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

I have often been surprised that **Mathematics**, the quintessence of Truth, should have found admirers so few and so languid. Frequent consideration and minute scrutiny have at length unravelled the cause: viz . that though Reason is feasted, Imagination is starved; whilst Reason is luxuriating in its proper Paradise, Imagination is wearily travelling on a dreary desert.

**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.

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.

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.

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 idea of an isolated American painting , so popular in this country during the thirties, seems absurd to me, just as the idea of a purely American **Mathematics** or physics would seem absurd... And in another sense, the problem doesn’t exist at all; or, if it did, would solve itself: An American is an American and his painting would naturally be qualified by the fact, whether he wills or not. But the basic problems of contemporary painting are independent of any one country.

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.

(Econometrics is) the unification of economic theory, statistics and **Mathematics** .

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**...

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** .

I cannot recall a period when I did not draw; and at school, the studies that were distasteful to me, **Mathematics** and grammar , were retarded by the indulgence of teachers who were proud of my drawing faculties, and passed over my neglect of uncongenial subjects.

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**.

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 .