James Clerk Maxwell

 (13 June 1831 – 5 November 1879) was a Scottish mathematical physicist, who formulated the classical theory of, bringing together for the first time electricity, magnetism, and light as manifestations of the same phenomenon.
 * See also: "On Action at a Distance", Matter and Motion, The Scientific Papers of James Clerk Maxwell, Theory of Heat,

Quotes


Happy is the man who can recognise in the work of to-day a connected portion of the work of life and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity. He strenuously works out his daily enterprises because the present is given him for a possession. Thus ought Man to be an impersonation of the divine process of nature, and to show forth the union of the infinite with the finite, not slighting his temporal existence, remembering that in it only is individual action possible; nor yet shutting out from his view that which is eternal, knowing that Time is a mystery which man cannot endure to contemplate until eternal Truth enlighten it.
 * He that would enjoy life and act with freedom must have the work of the day continually before his eyes. Not yesterday's work, lest he fall into despair; nor to-morrow's, lest he become a visionary—not that which ends with the day, which is a worldly work; nor yet that only which remains to eternity, for by it he cannot shape his actions.
 * Paper communicated to (1854) Æt. 23, as quoted in Lewis Campbell, William Garnett, The Life of James Clerk Maxwell: With Selections from His Correspondence and Occasional Writings (1884) pp. 144-145, and in, James Clerk Maxwell and Modern Physics (1896) pp. 39-40.


 * And last of all we have the secondary forms of crystals bursting in upon us, and sparkling in the rigidity of mathematical necessity and telling us, neither of harmony of design, usefulness or moral significance, — nothing but spherical trigonometry and Napier's analogies. It is because we have blindly excluded the lessons of these angular bodies from the domain of human knowledge that we are still in doubt about the great doctrine that the only laws of matter are those which our minds must fabricate, and the only laws of mind are fabricated for it by matter.
 * Essay "Analogies in Nature" (February 1856), reprinted in The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862 edited by P.M. Harman, p. 376 (the quote appears on p. 383)


 * Velocity of transverse undulations in our hypothetical medium, calculated from the electromagnetic experiments of 'MM'. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.
 * Lecture at Kings College (1862) as quoted by F. V. Jones, "The Man Who Paved the Way for Wireless," New Scientist (Nov 1, 1979) p. 348 & Andrey Vyshedskiy, On The Origin Of The Human Mind 2nd edition


 * The general equations are next applied to the case of a magnetic disturbance propagated through a non-conductive field, and it is shown that the only disturbances which can be so propagated are those which are transverse to the direction of propagation, and that the velocity of propagation is the velocity v, found from experiments such as those of Weber, which expresses the number of electrostatic units of electricity which are contained in one electromagnetic unit. This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.
 *  (1864) Introduction, p. 466, §20.


 * I have also cleared the electromagnetic theory of light from all unwarrantable assumption, so that we may safely determine the velocity of light by measuring the attraction between bodies kept at a given difference of potential, the value of which is known in electromagnetic measure.
 * Letter to C. Hockin, Esq. (Sept 7, 1864) as quoted by Lewis Campbell, William Garnett, The Life of James Clerk Maxwell: With Selections from His Correspondence and Occasional Writings (1884)


 * I have also a paper afloat, with an electromagnetic theory of light, which, till I am convinced to the contrary, I hold to be great guns.
 * Letter to C. H. Cay, (Jan 5,1865) as quoted in , 44(8), page 470, 1976-08


 * This characteristic of modern experiments — that they consist principally of measurements — is so prominent, that the opinion seems to have got abroad, that in a few years all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry on these measurements to another place of decimals. If this is really the state of things to which we are approaching, our Laboratory may perhaps become celebrated as a place of conscientious labour and consummate skill, but it will be out of place in the University, and ought rather to be classed with the other great workshops of our country, where equal ability is directed to more useful ends. But we have no right to think thus of the unsearchable riches of creation, or of the untried fertility of those fresh minds into which these riches will continue to be poured. It may possibly be true that, in some of those fields of discovery which lie open to such rough observations as can be made without artificial methods, the great explorers of former times have appropriated most of what is valuable, and that the gleanings which remain are sought after, rather for their abstruseness, than for their intrinsic worth. But the history of science shews that even during the phase of her progress in which she devotes herself to improving the accuracy of the numerical measurement of quantities with which she has long been familiar, she is preparing the materials for the subjugation of the new regions, which would have remained unknown if she had been contented with the rough methods of her early pioneers. I might bring forward instances gathered from every branch of science, shewing how the labour of careful measurement has been rewarded by the discovery of new fields of research, and by the development of new scientific ideas. But the history of the science of terrestrial magnetism affords us a sufficient example of what may be done by experiments in concert, such as we hope some day to perform in our Laboratory.
 * Introductory Lecture on Experimental Physics held at Cambridge in October 1871, re-edited by W. D. Niven (2003) in Volume 2 of The Scientific Papers of James Clerk Maxwell, Courier Dover Publications, p. 241; this has sometimes been misquoted in a way which considerably alters its intent: "in a few years, all the great physical constants will have been approximately estimated, and … the only occupation which will then be left to the men of science will be to carry these measurement to another place of decimals."


