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.

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

**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.

The principles of logic and **Mathematics** are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and **Mathematics** are analytic propositions or tautologies.

Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows no more uniformity than **Mathematics**. Nevertheless, programming languages do bring a different perspective. [...] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation.

As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond **Mathematics** itself. He knew his technical abilities; his virtuosity in following complicated reasoning and his insights were supreme; yet he lacked absolute self confidence.

It must be owned (...) that all the knowledge, whether of physic, astronomy, philosophy, or **Mathematics**, which flourished in Europe from the tenth century, was originally derived from them; and that the Spanish Saracens, in a more particular manner, may be looked upon as the fathers of European philosophy.

If in other sciences we should arrive at certainty without doubt and truth without error , it behooves us to place the foundations of knowledge in **Mathematics**...

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.

Lateral thinking... is the process of using information to bring about creativity and insight restructuring. Lateral thinking can be learned, practised and used. It is possible to acquire skill in it just as it is possible to acquire skill in **Mathematics** .

For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity , nor accommodated unto use with sufficient dexterity, without the aid and intervening of the **Mathematics** , of which sort are perspective, music , astronomy , cosmography , architecture , engineery, and divers others.

Men are constantly attracted and deluded by two opposite charms: the charm of competence which is engendered by **Mathematics** and everything akin to **Mathematics**, and the charm of humble awe, which is engendered by meditation on the human soul and its experiences. Philosophy is characterized by the gentle, if firm, refusal to succumb to either charm.

Trivialism arises from the idea that **Mathematics** is classical and there is contradiction in **Mathematics**, and therefore (under our old classical reasoning), all of **Mathematics** is true , we then get to the meaninglessness of any particular mathematical statement and wallow in our degenerate theory .