Mathematics Subject Quotes & Sayings

Mathematics is man's own handiwork, subject only to the limitations imposed by the laws of thought. — Edward Kasner

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. — Bertrand Russell

School work and intellectual interests such as music and the arts were not especially important to me while I was growing up, although mathematics, my favorite subject, was fun. Baseball was my first passion: I played sand lot and Little League and rooted for the Brooklyn Dodgers. — Robert C. Merton

Writing, I reminded them, can't be taught or learned in a vacuum. We must say to students in every area of knowledge: "This is how other people have written about this subject. Read it; study it; think about it. You can do it too." In many subjects, students don't even know that a literature exists - that mathematics, for instance, consists of more than right and wrong answers, that physics consists of more than right or wrong lab reports. I — William Zinsser

She knew only that if she did or said thus-and-so, men would unerringly respond with the complimentary thus-and-so. It was like a mathematical formula and no more difficult, for mathematics was the one subject that had come easy to Scarlett in her schooldays. — Margaret Mitchell

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. — Morris Kline

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things. — Aristotle.

As I considered the matter carefully it gradually came to light that all those matters only were referred to mathematics in which order and measurements are investigated, and that it makes no difference whether it be in numbers, figures, stars, sounds or any other object that the question of measurement arises. I saw consequently that there must be some general science to explain that element as a whole which gives rise to problems about order and measurement, restricted as these are to no special subject matter. This, I perceived was called 'universal mathematics'. — Rene Descartes

Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him. — G.H. Hardy

The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter. — Carl Gustav Hempel

My first contact with game theory was a popular article in 'Fortune Magazine' which I read in my last high school year. I was immediately attracted to the subject matter, and when I studied mathematics, I found the fundamental book by von Neumann and Morgenstern in the library and studied it. — Reinhard Selten

One of the most painful parts of teaching mathematics is seeing students damaged by the cult of the genius. The genius cult tells students it's not worth doing mathematics unless you're the best at mathematics, because those special few are the only ones whose contributions matter. We don't treat any other subject that way! I've never heard a student say, "I like Hamlet, but I don't really belong in AP English - that kid who sits in the front row knows all the plays, and he started reading Shakespeare when he was nine!" Athletes don't quit their sport just because one of their teammates outshines them. And yet I see promising young mathematicians quit every year, even though they love mathematics, because someone in their range of vision was "ahead" of them. — Jordan Ellenberg

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [ ... ] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate. — Bertrand Russell

The confusion, the difficulties, the contradictions which, in consequence of a want of accurate distinctions in this particular, have up to even a recent period encumbered mathematics in all those branches involving the consideration of negative and impossible quantities, will at once occur to the reader who is at all versed in this science, and would alone suffice to justify dwelling somewhat on the point, in connexion with any subject so peculiarly fitted to give forcible illustration of it as the Analytical Engine. — Ada Lovelace

Praxeology is a theoretical and systematic, not a historical, science. Its scope is human action as such, irrespective of all environmental, accidental, and individual circumstances of the concrete acts. Its cognition is purely formal and general without reference to the material content and the particular features of the actual case. It aims at knowledge valid for all instances in which the conditions exactly correspond to those implied in its assumptions and inferences. Its statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori. They are not subject to verification or falsification on the ground of experience and facts. — Ludwig Von Mises

The question as to which of these two theories applies to the actual world is, like all questions concerning the actual world, in itself irrelevant to pure mathematics.* But the argument against absolute position usually takes the form of maintaining that a space composed of points is logically inadmissible, and hence issues are raised which a philosophy of mathematics must discuss. In what follows, I am concerned only with the question: Is a space composed of points self-contradictory? It is true that, if this question be answered in the negative, the sole ground for denying that such a space exists in the actual world is removed; but this is a further point, which, being irrelevant to our subject, will be left entirely to the sagacity of the reader. — Bertrand Russell

I do not think the division of the subject into two parts - into applied mathematics and experimental physics a good one, for natural philosophy without experiment is merely mathematical exercise, while experiment without mathematics will neither sufficiently discipline the mind or sufficiently extend our knowledge in a subject like physics. — Balfour Stewart

I finally reached the conclusion that mathematics was the study I was best fitted to follow, though I did not clearly see in what way I should turn the subject to account. — Simon Newcomb

Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense. — Edward Kasner

The mathematic, then, is an art. As such it has its styles and style periods. It is not, as the layman and the philosopher (who is in this matter a layman too) imagine, substantially unalterable, but subject like every art to unnoticed changes form epoch to epoch. The development of the great arts ought never to be treated without an (assuredly not unprofitable) side-glance at contemporary mathematics. — Oswald Spengler

For all the time schools devote to the teaching of mathematics, very little (if any) is spent trying to convey just what the subject is about. Instead, the focus is on learning and applying various procedures to solve math problems. That's a bit like explaining soccer by saying it is executing a series of maneuvers to get the ball into the goal. Both accurately describe various key features, but they miss the what and the why of the big picture. — Keith Devlin

How do we change the way science is taught?
Ask anybody how many teachers truly made a difference in their life, and you never come up with more than the fingers on one hand. You remember their names, you remember what they did, you remember how they moved in front of the classroom. You know why you remember them? Because they were passionate about the subject. You remember them because they lit a flame within you. They got you excited about a subject you didn't previously care about, because they were excited about it themselves. That's what turns people on to careers in science and engineering and mathematics. That's what we need to promote. Put that in every classroom, and it will change the world. — Neil DeGrasse Tyson