 * We may find illustrations of the highest doctrines of science in games and gymnastics, in travelling by land and by water, in storms of the air and of the sea, and wherever there is matter in motion.
 * Introductory Lecture on Experimental Physics held at Cambridge in October 1871, re-edited by W. D. Niven (2003) in Volume 2 of The Scientific Papers of James Clerk Maxwell, Courier Dover Publications, p. 243.


 * The whole science of heat is founded Thermometry and, and when these operations are understood we may proceed to the third step, which is the investigation of those relations between the thermal and the mechanical properties of substances which form the subject of Thermodynamics. The whole of this part of the subject depends on the consideration of the Intrinsic Energy of a system of bodies, as depending on the temperature and physical state, as well as the form, motion, and relative position of these bodies. Of this energy, however, only a part is available for the purpose of producing mechanical work, and though the energy itself is indestructible, the available part is liable to diminution by the action of certain natural processes, such as conduction and radiation of heat, friction, and viscosity. These processes, by which energy is rendered unavailable as a source of work, are classed together under the name of the Dissipation of Energy.
 * Theory of Heat "Preface" (1871)


 * The vast interplanetary and interstellar regions will no longer be regarded as waste places in the universe, which the Creator has not seen fit to fill with the symbols of the manifold order of His kingdom. We shall find them to be already full of this wonderful medium; so full, that no human power can remove it from the smallest portion of Space, or produce the slightest flaw in its infinite continuity.
 * "On Action at a Distance" Nature (Mar. 6, 1873) Vol VII, Issue 175, p. 343.


 * Mathematicians may flatter themselves that they possess new ideas which mere human language is yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations of their minds.
 * "Thomson & Tait's Natural Philosophy" in Nature, Vol. 7 (Mar. 27, 1873) A review of  (1873) by Sir W. Thomson, P. G. Tait. See Nature, Vol. 7-8, Nov. 1872-Oct. 1873, pp. 399-400, or The Scientific Papers of James Clerk Maxwell, p. 328.


 * It is of great advantage to the student of any subject to read the original memoirs on that subject, for science is always most completely assimilated when it is in the nascent state...
 * A Treatise on Electricity and Magnetism (1873), Preface, p. xiii.


 * We shall see that the mathematical treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.
 * A Treatise on Electricity and Magnetism (1873), §36.


 * Colour as perceived by us is a function of three independent variables at least three are I think sufficient, but time will show if I thrive.
 * Maxwell, in a letter to William Thomson, The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862 (1990), p. 245.


 * The 2nd law of thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea, you cannot get the same tumblerful of water out again.
 * in a letter to Lord Rayleigh, as quoted in John William Strutt, Third Baron Rayleigh (1924), p. 47.


 * Aye, I suppose I could stay up that late.
 * Maxwell, on being told on his arrival at Cambridge University that there would be a compulsory 6 a.m. church service, as quoted in Spice in Science : The Best of Science Funnies (2006) by K. Krishna Murty


 * The equations at which we arrive must be such that a person of any nation, by substituting the numerical values of the quantities as measured by his own national units, would obtain a true result.
 * Encyclopedia Brittanica article, quoted by in Science A Four Thousand Year History (2009) citing Simon Schaffer article in The Values of Precision (1995) ed. M. Norton Wise

A Paradoxical Ode After Shelley (1878)

 * The last poem of Maxwell, written to Hermann Stoffkraft, Ph.D. in 1878. Published in The Life of James Clerk Maxwell (1882) by Lewis Campell and William Garnett, it is pastiche of a passage from the lyrical drama, Prometheus Unbound, by the English romantic poet Percy Bysshe Shelley

