General Mathematics Quotes & Sayings

Mathematics is merely the means to a general and ultimate knowledge of man. — Friedrich Nietzsche

When we say that the ancestors of the Blacks, who today live mainly in Black Africa, were the first to invent mathematics, astronomy, the calendar, sciences in general, arts, religion, agriculture, social organization, medicine, writing, technique, architecture; that they were the first to erect buildings out of 6 million tons of stone (the Great Pyramid) as architects and engineers - not simply as unskilled laborers; that they built the immense temple of Karnak, that forest of columns with its famed hypostyle hall large enough to hold Notre-Dame and its towers; that they sculpted the first colossal statues (Colossi of Memnon, etc.) - when we say all that we are merely expressing the plain unvarnished truth that no one today can refute by arguments worthy of the name. — Cheikh Anta Diop

In general, it would be a peculiar type of 'justice' to declare a majority all the better and more just the more overwhelming it is, and to maintain abstractly that ninety-eight people abusing two persons is by far not so unjust as fifty-one people mistreating forty-nine. At this point, pure mathematics becomes simple inhumanity. — Carl Schmitt

These estimates may well be enhanced by one from F. Klein (1849-1925), the leading German mathematician of the last quarter of the nineteenth century. 'Mathematics in general is fundamentally the science of self-evident things.' ... If mathematics is indeed the science of self-evident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sense - that of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not. — Eric Temple Bell

The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases. — Paul Halmos

In the one real, time-drenched universe, everything has a particular history precisely because it is finite, and not part of an infinite array. Moreover, the cosmological use of the infinite serves to mask the failure of a physical theory taken beyond the boundaries of its proper domain of application. The most notable instance is the inference in contemporary cosmology of an infinite initial singularity from the field equations of general relativity. Finally, the admission of the mathematical infinite into natural science effaces the difference, which we emphasize, between nature and mathematics. Nature works in time, with which mathematics has trouble. Mathematics offers, among other things, the infinite, which nature abhors. — Lee Smolin

As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics. — Carl Friedrich Gauss

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 in general is fundamentally the science of self-evident things. — Felix Klein

Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems - general and specific statements - can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences. — Christopher Zeeman

This book reminds me of James Gleick's Chaos. The ideas and stories in Loving and Hating Mathematics are timely, interesting, and sometimes even profound. The authors, writing for nonspecialists, take pains to explain technical ideas in nontechnical language, and the book should interest general readers as well as a large mathematical audience. — Steven G. Krantz

Though determinants and matrices received a great deal of attention in the nineteenth century and thousands of papers were written on these subjects, they do not constitute great innovations in mathematics ... Neither determinants nor matrices have influenced deeply the course of mathematics despite their utility as compact expressions and despite the suggestiveness of matrices as concrete groups for the discernment of general theorems of group theory ... — Morris Kline

General Systems Theory is a name which has come into use to describe a level of theoretical model-building which lies somewhere between the highly generalized constructions of pure mathematics and the specific theories of the specialized disciplines. Mathematics attempts to organize highly general relationships into a coherent system, a system however which does not have any necessary connections with the "real" world around us. It studies all thinkable relationships abstracted from any concrete situation or body of empirical knowledge. — Kenneth E. Boulding

Lots of people wrote to the magazine to say that Marilyn vos Savant was wrong, even when she explained very carefully why she was right. Of the letters she got about the problem, 92% said that she was wrong and lots of these were from mathematicians and scientists. Here are some of the things they said: 'I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error.' -Robert Sachs, Ph.D., George Mason University ... 'I am sure you will receive many letters from high school and college students. Perhaps you should keep a few addresses for future columns.' -W. Robert Smith, Ph.D., Georgia State University ... 'If all those Ph.D.'s were wrong, the country would be in very serious trouble.' -Everett Harman, Ph.D., U.S. Army Research Institute — Mark Haddon

Man is full of desires: he loves only those who can satisfy them all. "This man is a good mathematician," someone will say. But I have no concern for mathematics; he would take me for a proposition. "That one is a good soldier." He would take me for a besieged town. I need, that is to say, a decent man who can accommodate himself to all my desires in a general sort of way. — Blaise Pascal

Man is a fantastic animal; he was born of fantasy, he is the son of "the mad woman of the house." And universal history is the gigantic and thousand-year effort to go on putting order into that huge, disorderly, anti-animal fantasy. What we call reason is no more than fantasy put into shape. Is there anything in the world more fantastic than that which is the most rational? Is there anything more fantastic than the mathematical point, and the infinite line, and, in general, all mathematics and all physics? Is there a more fantastic fancy than what we call "justice" and the other thing that we call "happiness"? — Jose Ortega Y Gasset

Good general theory does not search for the maximum generality, but for the right generality. — Saunders Mac Lane

In the early universe - when the universe was small enough to be governed by both general relativity and quantum theory - there were effectively four dimensions of space and none of time. That means that when we speak of the "beginning" of the universe, we are skirting the subtle issue that as we look backward toward the very early universe, time as we know it does not exist! We must accept that our usual ideas of space and time do not apply to the very early universe. That is beyond our experience, but not beyond our imagination, or our mathematics. — Stephen Hawking

