A Quote by Brian Greene
Over the centuries, monumental upheavals in science have emerged time and again from following the leads set out by mathematics.
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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.
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.
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.
Making two possibilities a reality. Predicting the future of things we all know. Fighting off the diseased programming Of centuries, centuries, centuries, centuries. Science fails to recognise the single most Potent element of human existence. Letting the reigns go to the unfoldings faith, Science has failed our world. Science has failed our mother earth.
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.
There was a time, with the Berlin Wall down, that [it looked as if] the UN finally could do what it was set up to do, the rivalry between the two camps would dissipate, and we could all co-operate. And then, of course, Iraq came and blew it all apart. These upheavals will always take place in the world, and the design and construct of the UN ideally should be such that it can deal with these upheavals, and possibly influence them, and survive and thrive, but it doesn't work out that way, because as an organisation we are so dependent on the same member states.
We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.
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.
Over and over again, people had to disobey lawful authority to follow the voice of their conscience. This obedience to God and disobedience to the State has, over and over again, happened throughout history. It is time again to cry out against our 'leaders,' to question (since it is not for us to say that they are evil) whether or not they are sane.
I like science and mathematics. When I say mathematics, I don't mean algebra or math in that sense, but the mathematics of things.
The Suns, meanwhile, appeared to be hoisting a white flag over the Arizona desert. With a 12-22 record at the time, they were clearing out big contracts for salary-cap relief and a chance to start over again the following summer. We are taking a step backward in the immediate run, .. But we're certainly looking forward to the future.
I grew up in Adelaide, Australia. No one in my family had finished high school, and I was smart at mathematics, so I became an academic and got my Ph.D. in computer science at Stanford. I didn't set out to be a businessperson.
I'm convinced that imagination is at the heart of everything we do - in art, science, even astrophysics and higher mathematics. Imagination leads us to ask, "What if?"
The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.
If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics led me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.
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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