My soul’s an amphicheiral knot Upon a liquid vortex wrought By Intellect in the Unseen residing, While thou dost like a convict sit With marlinspike untwisting it Only to find my knottiness abiding; Since all the tools for my untying In four-dimensioned space are lying, Where playful fancy intersperses Whole avenues of universes; Where Klein and Clifford fill the void With one unbounded, finite homaloid, Whereby the Infinite is hopelessly destroyed.
 * I

II But when thy Science lifts her pinions In Speculation’s wild dominions, I treasure every dictum thou emittest; While down the stream of Evolution We drift, and look for no solution But that of the survival of the fittest. Till in that twilight of the gods When earth and sun are frozen clods, When, all its energy degraded, Matter in æther shall have faded, We, that is, all the work we’ve done, As waves in æther, shall for ever run In swift-expanding spheres, through heavens beyond the sun.

III Great Principle of all we see, Thou endless Continuity! By thee are all our angles gently rounded; Our misfits are by thee adjusted, And as I still in thee have trusted, So let my methods never be confounded! O never may direct Creation Break in upon my contemplation, Still may the causal chain, ascending, Appear unbroken and unending, And, where that chain is lost to sight Let viewless fancies guide my darkling flight Through Æon-haunted worlds, in order infinite. ∂p/∂t

The Life of James Clerk Maxwell (1882)
'''
 * Quotations from The Life of James Clerk Maxwell (1882) by and, Full text online.


 * I believe, with the Westminster Divines and their predecessors ad Infinitum that "Man's chief end is to glorify God and to enjoy him for ever." That for this end to every man has been given a progressively increasing power of communication with other creatures. That with his powers his susceptibilities increase. That happiness is indissolubly connected with the full exercise of these powers in their intended direction. That Happiness and Misery must inevitably increase with increasing Power and Knowledge. That the translation from the one course to the other is essentially miraculous, while the progress is natural. But the subject is too high. I will not, however, stop short, but proceed to Intellectual Pursuits.
 * Letter to Lewis Campbell (9 November 1851) in Ch. 6 : Undergraduate Life At Cambridge October 1850 to January 1854 — ÆT. 19-22, p. 158


 * In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data.
 * Letter to Lewis Campbell (9 November 1851) in Ch. 6 : Undergraduate Life At Cambridge October 1850 to January 1854 — ÆT. 19-22, p. 159


 * I maintain that all the evil influences that I can trace have been internal and not external, you know what I mean—that I have the capacity of being more wicked than any example that man could set me, and that if I escape, it is only by God's grace helping me to get rid of myself, partially in science, more completely in society, — but not perfectly except by committing myself to God as the instrument of His will, not doubtfully, but in the certain hope that that Will will be plain enough at the proper time. Nevertheless, you see things from the outside directly, and I only by reflexion, so I hope that you will not tell me you have little fault to find with me, without finding that little and communicating it.
 * Letter to Rev. C. B. Tayler ( 8 July 1853) in Ch. 6 : Undergraduate Life At Cambridge October 1850 to January 1854 — ÆT. 19-22, p. 189


 * I think men of science as well as other men need to learn from Christ, and I think Christians whose minds are scientific are bound to study science that their view of the glory of God may be as extensive as their being is capable. But I think that the results which each man arrives at in his attempts to harmonize his science with his Christianity ought not to be regarded as having any significance except to the man himself, and to him only for a time, and should not receive the stamp of a society.
 * Draft of a reply to an invitation to join the Victoria Institute (1875), in Ch. 12 : Cambridge 1871 To 1879, p. 404

Were he now to see his blunder, When he put his reason under The control of worldly Pride.
 * How the learned fool would wonder
 * Part III Poems, "A Vision Of a Wrangler, of a University, of Pedantry, and of Philosophy. " (November 10, 1852)

Questions strange I shout for ever, While echoes far and wide Seem to mock my vain endeavour; Still I shout, for though they never Cast my borrowed voice aside, '''Words from empty words they sever— Words of Truth from words of Pride.'''
 * By the hollow mauntain-side
 * Part III Poems, "Reflection from Various Surfaces" (April 18, 1853)

