"Who does not know Maxwell’s dynamic theory of gases? At first there is the majestic development of the variations of velocities, then enter from one side the equations of condition and from the other the equations of central motions, higher and higher surges the chaos of formulas, suddenly four words burst forth: 'Put n = 5', The evil demon V disappears like the sudden ceasing of the basso parts in music, which hitherto wildly permeated the piece; what before seemed beyond control is now ordered as by magic. There is no time to state why this or that substitution was made, he who cannot feel the reason may as well lay the book aside; Maxwell is no program-musician who explains the notes of his composition. Forthwith the formulas yield obediently result after result, until the temperature-equilibrium of a heavy gas is reached as a surprising final climax and the curtain drops." (Ludwig E Boltzmann, [ceremonial speech, 1887)
"From the outset Maxwell's theory excelled all others in elegance and in the abundance of the relations between the various phenomena which it included." (Heinrich Hertz, "Electric Waves", 1893)
"Maxwell, like every other pioneer who does not live to explore the country he opened out, had not had time to investigate the most direct means of access to the country, or the most systematic way of exploring it. This has been reserved for Oliver Heaviside to do. Maxwell’s treatise is cumbered with the débris of his brilliant lines of assault, of his entrenched camps, of his battles. Oliver Heaviside has cleared those away, has opened up a direct route, has made a broad road, and has explored a considerable tract of country." (George F Fitzgerald, [book review of Heaviside’s Electrical Papers in The Electrician] 1893)
"It has been said that no science is established on a firm basis unless its generalisations can be expressed in terms of number, and it is the special province of mathematics to assist the investigator in finding numerical relations between phenomena. After experiment, then mathematics. While a science is in the experimental or observational stage, there is little scope for discerning numerical relations. It is only after the different workers have 'collected data' that the mathematician is able to deduce the required generalisation. Thus a Maxwell followed Faraday and a Newton completed Kepler." (Joseph W Mellor, "Higher Mathematics for Students of Chemistry and Physics", 1902)
"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 th at 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 Poincaré, "La valeur de la science" ["The Value of Science"], 1904)
"First, the physicists in the persons of Faraday and Maxwell, proposed the 'electromagnetic field' in contradistinction to matter, as a reality of a different category. Then, during the last century, the mathematicians, […] secretly undermined belief in the evidence of Euclidean Geometry. And now, in our time, there has been unloosed a cataclysm which has swept away space, time, and matter hitherto regarded as the firmest pillars of natural science, but only to make place for a view of things of wider scope and entailing a deeper vision. This revolution was promoted essentially by the thought of one man, Albert Einstein." (Hermann Weyl," Space, Time, Matter", 1922)
"When Faraday filled space with quivering lines of force, he was bringing mathematics into electricity. When Maxwell stated his famous laws about the electromagnetic field it was mathematics. The relativity theory of Einstein which makes gravity a fiction, and reduces the mechanics of the universe to geometry, is mathematical research." (James B Shaw, "The Spirit of Research", The Monist No. 4, 1922)
"The law that entropy always increases - the Second Law of Thermodynamics - holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations - then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation - well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation." (Arthur S Eddington, "Gifford Lectures", 1927)
"The velocity of light is one of the most important of the fundamental constants of Nature. Its measurement by Foucault and Fizeau gave as the result a speed greater in air than in water, thus deciding in favor of the undulatory and against the corpuscular theory. Again, the comparison of the electrostatic and the electromagnetic units gives as an experimental result a value remarkably close to the velocity of light – a result which justified Maxwell in concluding that light is the propagation of an electromagnetic disturbance. Finally, the principle of relativity gives the velocity of light a still greater importance, since one of its fundamental postulates is the constancy of this velocity under all possible conditions." (A.A. Michelson, "Studies in Optics", 1927)
"The spirit of seeking which animates us refuses to regard any kind of creed as its goal. It would be a shock to come across a university where it was the practice of the students to recite adherence to Newton's laws of motion, to Maxwell's equations and to the electromagnetic theory of light. We should not deplore it the less if our own pet theory happened to be included, or if the list were brought up to date every few years. We should say that the students cannot possibly realise the intention of scientific training if they are taught to look on these results as things to be recited and subscribed to. Science may fall short of its ideal, and although the peril scarcely takes this extreme form, it is not always easy, particularly in popular science, to maintain our stand against creed and dogma." (Arthur S Eddington, "Science and the Unseen World", 1929)
