In his youth, Maxwell enjoyed geometry, and wrote a paper on ellipses at the age of 14. While he was not the top student in his class in mathematics, he continued his geometric approach and applied it with great success to physics. Maxwell is considered one of the greatest physicists ever.
From the way in which changes in a magnetic field produce electric fields, and the way in which changes in electric fields produced magnetic fields, Maxwell deduced a set of equations that describe them, Maxwell's Equations, in 1861. The equations predicted the possibility of electromagnetic waves. Other scientists looked for and detected these waves, which led both to the development of radio communication and to the discovery that light is a kind of electromagnetic wave.
Lorentz and Poincare relied heavily upon Maxwell's ideas, which were in turn mathematized forms of Michael Faraday's work, to create the theories of relativity. It has been suggested that relativity is Faraday and Maxwell's field theory applied to the stars, but relativity includes assumptions and claims that Maxwell may not have supported.
- No theory of evolution can be formed to account for the similarity of molecules, for evolution necessarily implies continuous change, and the molecule is incapable of growth or decay, of generation or destruction. None of the processes of Nature, since the time when Nature began, have produced the slightest difference in the properties of any molecule. We are therefore unable to ascribe either the existence of the molecules or the identity of their properties to any of the causes which we call natural. 
- Natural causes, as we know, are at work, which tend to modify, if they do not at length destroy, all the arrangements and dimensions of the earth and the whole solar system. But though in the course of ages catastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules out of which these systems are built—the foundation-stones of the material universe—remain unbroken and unworn. They continue this day as they were created—perfect in number and measure and weight; and from the ineffaceable characters impressed on them we may learn that those aspirations after accuracy in measurement, and justice in action, which we reckon among our noblest attributes as men, are ours because they are  essential constituents of the image of Him who in the beginning created, not only the heaven and the earth, but the materials of which heaven and earth consist. [ibid]
He also wrote:
- The true logic of this world is in the calculus of probabilities. 
- The only laws of matter are those that our minds must fabricate and the only laws of mind are fabricated for it by matter.
These quotations demonstrate Maxwell's rejection of the theory of evolution, despite pressure in England for acceptance of the theory. While Maxwell was not a biologist, was the leading English-speaking scientific mind of his time. Elsewhere Maxwell derisively referred to the theory of evolution as "speculations", and noted these speculations were absurd at the molecular level (Michael Behe made an analogous point in the new field of molecular biology over 100 years later):
- The molecules of the same substance are all exactly alike, but different from those of other substances. There is not a regular gradation in the mass of molecules from that of hydrogen, which is the least of those known to us, to that of bismuth; but they all fall into a limited number of classes or species, the individuals of each species being exactly similar to each other, and no intermediate links are found to connect one species with another by a uniform gradation.
- We are here reminded of certain speculations concerning the relations between the species of living things. We find that in these also the individuals are naturally grouped into species, and that intermediate links between the species are wanting. But in each species variations occur, and there is a perpetual generation and destruction of the individuals of which the species consist.
- Hence it is possible to frame a theory to account for the present state of things by means of generation, variation, and discriminative destruction.
- In the case of the molecules, however, each individual is permanent; there is no generation or destruction, and no variation, or rather no difference, between the individuals of each species.
- Hence the kind of speculation with which we have become so familiar under the name of theories of evolution is quite inapplicable to the case of molecules. 
It should also be noted that Maxwell wrote these words before atomic theory was widely accepted. Maxwell of course knew nothing of the chemical composition of molecules like proteins and DNA, nor did he know about sub-atomic or nuclear processes, all of which contradict his claims that "there is no generation or destruction, and no variation ..." among molecules and atoms.
Lewis Campbell and William Garnett, The Life of James Clerk Maxwell, London, Macmillan, 1882
- "Influence on the Development of the Conception of Physical Reality" by Albert Einstein, written for the centenary of Maxwell's birth (1931)
- James Clerk Maxwell, "The Theory of Heat", London, Longman's, Green, and Co., 1871. http://www.archive.org/stream/theoryofheat00maxwrich/