All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.
Interpretation
The quote highlights the connection between mathematics and the physical sciences, emphasizing how science aims to quantify natural phenomena.
James Clerk Maxwell suggests that all branches of mathematical sciences derive their principles from the relationships between physical laws and numerical laws. This reveals that the essence of exact science is to simplify and resolve the complexities of nature into quantifiable elements, allowing for a more systematic understanding through mathematical operations.
In practice
In a lecture on the importance of mathematics in scientific discoveries.
Science appears to us with a very different aspect after we have found out that it is not in lecture rooms only, and by means of the electric light projected on a screen, that we may witness physical phenomena, but that 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.
... that, in a few years, all great physical constants will have been approximately estimated, and that the only occupation which will be left to men of science will be to carry these measurements to another place of decimals.
Very few of us can now place ourselves in the mental condition in which even such philosophers as the great Descartes were involved in the days before Newton had announced the true laws of the motion of bodies.
What's the go of that? What's the particular go of that?
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.
If we betake ourselves to the statistical method, we do so confessing that we are unable to follow the details of each individual case, and expecting that the effects of widespread causes, though very different in each individual, will produce an average result on the whole nation, from a study of which we may estimate the character and propensities of an imaginary being called the Mean Man.
The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.
Going to Mars would evolve humankind into a two-planet species.
It is to them [fossils] alone that we owe the commencement of even a Theory of the Earth ... By them we are enabled to ascertain, with the utmost certainty, that our earth has not always been covered over by the same external crust, because we are thoroughly assured that the organized bodies to which these fossil remains belong must have lived upon the surface before they came to be buried, as they now are, at a great depth.
There is for me powerful evidence that there is something going on behind it all. . . It seems as though somebody has fine tuned nature's numbers to make the Universe. . . The impression of design is overwhelming.
The works of Lavoisier and his associates operated upon many of us at that time like the Sun's rising after a night of moonshine: but Chemistry is now betrothed to the Mathematics, and is in consequence grown somewhat shy of her former admirers.
The facts will eventually test all our theories, and they form, after all, the only impartial jury to which we can appeal.
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