A Quote by Eugene Wigner
The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it.
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The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics (having no rational explanation).
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
All mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.
There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured ... Of these sciences the gate and key is mathematics ... He who is ignorant of this [mathematics] cannot know the other sciences nor the affairs of this world.
If you ask ... the man in the street ... the human significance of mathematics, the answer of the world will be, that mathematics has given mankind a metrical and computatory art essential to the effective conduct of daily life, that mathematics admits of countless applications in engineering and the natural sciences, and finally that mathematics is a most excellent instrumentality for giving mental discipline... [A mathematician will add] that mathematics is the exact science, the science of exact thought or of rigorous thinking.
I started off thinking that maybe the social sciences ought to have the kinds of mathematics that the natural sciences had. That works a little bit in economics because they talk about costs, prices and quantities of goods.
Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.
There is in the universe something for the description and analysis of which the natural sciences cannot contribute anything. There are events beyond the range of those events that the procedures of the natural sciences are fit to observe and describe. There is human action.
The usefulness of mathematics in furthering the sciences is commonly acknowledged: but outside the ranks of the experts there is little inquiry into its nature and purpose as a deliberate human activity. Doubtless this is due to the inevitable drawback that mathematical study is saturated with technicalities from beginning to end.
The argument from design is ultimately an appeal to miraculous causes, i.e., causes that do not, and cannot, occur in the natural course of events. This is why an explanation via design is not a legitimate alternative to scientific and other naturalistic modes of explanation. To refer to a miraculous cause is to refer to something that is inherently unknowable, and this sanctuary of ignorance explains nothing at all. However much it may soothe the imagination of the ignorant, it does nothing to satisfy the understanding of a rational person.
The methods of the natural sciences cannot be applied to human behavior because this behaviorlacks the peculiarity that characterizes events in the field of the natural sciences, viz., regularity.
What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.
Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.
Almost everyone... seems to be quite sure that the differences between the methodologies of history and of the natural sciences are vast. For, we are assured, it is well known that in the natural sciences we start from observation and proceed by induction to theory. And is it not obvious that in history we proceed very differently? Yes, I agree that we proceed very differently. But we do so in the natural sciences as well.
You can keep counting forever. The answer is infinity. But, quite frankly, I don't think I ever liked it. I always found something repulsive about it. I prefer finite mathematics much more than infinite mathematics. I think that it is much more natural, much more appealing and the theory is much more beautiful. It is very concrete. It is something that you can touch and something you can feel and something to relate to. Infinity mathematics, to me, is something that is meaningless, because it is abstract nonsense.
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