How shall those you love be blest," Ask at once eternal Rest,    Peace and assurance giving. Rest of Life and not of death, Rest in Love and Hope and Faith, Til the God who gives their breath     Calls them to rest from living.
 * Ask no more, then, "what is best,
 * Part III Poems, "On St. David's Day. To Mrs. E. C. Morrieson." (March 1, 1854)

Is mingling its notes with our own! The discord is vanishing slowly, And melts in that dominant tone. And they that have heard it can never Return to confusion again, Their voices are music for ever, And join in the mystical strain.'''
 * '''But listen, what harmony holy
 * Part III Poems, To the Air of "Lörelei." (January, 1858)

And '''life may be labour in vain; But I'd rather be silly than lazy''', And would not quit life for its pain.
 * The world may be utterly crazy
 * Part III Poems, Tune, Il Segreto per esser felice (March 24, 1858)

Quotes about Maxwell



 * Pisarro explained the Neo-Impressionist theories to his dealer Durand-Ruel in a letter written towards the end of 1886. He stressed the importance of Seurat's role as inventor of the theory, and described the new function of colour, which replaced the mechanical mixtures of pigments with optical mixtures, where colours partially fused in the spectator's eye. The component parts of each optical colour mixture were to be painted in separate touches so that they retained their colour purity. When colours were mixed on the palette, they could only be combined with close neighbors on the colour circle, so as to avoid excessive dulling of the hues. Pissaro noted that the great colour theorists who had influenced Seurat's thinking were Chevreul, the Scott Maxwell, and the American Ogden Rood. Optical colour mixtures, they argued, were more luminous than mixed pigments.
 * Anthea Callen, Techniques of the Impressionists (1982) p. 138.


 * The influence of Quetelet's ideas spread throughout the sciences, even to the physical sciences. The two primary founders of the modern kinetic theory of gases, based on considerations of probability, were James Clerk Maxwell and Ludwig Boltzmann. Both acknowledged their debt to Quetelet. ...historians generally consider the influence of the natural sciences on the social sciences, whereas in the case of Maxwell and Boltzmann, there is an influence of the social sciences on the natural sciences, as Theodore Porter has shown.
 * I. Bernard Cohen, The Triumph of Numbers: How Counting Shaped Modern Life (2005)


 * In order to appreciate the nature of Maxwell's contributions, let us recall how matters stood in his day. ... ...states that a variable magnetic field generates an electric field. Maxwell, however, considered that this law, standing alone, lacked symmetry; so he formulated the hypothesis that conversely a variable electric field should generate a magnetic one, and proceeded to construct his theory... no experimental results could be claimed to have justified any such assumption... His celebrated equations of electromagnetics represented, therefore, the results of experiment, supplemented by this additional hypothetical assumption. The advisability of making this hypothesis was accentuated when it was found to ensure the law of conservation of electricity. ...In the particular case of free space in which only fields but no charges or currents are present, Maxwell's equations of electromagnetics, termed field-equations (since they describe the state of the electromagnetic field), can be written:
 * where E represents electric field intensity, H magnetic field density, t denotes time, and c a most important constant... (2) represents Faraday's law of induction, while (4) constitutes the hypothetical law postulated by Maxwell... Prior to Maxwell's investigations the fourth equation would have been written "curl H = 0"...From his field equations, Maxwell... was able to deduce the two additional ones:

If two magnetic poles of equal strength, situated in empty space... one centimetre apart, attract or repel each other with a force of one dyne, either pole is said to represent one unit of magnetic pole strength in the electromagnetic system of units. Owing to the interconnections between magnetism and electricity, we can deduce therefrom the unit of electric charge also in the electromagnetic system. Likewise, if two electric charges of equal strength... in empty space at a distance of one centimetre apart, attract or repel each other with a force of one dyne, either charge is said to represent one unit of electric charge in the electrostatic system of units. From this we can derive the unit of magnetic pole strength in the electrostatic system. Precise measurements... then proved that the value of this ratio was about 186,000 miles per second; whence it became necessary to assume that periodic perturbations in the strains and stresses of the field would be propagated in the form of waves moving through the ether with this particular speed. But this velocity was precisely that of light waves propagated through the luminiferous ether.
 * ...these last two equations connote that varying electric and magnetic intensities will be propagated through the ether in wave form with a velocity c... This discovery removed all possibility of action at a distance, since the field perturbations now appeared to be propagated from place to place with a finite velocity. It was... of interest to determine the precise value of c. ...Physicists ...were unable, in Maxwell's day, to devise a means of performing such delicate experiments. ...Maxwell remarked that it would be given by the ratio of the magnitude of any electric charge, measured in terms of electrostatic units (based on electricity), and then of electromagnetic units (based on magnetism).
 * A. D'Abro, The Evolution of Scientific Thought from Newton to Einstein (1927) pp. 126-127.

