A Quote by Immanuel Kant
In every department of physical science there is only so much science, properly so-called, as there is mathematics.
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Mathematics has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.
Yet things are knowable! They are knowable, because, being from one, things correspond. There is a scale: and the correspondence of heaven to earth, of matter to mind, of the part to the whole, is our guide. As there is a science of stars, called astronomy; and science of quantities, called mathematics; a science of qualities, called chemistry; so there is a science of sciences,--I call it Dialectic,--which is the Intellect discriminating the false and the true.
The best road to correct reasoning is by physical science; the way to trace effects to causes is through physical science; the only corrective, therefore, of superstition is physical science.
Mathematics is often defined as the science of space and number . . . it was not until the recent resonance of computers and mathematics that a more apt definition became fully evident: mathematics is the science of patterns.
I could never have gone far in any science because on the path of every science the lion Mathematics lies in wait for you.
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.
Science is intimately integrated with the whole social structure and cultural tradition. They mutually support one other-only in certain types of society can science flourish, and conversely without a continuous and healthy development and application of science such a society cannot function properly.
Do not trust financial market risk models. Despite the predilection of some analysts to model the financial markets using sophisticated mathematics, the markets are governed by behavioral science, not physical science.
The only science that gives purpose to every other science is the science of religion - the science of our happy relationship with, and our providential dependence on God and our neighbor.
I can think of very few science books I've read that I've called useful. What they've been is wonderful. They've actually made me feel that the world around me is a much fuller, much more wonderful, much more awesome place than I ever realized it was. That has been, for me, the wonder of science. That's why science fiction retains its compelling fascination for people. That's why the move of science fiction into biology is so intriguing. I think that science has got a wonderful story to tell.
We had principles in mathematics that were granted to be absolute in mathematics for over 800 years, but new science has gotten rid of those absolutism, gotten forward other different logics of looking at mathematics, and sort of turned the way we look at it as a science altogether after 800 years.
It seems perfectly clear that Economy, if it is to be a science at all, must be a mathematical science. There exists much prejudice against attempts to introduce the methods and language of mathematics into any branch of the moral sciences. Most persons appear to hold that the physical sciences form the proper sphere of mathematical method, and that the moral sciences demand some other method-I know not what.
One of the things that got me transitioning from physical science to brain science was asking, Why do we understand so much about the universe?
In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.
Statistics is the most important science in the whole world: for upon it depends the practical application of every other science and of every art: the one science essential to all political and social administration, all education, all organization based on experience, for it only gives results of our experience.
The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept "science"; for it is as a part of science that mathematics originally took its place in human thought.
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