Mathematics Quotes

Hippasus’ proof—or at least Nico’s retelling of it—was really so simple that when he finished sketching it out, I wasn’t even aware that we had actually proven anything. Nico paused for a few minutes to let us mull it over.It was Peter who broke the silence, “I’m not sure I understand what we have done.”Nico seemed to be expecting such a response. “Step back and examine the proof; in fact, you should try and do this with every proof you see or have to work out for yourself. ...He again waited for his words to sink in, and it began to make sense for me. All my mathematics teachers (other than Bauji and Nico) always seemed to evade this part of their responsibility. They had been content to merely write out a proof on the blackboard and carry on, seemingly without concern for what the proof meant and what it told us.“But you should not stop here. Even when you have understood a proof, and I hope you have indeed understood this proof, ask yourself the next question, the obvious one, but as critical: So what? Or, why are we proving this? What is the point? What is the context? How does it relate to us? To answer these questions we have to step back a little. Let me show you—it’s really quite delightful.” Now there was excitement in Nico’s voice.

~ Gaurav Suri

Someone. Everyone. Anyone. No-one. One. One can't be everyone, but there isn't more than one everyone, at the same time. And at the same time no-one can't be someone, but anyone can be one, and also anyone can be a no-one. To sum up - everyone is someone, and any-one becomes a no-one if you divide the one part long enough by every part of every-one, so in conclusion, I have no idea what I’m talking about, basically.

~ Will Advise

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.

~ Paul R. Halmos

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.

~ Richard Courant

Mathematics is one of the major modern mysteries. Perhaps it is the leading one, occupying a place in our society similar to the religious mysteries of another age. If we want to know something about what our age is all about, we should have some understanding of what mathematics is, and of how the mathematician operates and thinks.

~ Mortimer J. Adler

Heresy would like to think of itself as 'invented Truth'. But of course, all Reason and Logic would agree that no man can ever create Truth; he can only discover it. If heresy were ever at all beneficial, God would use it really to bring one right back to Truth, as countless 'inventions' have brought men to discovery.

~ Criss Jami

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

~ Mark Kac

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

~ Henri Poincaré

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very 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.

~ Vannevar Bush

A key ingredient in appreciating what mathematics is about is to realize that it is concerned with ideas, understanding, and communication more than it is with any specific brand of symbols....It is almost as if ideas set in mathematical form melt and become liquid and just as rivers can, from the most humble beginnings, flow for thousands of miles, through the most varied topography bringing nourishment and life with them wherever they go, so too can ideas cast in mathematical form flow far from their original sources, along well-defined paths, electrifying and dramatically affecting much of what they touch. pp. xii - xiii.

~ G. Arnell Williams

Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.

~ Gian-Carlo Rota

Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding.

~ Gian-Carlo Rota

Mathematics is a wonderful common sense,To understand the harmony in nature magnificent; The wondrous language, & popular in terms of @ financeIts’ unique, and abundantly rich in terms of substance

~ Priyavrat Thareja

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

~ Richard Courant

Jack had wondered how geometers could be so inventive as to produce so many types and families of curves. Later he had come to perceive that of curves there was no end, and the true miracle was that poets, or writers, or whoever it was that was in charge of devising new words, could keep pace with those hectic geometers, and slap names on all the whorls and snarls in the pages of the Doctor's geometry-books.

~ Neal Stephenson

Questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.

~ Giuseppe Peano

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

~ G.h. Hardy

Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates.

~ Melvin Schwartz

The language of mathematics differs from that of everyday life, because it is essentially a rationally planned language. The languages of size have no place for private sentiment, either of the individual or of the nation. They are international languages like the binomial nomenclature of natural history. In dealing with the immense complexity of his social life man has not yet begun to apply inventiveness to the rational planning of ordinary language when describing different kinds of institutions and human behavior. The language of everyday life is clogged with sentiment, and the science of human nature has not advanced so far that we can describe individual sentiment in a clear way. So constructive thought about human society is hampered by the same conservatism as embarrassed the earlier naturalists. Nowadays people do not differ about what sort of animal is meant by Cimex or Pediculus, because these words are used only by people who use them in one way. They still can and often do mean a lot of different things when they say that a mattress is infested with bugs or lice. The study of a man's social life has not yet brought forth a Linnaeus. So an argument about the 'withering away of the State' may disclose a difference about the use of the dictionary when no real difference about the use of the policeman is involved. Curiously enough, people who are most sensible about the need for planning other social amenities in a reasonable way are often slow to see the need for creating a rational and international language.

