The true spirit of delight, the exaltation, the sense of being more than
man, which is the touchstone of the highest excellence,
is to be found in **mathematics** as surely as in
poetry.

**mathematics** is the door and key to the sciences.

[There is] a delusion that macro-economics is both viableanduseful (a
delusionencouraged by its extensive use of **mathematics**,
which must always impress politicians lacking
any mathematical education, and which is really the
nearest thing to the practice of magic that occurs among
professional economists).

Vanite desVanite s;Vanite de la ge ome trie. Vanity of vanities!
Vanity of **mathematics**!

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).

If you are receptive and humble, **mathematics** will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the **mathematics** led me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.

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

Anyone who cannot cope with **mathematics** is not fully human. At best he is a tolerable sub-human who has learned to wear shoes, bathe, and not make messes in the house.

Three principles — the conformability of nature to herself, the applicability of the criterion of simplicity, and the "unreasonable effectiveness" of certain parts of **mathematics** in describing physical reality — are thus consequences of the underlying law of the elementary particles and their interactions. Those three principles need not be assumed as separate metaphysical postulates. Instead, they are emergent properties of the fundamental laws of physics.

Toward the end of his life, Gödel feared that he was being poisoned, and he starved himself to death. His theorem is one of the most extraordinary results in **mathematics**, or in any intellectual field in this century. If ever potential mental instability is detectable by genetic analysis, an embryo of someone with Kurt Gödel's gifts might be aborted.

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.

Chess is not **mathematics**, where ten is always more than one; in chess the King with a pawn can beat opponent's King with all pieces if they are placed badly.

Poetry is a sort of inspired **mathematics**, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.

I came into history from a primary concern with **mathematics** and science. This has been a tremendous help to me as a person and as a historian, although it must be admitted it has served to make my historical interpretations less conventional than may be acceptable of many of my colleagues in the field.

Today's scientists have substituted **mathematics** for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

**mathematics** is one of the essential emanations of the human spirit, a thing to be valued in and for itself, like art or poetry.

Histories make men wise; poets, witty; the **mathematics**, subtile; natural philosophy, deep; morals, grave; logic and rhetoric, able to contend.

Without **mathematics**, we are blind.

Do not worry about your difficulties in **mathematics**. I can assure you mine are still greater.

Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of **mathematics**.

For all the sublimity of art, physics, music, **mathematics**, and other manifestations of human genius, everything depends on the mundane, frustrating, often debased vocation known as politics (and its most exacting subspecialty – statecraft). Because if we don't get politics right, everything else risks extinction.

The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. ... **mathematics** cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.

The study of **mathematics** is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

During the 1950s and 1960s most of the work which was called cybernetics tended to focus on control systems in engineering or on applications of the concept of feedback in fields ranging from **mathematics** to sociology. At the 1970 meeting of the American Society for Cybernetics in Philadelphia Heinz von Foerster sought to redirect attention to the original interests which had led to the founding of the field of cybernetics. In a paper titled "Cybernetics of Cybernetics" he made a distinction between first order cybernetics, the cybernetics of observed systems, and second order cybernetics, the cybernetics of observing systems.

One of the most frequently mentioned equations was Euler 's equation, Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty "; and " mind -blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing ?" The equation contains nine basic concepts of **mathematics** once and only once in a single expression. These are: e (the base of natural logarithms); the exponent operation; ?; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero.

Pythagoras raised **mathematics** to the rank of a science. Arithmetic was courted by him as fervently as geometry. In fact, arithmetic is the foundation of his philosophic system.

If scientific reasoning were limited to the logical processes of arithmetic, we should not get far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the **mathematics** of probability. The abacus, with its beads strung on parallel wires, led the Arabs to positional numeration and the concept of zero many centuries before the rest of the world; and it was a useful tool so useful that it still exists.

Even in **mathematics** his whimsical fancy was sometimes suffered to peep out, and little girls who learnt the rudiments of calculation at his knee found the path they had imagined so thorny set about with roses by reason of the delightful fun with which he would turn a task into a joy. But when the fun was over the little girl would find that she had learnt the lesson (all unknowingly) just the same. Happy little girls who had such a master.

We can no more have exact religious thinking without theology, than exact mensuration and astronomy without **mathematics**, or exact iron-making without chemistry,

Grosseteste was deeply concerned with the detailed investigation of natural phenomena. It was the inspiration of this attitude of mind, together with Grosseteste's emphasis on the importance of **mathematics**, that was perhaps his chief legacy to thinkers in fourteenth-century Oxford who were developing the beginnings of a mathematical physics.