Another diversity of Methods is according to the subject or matter which is handled; for there is a great difference in delivery of the Mathematics, which are the most abstracted of knowledges, and Policy, which is the most immersed ... , yet we see how that opinion, besides the weakness of it, hath been of ill desert towards learning, as that which taketh the way to reduce learning to certain empty and barren generalities; being but the very husks and shells of sciences, all the kernel being forced out and expulsed with the torture and press of the method. — Francis Bacon

I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof. — G.H. Hardy

Why do children dread mathematics? Because of the wrong approach. Because it is looked at as a subject. — Shakuntala Devi

It saddens me that educated people don't even know that my subject exists. — Paul Halmos

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. — Sylvia Townsend Warner

In a way, mathematics is the only infinite human activity. It is conceivable that humanity could eventually learn everything in physics or biology. But humanity certainly won't ever be able to find out everything in mathematics, because the subject is infinite. Numbers themselves are infinite. That's why mathematics is really my only interest. — Paul Erdos

Poor teaching leads to the inevitable idea that the subject (mathematics) is only adapted to peculiar minds, when it is the one universal science and the one whose four ground-rules are taught us almost in infancy and reappear in the motions to the universe. — Henry John Stephen Smith

One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject, its symbolism and formality, its baffling terminology, its apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were to be summed up as "a lot of tadpoles drawn on a row of lines"; but that"s all that the untrained eye can see in a page of sheet music ... In the same way, the symbolism of mathematics is merely its coded form, not its substance. — Ian Stewart

All creative people hate mathematics. It's the most uncreative subject you can study. — Alec Guinness

Economics is haunted by more fallacies than any other study known to man. This is no accident. The inherent difficulties of the subject would be great enough in any case, but they are multiplied a thousandfold by a factor that is insignificant in, say, physics, mathematics or medicine - the special pleading of selfish interests. — Henry Hazlitt

I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it. — Malcolm X

Unlike at the Academy or the Lyceum, women, some of them concubines and mistresses, as well as a few slaves, joined the conversation; further, many of the students here had arrived without academic credentials in mathematics or music, de rigueur for entry to the other Athenian schools of higher learning. Everyone in the Garden radiated earnestness and good cheer. The subject under discussion was happiness. — Epicurus

All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They're adults in the crystalline world, infants in the real one. — Sylvain Cappell

Let me then remind you that justice is an immutable, natural principle; and not anything that can be made, unmade, or altered by any human power. It is also a subject of science, and is to be learned, like mathematics, or any other science. It does not derive its authority from the commands, will, pleasure, or discretion of any possible combination of men, whether calling themselves a government, or by any other name. It is also, at all times, and in all places, the supreme law. And being
everywhere and always the supreme law, it is necessarily everywhere and always the only law. — Lysander Spooner

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

Very few people can communicate with one another. The only language that's not subject to interpretation is mathematics, chemistry, basic science, engineering principles, and applied agriculture. But other than that, many systems today are subject to interpretation. — Jacque Fresco

Of Belief Human mathematics, so to speak, like the length of life, are subject to the doctrine of chances. — William Godwin

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

Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavour does: the extent of the negation of man's corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented. — Stanislaw Lem

Blindness to the aesthetic element in mathematics is widespread and can account for a feeling that mathematics is dry as dust, as exciting as a telephone book ... Contrariwise, appreciation of this element makes the subject live in a wonderful manner and burn as no other creation of the human mind seems to do. — Philip J. Davis

The total subject of mathematics is clearly too broad for any of us. I do not think that any mathematician since Gauss has covered it uniformly and fully; even Hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than Hilbert. — John Von Neumann

The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept "science"; for it is as a part of science that mathematics originally took its place in human thought. — L. E. J. Brouwer

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. — Benjamin Peirce

This splendid subject [mathematics], queen of all exact sciences, and the ideal and norm of all careful thinking ... — G. Stanley Hall

Probably no branch of mathematics has experienced a more surprising growth than has ... topology ... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories. — Raymond Louis Wilder

Modern economics is sick. Economics has increasingly become an intellectual game played for its own sake and not for its practical consequences for understanding the economic world. Economists have converted the subject into a sort of social mathematics in which analytical rigour is everything and practical relevance is nothing. — Mark Blaug

I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time. — Carl Friedrich Gauss

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

Immortality is often ridiculous or cruel: few of us would have chosen to be Og or Ananias or Gallio. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel's Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country's greatest man. But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments. — G.H. Hardy

Debts are subject to the laws of mathematics rather than physics. Unlike wealth, which is subject to the laws of thermodynamics, debts do not rot with old age and are not consumed in the process of living. On the contrary, they grow at so much per cent per annum, by the well-known mathematical laws of simple and compound interest ... It is this underlying confusion between wealth and debt which has made such a tragedy of the scientific era. — Frederick Soddy

The word "Verse" is used here as the term most convenient for expressing, and without pedantry, all that is involved in the consideration of rhythm, rhyme, meter, and versification ... the subject is exceedingly simple; one tenth of it, possibly may be called ethical; nine tenths, however, appertains to the mathematics. — Edgar Allan Poe

Every time you observe that more of a good thing is not always better; or you remember that improbable things happen a lot, given enough chances, and resist the lure of the Baltimore stockbroker; or you make a decision based not just on the most likely future, but on the cloud of all possible futures, with attention to which ones are likely and which ones are not; or you let go of the idea that the beliefs of groups should be subject to the same rules as beliefs of individuals; or, simply, you find that cognitive sweet spot where you can let your intuition run wild on the network of tracks formal reasoning makes for it; without writing down an equation or drawing a graph, you are doing mathematics, the extension of common sense by other means. When are you going to use it? You've been using mathematics since you were born and you'll probably never stop. Use it well. — Jordan Ellenberg