Quotes About Mathematics

. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.

There is no thing as a man who does not create mathematics and yet is a fine mathematics teacher. Textbooks, course material-these do not approach in importance the communication of what mathematics is really about, of where it is going, and of where it currently stands with respect to the specific branch of it being taught. What really matters is the communication of the spirit of mathematics. It is a spirit that is active rather than contemplative-a spirit of disciplined search for adventures of the intellect. Only as adventurer can really tell of adventures.

Life is good for only two things, discovering mathematics and teaching mathematics.

Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.

[The error in the teaching of mathematics is that] mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher's assurance that it will be helpful in later life. [And yet,] mathematlcs is the key to understanding and mastering our physical, social and biological worlds.

Yes, I share your concern: how to program well -though a teachable topic- is hardly taught. The situation is similar to that in mathematics, where the explicit curriculum is confined to mathematical results; how to do mathematics is something the student must absorb by osmosis, so to speak. One reason for preferring symbol-manipulating, calculating arguments is that their design is much better teachable than the design of verbal/pictorial arguments. Large-scale introduction of courses on such calculational methodology, however, would encounter unsurmoutable political problems.

If you want to be a physicist, you must do three things-first, study mathematics, second, study more mathematics, and third, do the same.

A Christian boy or girl can learn mathematics, for example, from a teacher who is not a Christian; and truth is truth however learned. But while truth is truth however learned, the bearing of truth, the meaning of truth, the purpose of truth, even in the sphere of mathematics, seem entirely different to the Christian from that which they seem to the non-Christian; and that is why a truly Christian education is possible only when Christian conviction underlies not a part but all, of the curriculum of the school.

One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.

The proof of Fermat's Last Theorem underscores how stable mathematics is through the centuries - how mathematics is one of humanity's long continuous conversations with itself.

On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things whlch are of no concern at all to man.

Theology, Mr. Fortune found, is a more accommodating subject than mathematics; its technique of exposition allows greater latitude. For instance when you are gravelled for matter there is always the moral to fall back upon. Comparisons too may be drawn, leading cases cited, types and antetypes analysed and anecdotes introduced. Except for Archimedes mathematics is singularly naked of anecdotes.

Doing research in mathematics is frustrating and if being frustrated is something you cannot get used to, then mathematics may not be an ideal occupation for you.

Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.

In mathematics I can report no deficiency, except it be that men do not sufficiently understand the excellent use of Pure Mathematics.

The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.

To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples.

It was as though applied mathematics was my spouse, and pure mathematics was my secret lover.

Applied mathematics will always need pure mathematics just as anteaters will always need ants.

Mathematicians care no more for logic than logicians for mathematics.

The infinite in mathematics is always unruly unless it is properly treated.

If all of mathematics disappeared, physics would be set back by exactly one week.

All the sciences have a relation, greater or less, to human nature; and...however wide any of them may seem to run from it, they still return back by one passage or another. Even Mathematics, Natural Philosophy, and Natural Religion, are in some measure dependent on the science of MAN; since they lie under the cognizance of men, and are judged of by their powers and faculties.

The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.

Nature imitates mathematics.

Outside of mathematics and logic, there are common sense truths, such as that it is snowing that normal observers, in a specified context can agree on, subject to vagueness considerations, and theoretical truths, such as that snow is crystallised water vapour, and maybe in-between truths.

... though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.

The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.

What humans do with the language of mathematics is to describe patterns.

The importance of the "New Mathematics" lies mainly in the fact that it has taught us the difference between the disc and the circle.

But I simply can't stand a view limited to this earth, I feel life is so small unless it has windows into other worlds...I like mathematics largely because it is not human.

Mathematics is the abstract key which turns the lock of the physical universe.

There are fields of scientific work...which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology...in which every single notion receives a separate and different name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.

What is especially striking and remarkable is that in fundamental physics, a beautiful or elegant theory is more likely to be right than a theory that is inelegant. A theory appears to be beautiful or elegant (or simple, if you prefer) when it can be expressed concisely in terms of mathematics we already have. Symmetry exhibits the simplicity. The Foundamental Law is such that the different skins of the onion resemble one another and therefore the math for one skin allows you to express beautifully and simply the phenomenon of the next skin.

There is nothing mysterious, as some have tried to maintain, about the applicability of mathematics. What we get by abstraction from something can be returned.

Unless the chemist learns the language of mathematics, he will become a provincial and the higher branches of chemical work, that require reason as well as skill, will gradually pass out of his hands.

The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.

Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.

Why does man freeze to death trying to reach the North Pole? Why does man drive himself to suffer the steam and heat of the Amazon? Why does he stagger his mind with the mathematics of the sky? Once the question mark has arisen in the human brain the answer must be found, if it takes a hundred years. A thousand years.

It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.

A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.

Modern bodybuilding is ritual, religion, sport, art, and science, awash in Western chemistry and mathematics. Defying nature, it surpasses it.

Being exposed to theory, stimulated by a basic love of concepts and mathematics, was a marvelous experience.

As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure.

Mathematics is a field which has often been compared with chess, but differs from the latter in that it is only one's best moments that count and not one's worst.

When we cannot use the compass of mathematics or the torch of experience...it is certain we cannot take a single step forward.

In my youth it was said that what was too silly to be said may be sung. In modern economics it may be put into mathematics.

Things like the financial markets - a proper grounding in mathematics could help the common man. I believe that if people are more familiar with mathematical concepts... it can help deal with modern life, which is increasingly complex.