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.
To set foot on the soil of the asteroids, to lift by hand a rock from the Moon, to observe Mars from a distance of several tens of kilometers, to land on its satellite or even on its surface, what can be more fantastic? From the moment of using rocket devices a new great era will begin in astronomy: the epoch of the more intensive study of the firmament.
I've been so lucky to have done two spacewalks. If you looked at your wristwatch, I was outside about 15 hours, which is about 10 times around the world. And, you know, there's a whole time dilation, distortion thing.
I was interested in the nature of human mental processes, which is what got me interested in psychoanalysis. And it became clear to me after a while that mental processes come from the brain, and in order to understand them, you need to be a biologist of the brain.
Inside of a living cell there are thousands of proteins that enable it to make more of itself and make your malaria drug, for instance. We don't understand those. We don't understand how they work together.
The observation that species are amazingly conservative and static entities throughout long periods of time has all the qualities of the emperor's new clothes: everyone knew it but preferred to ignore it. Paleontologists, faced with a recalcitrant record obstinately refusing to yield Darwin's predicted pattern, simply looked the other way.
The atomic bomb certainly is the most powerful of all weapons, but it is conclusively powerful and effective only in the hands of the nation which controls the sky.
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