~ Lancelot Hogben

The sciences are not sectarian. People do not persecute each other on account of disagreements in mathematics. Families are not divided about botany, and astronomy does not even tend to make a man hate his father and mother. It is what people do not know, that they persecute each other about. Science will bring, not a sword, but peace.

~ Robert G. Ingersoll

No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence--a duty and a duty alone--and no hint of magic or beauty of the subject might be allowed to come through.

~ Roger Penrose

Thousands of years ago the ancients had an advanced mathematical understanding of universe that is revealed in many sources. There is a consistent link to knowledge of the golden mean, but the way in which the ancients were able to formulate and use this information speaks of a technical grasp of the subject that exceeds what we know about it in the present day.

~ Alison Charlotte Primrose

Everyone knows that physicists are concerned with the laws of the universe and have the audacity sometimes to think they have discovered the choices God made when He created the universe in thus and such a pattern. Mathematicians are even more audacious. What they feel they discover are the laws that God Himself could not avoid having to follow.

~ David Mumford

Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy.Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.

~ Joseph Fourier

From the age of 13, I was attracted to physics and mathematics. My interest in these subjects derived mostly from popular science books that I read avidly. Early on I was fascinated by theoretical physics and determined to become a theoretical physicist. I had no real idea what that meant, but it seemed incredibly exciting to spend one's life attempting to find the secrets of the universe by using one's mind.

~ David Gross

The astonishing fact is that similar mathematics applies so well to planets and to clocks. It needn’t have been this way. We didn’t impose it on the Universe. That’s the way the Universe is. If this is reductionism, so be it.

~ Carl Sagan

There have been many authorities who have asserted that the basis of science lies in counting or measuring, i.e. in the use of mathematics. Neither counting nor measuring can however be the most fundamental processes in our study of the material universe—before you can do either to any purpose you must first select what you propose to count or measure, which presupposes a classification.

~ Roy A. Crowson

Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.

~ Frank Plumpton Ramsey

It is the story that matters not just the ending.

~ Paul Lockhart

As the several items can be exchanged, they must be equal; but in what terms? Not in pounds, yards, or hours; they are equal in value. Then what is wanted is a unit of value to reckon by.

~ Isabel Paterson

There is the potential for a particle of matter to be located where we expect it to be or to be located anywhere in the physical world. So it is with our lives – our very next moment can occur along the most probable path or it can occur on a path entirely discontinuous with the expectations that others have for us, but more likely in line with the expectations that we have for ourselves.

~ Kevin Michel

What believer of faith among us can claim to understand the exact mechanistic structure of a world created by a god/God?

~ Kevin Michel

By simple mathematics giving is key to the world you seek to live in. If I take I alone gain. If I give or share then two at least are enriched.

~ Rasheed Ogunlaru

We tend to teach mathematics as a long list of rules.You learn them in order and you have to obey them, because if you don't obey them you get a C-.This is not mathematics. Mathematics is the study if things that come out a certain way because there is no other way they could possibly be.

~ Jordan Ellenberg

If there is anything that can bind the mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living,—then it is verily the enjoyment of the mathematical sciences and astronomy.

~ Johannes Kepler

Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.

~ Chen Ning Yang

If the institution of mathematics told a story . . . how would it end?

~ Lindsey Drager

We often hear that mathematics consists mainly of 'proving theorems.' Is a writer's job mainly that of 'writing sentences?

~ Gian-Carlo Rota

For the first time in his life, he decided to focus on his math homework.

~ Greg Pincus

One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

~ George Pólya