A Quote by Eugene Wigner
... mathematics is the science of skillful operations with concepts and rules invented just for this purpose.
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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.
The science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value.
But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.
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.
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.
Music is a science which should have definite rules; these rules should be drawn from an evident principle; and this principle cannot really be known to us without the aid of mathematics.
While I've done over 10,000 heart operations and invented operations and devices that are used every day in heart surgery, the joy I receive from watching even one person take back their health just can't be surpassed, and certainly can't be measured monetarily.
There are so many rules about how you make a film and so many conventions that you can and can't do. I think people have forgotten that they are just rules that were invented for convenience - sometimes it is more convenient not to obey the rules.
One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.
I like science and mathematics. When I say mathematics, I don't mean algebra or math in that sense, but the mathematics of things.
I think math is a hugely creative field, because there are some very well-defined operations that you have to work within. You are, in a sense, straightjacketed by the rules of the mathematics. But within that constrained environment, it's up to you what you do with the symbols.
Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.
My Ph.D. is in operations research. I was interested in making things work better and using mathematics to help do that. So operations research is what I studied as an undergraduate and graduate student.
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.
The life and soul of science is its practical application, and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in the earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.
Mathematics is really an art, not a science. You could say science also is an art. So I would say the difference is something you can't really describe - you can only recognize. You hear somebody playing the violin, and it was Fritz Kreisler or it was somebody else, and you can tell the difference. It is so in almost every art. We just don't understand why it is that there are just a few people who are just completely off the scale and the rest of them are just mediocre. And we don't know why. But I say it's certainly true of mathematics.
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