"Almost all great advances have sprung originally from disinterested motives. Scientific discoveries have been made for their own sake and not for their utilization, and a race of men without a disinterested love of knowledge would never have achieved our present scientific technique. […] Faraday, Maxwell, and Hertz, so far as can be discovered, never for a moment considered the possibility of any practical application of their investigations." (Bertrand Russell,"The Scientific Outlook", 1931)
"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. So far this transformation from the force to the potential, from the action at a distance to the field, is only a purely mathematical operation." (Willem de Sitter,"Kosmos", 1932)
"Faraday, Maxwell, Larmor and a great number of others tried to explain electromagnetic action on these lines, but all attempts failed, and it began to seem impossible that any properties of ether could explain the observed pattern of events." (James Jeans, "Physics and Philosophy", 1942)
"It did not cause anxiety that Maxwell’s equations did not apply to gravitation, since nobody expected to find any link between electricity and gravitation at that particular level. But now physics was faced with an entirely new situation. The same entity, light, was at once a wave and a particle. How could one possibly imagine its proper size and shape? To produce interference it must be spread out, but to bounce off electrons it must be minutely localized. This was a fundamental dilemma, and the stalemate in the wave-photon battle meant that it must remain an enigma to trouble the soul of every true physicist. It was intolerable that light should be two such contradictory things. It was against all the ideals and traditions of science to harbor such an unresolved dualism gnawing at its vital parts. Yet the evidence on either side could not be denied, and much water was to flow beneath the bridges before a way out of the quandary was to be found. The way out came as a result of a brilliant counterattack initiated by the wave theory, but to tell of this now would spoil the whole story. It is well that the reader should appreciate through personal experience the agony of the physicists of the period. They could but make the best of it, and went around with woebegone faces sadly complaining that on Mondays, Wednesdays, and Fridays they must look on light as a wave; on Tuesdays, Thursdays, and Saturdays, as a particle. On Sundays they simply prayed." (Banesh Hoffmann, "The Strange Story of the Quantum", 1947)
"The second law of thermodynamics is, without a doubt, one of the most perfect laws in physics. Any reproducible violation of it, however small, would bring the discoverer great riches as well as a trip to Stockholm. The world’s energy problems would be solved at one stroke. […] Not even Maxwell’s laws of electricity or Newton’s law of gravitation are so sacrosanct, for each has measurable corrections coming from quantum effects or general relativity. The law has caught the attention of poets and philosophers and has been called the greatest scientific achievement of the nineteenth century." (Ivan P. Bazarov, "Thermodynamics", 1964)
"Liebig himself seems to have occupied the role of a gate, or sorting-demon, such as his younger contemporary Clerk Maxwell once proposed, helping to concentrate energy into one favored room of the Creation at the expense of everything else." (Thomas Pynchon, "Gravity's Rainbow", 1973)
"The rigid electron is in my view a monster in relation to Maxwell's equations, whose innermost harmony is the principle of relativity [...] the rigid electron is no working hypothesis, but a working hindrance. Approaching Maxwell's equations with the concept of the rigid electron seems to me the same thing as going to a concert with your ears stopped up with cotton wool. We must admire the courage and the power of the school of the rigid electron which leaps across the widest mathematical hurdles with fabulous hypotheses, with the hope to land safely over there on experimental-physical ground." (Hermann Minkowski [in Arthur I Miller, "Albert Einstein's Special Theory of Relativity", 1981)
"Einstein was thus faced with the following apparent problem. Either give up the principle of relativity, which appears to make physics possible by saying that the laws of physics are independent of where you measure them, as long as you are in a state of uniform motion; or give up Maxwell’s beautiful theory of electromagnetism and electromagnetic waves. In a truly revolutionary move, he chose to give up neither. [...] It is a testimony to his boldness and creativity not that he chose to throw out existing laws that clearly worked, but rather that he found a creative way to live within their framework. So creative, in fact, that it sounds nuts." (Lawrence M Krauss, "Fear of Physics: A Guide for the Perplexed", 1993)
"Maxwell's equations […] originally consisted of eight equations. These equations are not`beautiful`. They do not possess much symmetry. In their original form, they are ugly. […] However, when rewritten using time as the fourth dimension, this rather awkward set of eight equations collapses into a single tensor equation. This is what a physicist calls 'beauty'. (Michio Kaku, "Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension", 1995)
