**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.

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.

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

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.

When I came back from Munich, it was September, and I was Professor of **Mathematics** at the Eindhoven University of Technology. Later I learned that I had been the Department's third choice, after two numerical analysts had turned the invitation down; the decision to invite me had not been an easy one, on the one hand because I had not really studied **Mathematics**, and on the other hand because of my sandals, my beard and my "arrogance" (whatever that may be).

**Mathematics** would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.

**Mathematics** is good for the soul, getting things right enlivens a sense of truth, efforts to understand automatically purify desires.

There is no branch of **Mathematics**, however abstract, which may not some day be applied to phenomena of the real world.

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.

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.

Addition and multiplication In our study of oscillating systems we shall have occasion to use one of the most remarkable, almost astounding, formulas in all of **Mathematics**. From the physicist's point of view we could bring forth this formula in two minutes or so, and be done with it. But science is as much for intellectual enjoyment as for practical utility, so instead of just spending a few minutes, we shall surround the jewel by its proper setting in the grand design of that branch of **Mathematics** called elementary algebra.

The apparently ancient reports of the importance of Pythagoras and his pupils in laying the foundations of **Mathematics** crumble on touch, and what we can get hold of is not authentic testimony by the efforts latecomers to paper over a crack, which they obviously found surprising, by the use of various kinds of reconstruction and reinterpretation. On the other hand, there are ancient and unassailable indications of a Greek **Mathematics** antedating Pythagoras and quite outside his sphere of influence.

It is a well-known experience that the only truly enjoyable and profitable way of studying **Mathematics** is the method of "filling in details" by one's own efforts.

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