Yet, had men realised that our world was one of four-dimensional Minkowskian space-time, and not one of separate space and time, things would have been different. By extending the well-known stationary laws to four-dimensional space-time, through the mere addition of time components to the various trios of space ones, we should have written out inadvertently the laws governing varying fields, or, in other words, we should have constructed Maxwell's celebrated equations. Electromagnetic induction, discovered experimentally by Faraday, the additional electrical term introduced tentatively by Maxwell, radio waves, everything in the electromagnetics of the field, could have been foreseen at one stroke of the pen. A century of painstaking effort could have been saved. We are assuming that a four-dimensional vector calculus would have been in existence; but this is purely a mathematical question.
 * In the study of electricity and magnetism we may consider phenomena in which conditions do not vary as time passes by; the electric charges and the magnets remain at rest, and the currents flowing in fixed wires do not vary in intensity. Conditions are then termed stationary [static]; it is as though time played no part. The laws which govern this type of phenomena were discovered empirically over a century ago, and were expressed mathematically in terms of spatial vectors. The problem of ascertaining how electric and magnetic phenomena would behave when conditions ceased to be stationary was one that could not be predicted; further experimental research was necessary before the general laws could be obtained. Even so, the difficulties were considerable, and it needed Maxwell's genius to establish the laws from the incomplete array of experimental evidence then at hand. All this work extended over nearly a century; it was slow and laborious.
 * A. D'Abro, The Evolution of Scientific Thought from Newton to Einstein (1927) pp. 319-320.


 * The first clear sign of a breakdown in communication between physics and mathematics was the extraordinary lack of interest among mathematicians in James Clerk Maxwell's discovery of the laws of electromagnetism. Maxwell discovered his equations, which describe the behavior of electric and magnetic fields under the most general conditions, in the year 1861, and published a clear and definitive statement of them in 1865. This was the great event of nineteenth century physics, achieving for electricity and magnetism what Newton had achieved for gravitation two hundred years earlier. Maxwell's equations contained, among other things, the explanation of light as an electromagnetic phenomenon, and the basic principles of electric power transmission and radio technology. ...But in addition to their physical applications, Maxwell's equations had abstract mathematical qualities which were profoundly new and important. Maxwell's theory was formulated in terms of a new style of mathematical concept, a extending throughout space and time and obeying coupled partial differential equations of peculiar symmetry. ...If they had taken Maxwell's equations to heart as Euler took Newton's, they would have discovered, among other things, Einstein's theory of special relativity, the theory of s and their linear representations, and probably large pieces of the theory of hyperbolic differential equations and functional analysis. A great part of twentieth century physics and mathematics could have been created in the nineteenth century, simply by exploring to the end the mathematical concepts to which Maxwell's equations naturally lead.
 * Freeman Dyson, "Missed opportunities" (1972) Gibbs Lecture, Bulletin of the American Mathematical Society (1972) Vol. 78, no. 5, pp. 635--652.


 * If the idea of physical reality had ceased to be purely atomic, it still remained for the time being purely mechanistic; people still tried to explain all events as the motion of inert masses; indeed no other way of looking at things seemed conceivable. Then came the great change, which will be associated for all time with the names of Faraday, Clerk Maxwell, and Hertz. The lion's share in this revolution fell to Clerk Maxwell. He showed that the whole of what was then known about light and electro-magnetic phenomena was expressed in his well known double system of differential equations, in which the electric and magnetic fields appear as the dependent variables. Maxwell did, indeed try to explain, or justify, these equations by intellectual constructions. But... the equations alone appeared as the essential thing and the strength of the fields as the ultimate entities, not to be reduced to anything else.
 * Albert Einstein, "Clerk Maxwell's Influence on the Evolution of the Idea of Physical Reality" in Essays in Science (1934)


 * The special theory of relativity owes its origins to Maxwell's equations of the electromagnetic field.
 * Albert Einstein, as quoted in New Scientist, Vol. 130 (1991), p. 49


 * The work of James Clerk Maxwell changed the world forever.
 * Albert Einstein, as quoted at "James Clerk Maxwell" at BBC History


