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.

Although a physical law may never admit of a perfectly abrupt change, there is no limit to the approach which it may make to abruptness.

How do we discover the individual laws of Physics, and what is their nature? It should be remarked, to begin with, that we have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future. It is perfectly conceivable that one fine day Nature should cause an unexpected event to occur which would baffle us all; and if this were to happen we would be powerless to make any objection, even if the result would be that, in spite of our endeavors, we should fail to introduce order into the resulting confusion. In such an event, the only course open to science would be to declare itself bankrupt. For this reason, science is compelled to begin by the general assumption that a general rule of law dominates throughout Nature.

I believe that the human mind, or even the mind of a cat, is more interesting in its complexity than an entire galaxy if it is devoid of life.

If I get the impression that Nature itself makes the decisive choice [about] what possibility to realize, where quantum theory says that more than one outcome is possible, then I am ascribing personality to Nature, that is to something that is always everywhere. [An] omnipresent eternal personality which is omnipotent in taking the decisions that are left undetermined by physical law is exactly what in the language of religion is called God.

It is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong.

Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework.

Professor Ayrton said that we were gradually coming within thinkable distance of the realization of a prophecy he had ventured to make four years before, of a time when, if a person wanted to call to a friend he knew not where, he would call in a very loud electromagnetic voice, heard by him who had the electromagnetic ear, silent to him who had it not. “Where are you?” he would say. A small reply would come, “I am at the bottom of a coalmine, or crossing the Andes, or in the middle of the Atlantic.” Or, perhaps in spite of all the calling, no reply would come, and the person would then know that his friend was dead. Think of what this would mean ... a real communication from a distance based on true physical laws.
[His prophecy of cell phones, as a comment on Marconi's paper, 'Syntonic Wireless Telegraphy,' read before the Society of Arts, 15 May 1901, about his early radio signal experiments.]

Research is industrial prospecting. The oil prospectors use every scientific means to find new paying wells. Oil is found by each one of a number of methods. My own group of men are prospecting in a different field, using every possible scientific means. We believe there are still things left to be discovered. We have only stumbled upon a few barrels of physical laws from the great pool of knowledge. Some day we are going to hit a gusher.

Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws.

The man in the street will, therefore, twist the statement that the scientist has come to the end of meaning into the statement that the scientist has penetrated as far as he can with the tools at his command, and that there is something beyond the ken of the scientist. This imagined beyond, which the scientist has proved he cannot penetrate, will become the playground of the imagination of every mystic and dreamer. The existence of such a domain will be made the basis of an orgy of rationalizing. It will be made the substance of the soul; the spirits of the dead will populate it; God will lurk in its shadows; the principle of vital processes will have its seat here; and it will be the medium of telepathic communication. One group will find in the failure of the physical law of cause and effect the solution of the age-long problem of the freedom of the will; and on the other hand the atheist will find the justification of his contention that chance rules the universe.

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.

We already know the physical laws that govern everything we experience in everyday life … It is a tribute to how far we have come in theoretical physics that it now takes enormous machines and a great deal of money to perform an experiment whose results we cannot predict.

We have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future.

Yet is it possible in terms of the motion of atoms to explain how men can invent an electric motor, or design and build a great cathedral? If such achievements represent anything more than the requirements of physical law, it means that science must investigate the additional controlling factors, whatever they may be, in order that the world of nature may be adequately understood. For a science which describes only the motions of inanimate things but fails to include the actions of living organisms cannot claim universality.