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.

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 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.

Grattan-Guiness's uniformly interesting and valuable account of the interwoven development of logic and related fields of **Mathematics** . . . between 1870 and 1940 presents a significantly revised analysis of the history of the period. . . . [His] book is important because it supplies what has been lacking: a full account of the period from a primary mathematical perspective.

Discovery in **Mathematics** is not a matter of logic. It is rather the result of mysterious powers which no one understands, and in which unconscious recognition of beauty must play an important part. Out of an infinity of designs, a mathematician chooses one pattern for beauty's sake and pulls it down to earth.

When we ask what ought to be the relative remunerations of a nurse or a butcher, or a coal miner and a judge at a high court, of the deep sea diver of the cleaner of sewers, of the organiser of a new industry and a jockey, of the inspector of taxes and the inventor of a life-saving drug, of the jet-pilot or the professor of **Mathematics**, the appeal to 'social justice' does not give us the slightest help in deciding…

Mechanical Engineering may be defined as being the application of **Mathematics** to Science, with particular reference to the design and fabrication of all forms of machinery. Since engineering is the combined science and art of utilizing the

The practice of first developing a clear and precise definition of a process without regard for efficiency, and then using it as a guide and a test in exploring equivalent processes possessing other characteristics, such as greater efficiency, is very common in **Mathematics**. It is a very fruitful practice which should not be blighted by premature emphasis on efficiency in computer execution.

But one will say, 'What is the principal behind these scales, and what, if not acoustic phenomena and the laws of **Mathematics**, has set the order of their tones?' I respond that this principle is purely metaphysical [anthropological]. We conceive this order and the melodic and harmonic phenomena that spring from it out of our conformation and education. (p.249)

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

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