 * '''From a long view of the history of mankind — seen from, say, ten thousand years from now — there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.
 * Richard Feynman, in  (1964) Volume II, 1-6


 * What does distinguish Maxwell to a great degree is a strong intuition, rising at times to divination, which goes hand in hand with rich power of imagination. For the latter quality much evidence can be cited: his predilection for diagrams, his use of roll-curves [Rollkui'Ven], of stereoscopic figures, of reciprocal force-planes [Kraefteplaenen].
 * , in Development of Mathematics in the 19th Century, Volume 9, pg. 229


 * He achieved greatness unequalled.
 * Max Planck


 * I want to talk about thought experiments and how they can work, and I want to do that by talking about my favorite example which is Maxwell's equations, the laws of electromagnetism. Again, these are more equations, but it's ok because they're on a T-shirt. So these laws govern the behavior of electric and magnetic fields, but actually, when Maxwell was a boy... there was a missing term. ...When Maxwell got into the field these were the equations, and they had been discovered experimentally, and I want to say a little bit about them. So this bit here is Gauss's law $$\nabla \cdot \mathbf{D} = \rho_\mathrm{v}$$ it says that electric charges produce electric fields. This bit is Ampere's law $$\mathbf{\nabla} \times \mathbf{H} = \mathbf{J}$$ it says that a electric currents produce magnetic fields. Faraday's law $$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$$ says that oscillating magnetic fields can also produce electric fields... These were discovered and confirmed by a tremendous amount of data. They were consistent with all known measurements/observations of electromagnetism in Maxwell's day, but there are a problem, and the problem was exposed by a . The thought experiment is simply to consider a rapidly oscillating current with a break in the circuit, a ... and the problem is that if you use those equations to calculate the magnetic field next to the capacitor you don't get definite answer, you get two different answers, depending on how you use the equations. So there is something wrong. Even without doing this experiment you know that there is something wrong with those equations, and from this clue and a lot more reasoning... Maxwell was able to figure out that he could fix this by adding one more term [to Ampere's law]... $$\nabla \times \mathbf{H} = \mathbf{J} +\frac{\partial \mathbf{D}} {\partial t}$$ and with this the equations are mathematically and physically well posed. They give unambiguous answers to questions like the one I mentioned. Now, Maxwell got a huge bonus because... Faraday's law says that an oscillating magnetic field produces an electric field. Maxwell's new term says that an oscillating electric field produces a magnetic field. So each can produce the other, and so you can get a disturbance which is self-sustaining, and which doesn't just sustain... but moves... Faraday, Maxwell, Faraday, Maxwell... you get a self-sustaining disturbance which moves at a velocity that you get from the equations, and the velocity is the speed of light. So Maxwell got a huge bonus for understanding the unification of electricity and magnetism. He understood the nature of light! When I first heard about this in high school I thought this was the coolest thing, and I still do. It's what we're all trying to do.
 * Joseph Polchinski, "Space-time versus the Quantum" (November 25, 2014) 59th Annual Faculty Research Lecture, University of California, Santa Barbara (aired Nov 16, 2015)


 * One reason for the success of Maxwell's teaching texts, and those of Thomson and Tait, is that they were... expounding in clear and persuasive language the new understanding in basic physics that their authors had been responsible for developing... In a way, Maxwell's contributions to the great ninth edition of the Encyclopaedia Britannica were a natural development of his zeal for teaching. They covered Atom, Attraction, Capillary action, Constitution of bodies, Diagrams, Diffusion, Ether, Faraday, Harmonic analysis, and Physical sciences. ...Maxwell deserves to be remembered as one of the nineteenth century's notable pedagogues. ...His expertise was built upon understanding, enthusiasm, hard work, and experience.
 * John S. Reid, "Maxwell at Aberdeen" in James Clerk Maxwell: Perspectives on His Life and Work (2014) p. 27, ed. Raymond Flood, Mark McCartney, Andrew Whitaker.