"The appeal of Monstrous Moonshine lies in its mysteriousness: it unexpectedly associates various special modular functions with the Monster, even though modular functions and elements of Mare conceptually incommensurable. Now, ‘understanding’ something means to embed it naturally into a broader context. Why is the sky blue? Because of the way light scatters in gases. Why does light scatter in gases the way it does? Because of Maxwell’s equations. In order to understand Monstrous Moonshine, to resolve the mystery, we should search for similar phenomena, and fit them all into the same story." (Terry Gannon, "Moonshine Beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics", 2006)
"Topology is rooted in Maxwell’s theory on the electromagnetic field." (Eberhard Zeidler, "Quantum Field Theory I: Basics in Mathematics and Physics", 2006)
"In a Newtonian view, space and time are separate and different. Symmetries of the laws of physics are combinations of rigid motions of space and an independent shift in time. But... these transformations do not leave Maxwell's equations invariant. Pondering this, the mathematicians Henri Poincaré and Hermann Minkowski were led to a new view of the symmetries of space and time, on a purely mathematical level. If they had described these symmetries in physical terms, they would have beaten Einstein to relativity, but they avoided physical speculations. They did understand that symmetries in the laws of electromagnetism do not affect space and time independently but mix them up. The mathematical scheme describing these intertwined changes is known as the Lorentz group, after the physicist, Hendrik Lorentz." (Ian Stewart, "Why Beauty Is Truth: The History of Symmetry", 2008)
"The concept of a field was actually introduced first in the context of electricity and magnetism by Michael Faraday as a means of 'visualizing' electromagnetic effects to replace certain mathematical ideas for which he had little talent. However, in the hands of James Maxwell, fields were molded into a physical entity having an existence of their own in the form of electromagnetic waves to be produced in 1887 by Hertz and used in 1901 by Marconi in the development of radio." (Sadri Hassani, "Mathematical Methods: For Students of Physics and Related Fields", 2009)
"Clausius, Maxwell, Boltzmann and Gibbs had a feeling for the statistical interpretation of the second principle of thermodynamics and defended it. But their explanations were based on thought experiments coming from the postulate of the existence of molecules. Only after the discovery of Brownian motion does the interpretation of the second principle of thermodynamics as an absolute law become impossible. Brownian particles rising and falling as a result of the thermal motion of the molecules is a clear demonstration for us of a perpetual motion machine of the second kind. Therefore at the end of the 19th century the investigation of Brownian motion acquired enormous theoretical significance and attracted the attention of many theoretical physicists including Einstein." (Vladimir Zorich, "Mathematical Analysis of Problems in the Natural Sciences", 2010)
"The classical theories of space, time, and matter were brought to their peak in James Clerk Maxwell’s equations for electromagnetism. This elegant system of equations unified two of nature’s forces, previously thought to be distinct. In place of electricity and magnetism, there was a single electromagnetic field. A field pervades the whole of space, as if the universe were filled with some kind of invisible fluid. At each point of space we can measure the strength and direction of the field, as if that fluid were flowing in mathematical patterns. For some purposes the electromagnetic field can be split into two components, the electric field and the magnetic field. But a moving magnetic field creates an electric one, and conversely, so when it comes to dynamics, both fields must be combined into a single more complex one." (Ian Stewart, "Visions of Infinity", 2013)
"Our most successful theories in physics are those that explicitly leave room for the unknown, while confining this room sufficiently to make the theory empirically disprovable. It does not matter whether this room is created by allowing for arbitrary forces as Newtonian dynamics does, or by allowing for arbitrary equations of state for matter, as General Relativity does, or for arbitrary motions of charges and dipoles, as Maxwell's electrodynamics does. To exclude the unknown wholly as a 'unified field theory' or a 'world equation' purports to do is pointless and of no scientific significance." (Hermann Bondi)
"The rigid electron is in my view a monster in relation to Maxwell's equations, whose innermost harmony is the principle of relativity [...] the rigid electron is no working hypothesis, but a working hindrance. Approaching Maxwell's equations with the concept of the rigid electron seems to me the same thing as going to a concert with your ears stopped up with cotton wool. We must admire the courage and the power of the school of the rigid electron which leaps across the widest mathematical hurdles with fabulous hypotheses, with the hope to land safely over there on experimental-physical ground." (Hermann Minkowski)
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