Origami helps in the study of **Mathematics** and science in many ways. ... Using origami anyone can become a scientific experimenter with no fuss.

Martin Kruskal, a mathematician at Rutgers University, as quoted by Science Daily Origami Helps Scientists Solve Problems, February 21, 2002.

General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure **Mathematics** and the specific theories of the specialized disciplines. **Mathematics** attempts to organize highly general relationships into a coherent system, a system however which does not have any necessary connections with the "real" world around us. It studies all thinkable relationships abstracted from any concrete situation or body of empirical knowledge.

**Mathematics** as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.

Like all of **Mathematics**, game theory is a tautology whose conclusions are true because they are contained in the premises.

Chapter 10, What Have We Learned?, p. 164

At present, when the prevailing forms of society have become hindrances to the free expression of human powers, it is precisely the abstract branches of science, **Mathematics** and theoretical physics, which ... offer a less distorted form of knowledge than other branches of science which are interwoven with the pattern of daily life, and the practicality of which seemingly testifies to their realistic character.

p. 133 ("The Latest Attack on Metaphysics" (1937))

The land of easy **Mathematics** where he who works adds up and he who retires subtracts.

In the short story

The subject of management science has evolved for more than 60 years and is now a mature field within the broad category of applied **Mathematics**. This book will emphasize both the applied and mathematical aspects of management science.

It is noteworthy that modern Platonists , almost without exception, are ignorant of **Mathematics**, in spite of the immense importance that Plato attached to arithmetic and geometry, and the immense influence that they [these studies] had on his philosophy. This is an example of the evils of specialization: a man must not write on Plato unless he has spent so much of his youth on Greek as to have no time for the things that Plato thought important.

**Mathematics** is the gate and key of the sciences... Neglect of **Mathematics** works injury to all knowledge , since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy.

cited in: Morris Kline (1969)

Roger Bacon, a disciple of the Arabs, also insisted on the primary necessity of **Mathematics**, without which no other science can be known; yet by **Mathematics** it is clear that he meant something very different from what we mean, including under that head even dancing, singing, gesticulation, and performance on musical instruments.

George Henry Lewes,

A mathematical formula should never be "owned" by anybody! **Mathematics** belong to God.

**Mathematics** takes us still further from what is human, into the region of absolute necessity, to which not only the world, but every possible world, must conform.

Bertrand Russell,

To those who ask what the infinitely small quantity in **Mathematics** is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.

As quoted in

The branches of **Mathematics** are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate **Mathematics**. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.

§ 2

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.

Columbia University speech, 24 September 2007

"Iran's president at Columbia University - a transcript".

To those who do not know **Mathematics** it is difficult to get across a real feeling as to the beauty , the deepest beauty, of nature . ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

chapter 2, “The Relation of Mathematics to Physics,” p. 58

For **Mathematics** education and the world of problem solving it marked a line of demarcation between two eras, problem solving before and after Polya.

A. H. Schoenfeld, in "Polya, Problem Solving, and Education" in

It was, however, from Spain, and not from Arabia, that a knowledge of eastern **Mathematics** first came into western Europe. The Moors had established their rules in Spain in 747, and by the tenth or eleven century had attained a high degree of civilisation.

No one really knew the sciences except the Lord Robert, Bishop of Lincoln, by reason of his length of life and experience, as well as of his studiousness and zeal. He knew **Mathematics** and perspective, and there was nothing which he was unable to know; and at the same time he was sufficiently acquainted with languages to be able to understand the saints and the philosophers and the wise men of antiquity but his knowledge of languages was not such as to enable him to effect translations until the latter portion of his life...

Roger Bacon,

Like all of **Mathematics**, game theory is a tautology whose conclusions are true because they are contained in the premises.

Math is perfect (in principle), but mathematicians are not (because they are humans), hence the **Mathematics** that (human) mathematicians do is influenced by the weltanschauung of the people around them.

India was the motherland of our race, and Sanskrit the mother of Europe's languages: she was the mother of our philosophy; mother, through the Arabs, of much of our **Mathematics**; mother, through the Buddha, of the ideals embodied in Christianity; mother, through the village community, of self-government and democracy. Mother India is in many ways the mother of us all.

If perchance there should be foolish speakers who, together with those ignorant of all **Mathematics** , will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash .

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