 * Maxwell's equations have had a greater impact on human history than any ten presidents.
 * Carl Sagan


 * In electromagnetism... the law of the inverse square had been supreme, but, as a consequence of the work of Faraday and Maxwell, it was superseded by the field. And the same change took place in the theory of gravitation. By and by the material particles, electrically charged bodies, and magnets which are the things that we actually observe come to be looked upon only as "singularities" in the field.
 * Willem de Sitter, "Relativity and Modern Theories of the Universe," Kosmos (1932)


 * Maxwell's importance in the history of scientific thought is comparable to Einstein's (whom he inspired) and to Newton's (whose influence he curtailed)

In studying the problem of Galactic rotation we are almost entirely dependent on the determination of velocities in the line of sight, which can be measured spectroscopically by the. ...On the theory of Galactic rotation stars which are further from the centre than the sun will tend, in general, to move more slowly, i.e. relative to the sun they will lag behind, whereas stars nearer to the centre will race ahead.
 * In a famous memoir, Clerk Maxwell showed nearly a hundred years ago that Saturn's rings would be unstable if they were solid, and that they must consist of a swarm of separate bodies. In a system of particles rotating about a centre of gravitational attraction the innermost particles will rotate more rapidly than the outermost, in order to counteract the stronger gravitational pull towards the centre.
 * Gerald James Whitrow, The Structure of the Universe: An Introduction to Cosmology (1949)


 * Changing electric fields produce magnetic fields, and changing magnetic fields produce electric fields. Thus the fields can animate one another in turn, giving birth to self-reproducing disturbances that travel at the speed of light. Ever since Maxwell, we understand that these disturbances are what light is.
 * Frank Wilczek, The Lightness of Being (2008)

A Beautiful Math (2006)

 * : John Nash, Game Theory, and the Quest for a Modern Code of Nature by Tom Siegfried


 * [I]n the mid-19th century math seemed... useless for physicists pondering the complexities of molecular motions in gases. ...How could anyone grasp the inner workings of a mass of molecules too numerous to count and too small to be seen? Yet... Maxwell found a way, by using statistics—mathematical descriptions of large groups of molecules. ...Maxwell got the idea to use statistics in physics from social scientists applying math to society!


 * Maxwell... mastered electricity and magnetism, light and heat, pretty much mopping up all the major areas of physics beyond those that Newton had... taken care of—gravitation and the laws of motion. ...Maxwell detected an essential shortcoming in Newton's laws of motion, too. They worked... for macroscopic objects, like cannonballs and rocks. But what about the submicroscopic molecules from which such objects were made? ...Newton's laws ...did you no good because you could not possibly trace the motion of an individual molecule ...Maxwell applied the sort of statistical thinking that Quetelet had promoted.


 * Maxwell probably first encountered Quetelet in an article by... John Herschel... (...familiar with Quetelet as a fellow astronomer). Later, in 1857, Maxwell read a newly published book by... Henry Thomas Buckle. Buckle, himself clearly influenced by Quetelet, believed that science could discover the "laws of the human mind" and that human actions are a part of "one vast system of universal order." ...Though Maxwell found Buckle's book "bumptious," he recognized it as a source of original ideas, and the statistical reasoning Buckle applied to society seemed just the thing... needed to deal with molecular motion.


 * The essential feature of Maxwell's work was showing that the properties of gases made sense not if gas molecules all flew around at a similar "average" velocity, as Clausius had surmised, but only if they moved at all sorts of speeds, most near the average, but some substantially faster or slower, and a few very fast or slow. ...Just as Quetelet's average man was fictitious, and key insights into society came from analyzing the spread of features around the average, understanding gases meant figuring out the range and distribution of molecular velocities around the average. And that distribution, Maxwell calculated, matched the bell-shaped curve describing the range of measurement errors.


 * Maxwell... during the 1860s... showed that when the velocities reached the bell-shaped distribution, no further net change was likely. (...Ludwig Boltzmann further elaborated... and strengthened Maxwell's results). Any specific molecule would speed up or slow down, but... other molecules would change in speed to compensate. When a gas reached that state... the gas was at equilibrium. ...[T]his notion of equilibrium is precisely analogous to the Nash equilibrium in game theory. ...[J]ust as the Nash equilibrium is typically a mixed set of strategies, a gas seeks an equilibrium state with a mixed distribution of molecular velocities.

The success... has driven the belief among many physicists that it could be applied with similar success to society. ...[E]verything from the flow of funds in the stock market to the flow of traffic on interstate highways ...
 * Maxwell, and then Boltzmann, and then... J. Willard Gibbs consequently expended enormous intellectual effort in devising..., or... . The uses... extend far beyond gases... describing electric and magnetic interactions, chemical reactions, phase transitions... and all other manner of exchanges of matter and energy.