The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon ... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms. — Joseph Fourier

When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home. — Edward Kasner

Most of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose. — Cornelius Lanczos

There was yet another disadvantage attaching to the whole of Newton's physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula. — George Boole

The staunchest conservatives advocate a range of changes which differ in specifics, rather than in number or magnitude, from the changes advocated by those considered liberal ... change, as such, is simply not a controversial issue. Yet a common practice among the anointed is to declare themselves emphatically, piously, and defiantly in favor of 'change.' Thus those who oppose their particular changes are depicted as being against change in general. It is as if opponents of the equation 2+2=7 were depicted as being against mathematics. Such a tactic might, however, be more politically effective than trying to defend the equation on its own merits. — Thomas Sowell

It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general more difficult) the idea. Thus the idea of an 'irrational' is deeper than that of an integer; and Pythagoras's theorem is, for that reason, deeper than Euclid's. — G.H. Hardy

The general mental qualification necessary for scientific advancement is that which is usually denominated "common sense," though added to this, imagination, induction, and trained logic, either of common language or of mathematics, are important adjuncts. — Joseph Henry

It is the definition of the word 'object' which destroys all religions. — Bill Gaede

The completion of a rigorous course in mathematics - it is not even necessary that the student does well in such a course - appears to be an excellent means of sharpening the mind and developing mental skills that are of general benefit. — Keith Devlin

Einstein and the Quantum is delightful to read, with numerous historical details that were new to me and cham1ing vignettes of Einstein and his colleagues. By avoiding mathematics, Stone makes his book accessible to general readers, but even physicists who are well versed in Einstein and his physics are likely to find new insights into the most remarkable mind of the modern era. — Daniel Kleppner

Getting even was the basis of many primate semantic confusions, such as"expropriating the expropriators," "an absolute crime demands an absolute penalty," "they did it to me so I can do it to them," and, in general, the emotional mathematics of "one plus one equals zero" (1 + 1 = 0).

The primates were so dumb they didn't realize that one plus one equals two (1 + 1 = 2) and one murder plus one murder equals two murders, one crime plus one crime equals two crimes, etc. — Robert Anton Wilson

A mathematician tells you that the wall of warped space prevents the Moon from flying out of its orbit yet can't tell you why an astronaut can go back and forth across that same space. — Bill Gaede

Of the properties of mathematics, as a language, the most peculiar one is that by playing formal games with an input mathematical text, one can get an output text which seemingly carries new knowledge. The basic examples are furnished by scientific or technological calculations: general laws plus initial conditions produce predictions, often only after time-consuming and computer-aided work. One can say that the input contains an implicit knowledge which is thereby made explicit. — Yuri Manin

Evidence in support of general relativity came quickly. Astronomers had long known that Mercury's orbital motion around the sun deviated slightly from what Newton's mathematics predicted. In 1915, Einstein used his new equations to recalculate Mercury's trajectory and was able to explain the discrepancy, a realization he later described to his colleague Adrian Fokker as so thrilling that for some hours it gave him heart palpitations. — Brian Greene

A peculiarity of the higher arithmetic is the great difficulty which has often been experienced in proving simple general theorems which had been suggested quite naturally by numerical evidence. — Harold Davenport

The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is feasible. — George Polya

There has come about a general public awareness that America is not automatically, and effortlessly, and unquestionably the leader of the world in science and technology. This comes as no surprise to those of us who have watched and tried to warn against the steady deterioration in the teaching of science and mathematics in the schools for the past quarter century. It comes as no surprise to those who have known of dozens of cases of scientists who have been hounded out of jobs by silly disloyalty charges, and kept out of all professional employment by widespread blacklisting practices. — Edward Condon

We the undersigned, intend to establish an instruction and training institution which differs from the common elementary schools principally in that it will embrace, outside of (in addition to) the general and elementary curriculum, all branches of the classical high school, which are necessary for a true Christian and scientific education, such as: Religion, the Latin, Greek, Hebrew, German, French and English languages; History, Geography, Mathematics, Physics, natural history, Introduction to Philosophy, Music, and Drawing. — C.F.W. Walther

To calculate 'the' fine structure constant, 1/137, we would need a realistic model of just about everything, and this we do not have. In this talk I want to return to the old question of what it is that determines gauge couplings in general, and try to prepare the ground for a future realistic calculation. — Steven Weinberg

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

I started attending community college when I was 14 or 15, just doing general education stuff like history and mathematics. Then I went on to California State University Long Beach to pursue a degree in journalism. And then I ended up dropping out to found Oculus. — Palmer Luckey

The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps ... — Alexander Grothendieck

A mathematician says that an electromagnetic wave travels from Andromeda to your eye and that it also extends from Andromeda to your eye. — Bill Gaede

There is a noticeable general difference between the sciences and mathematics on the one hand, and the humanities and social sciences on the other. It's a first approximation, but one that is real. In the former, the factors of integrity tend to dominate more over the factors of ideology. It's not that scientists are more honest people. It's just that nature is a harsh taskmaster. You can lie or distort the story of the French Revolution as long as you like, and nothing will happen. Propose a false theory in chemistry, and it'll be refuted tomorrow. — Noam Chomsky

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