger H. (1983). Springs of Scientific Creativity: Essays on the Founders of Modern Science (ch. 5: The Scientific Style of Josiah Willard Gibbs, pgs. 142-62; esp. pg. 150). University of Minnesota Press.
● Reingold, Nathan. (1985). Science in Nineteenth-Century America: A Documented History (section: J. Willard Gibbs, pgs 315-22). University of Chicago Press.
● Klein, Martin J. (1989). “The Scientific Style of Josiah Willard Gibbs”, in: A Century of Mathematics in America, Vol 11., edited by P.M. Harman. Cambridge University Press.
● Josiah Willard Gibbs – Wikipedia.
● Josiah Willard Gibbs Lectures (est. 1923) - American Mathematical Society.
● Gibbs Society of Biological Thermodynamics - University of Virginia.
● Suo, Zhigang. (2007). “Josiah Willard Gibbs and his Two Shorter Papers on Thermodynamics”, iMechanica.org blog, Jan, 06.