Quotes about equation (379 quotes, page 3)

“The Hindus saw clearly that if the arithmetic operations… were properly defined for negative numbers, these numbers could be employed to as good advantage as people had previously derived from positive numbers. …To people to whom the word number had always meant positive whole numbers and positive fractions, the very idea that there could be other numbers came hard. For many centuries negative numbers were either rejected or treated as second-class citizens.
What was especially difficult for mathematicians to swallow was that negative numbers could be acceptable roots of equations.”

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 51.

People , Idea

“To take what might seem an "objective", macro-economic approach to the origins of the world economy would be to treat the behavior of early European explorers, merchants, and conquerors as if they were simply rational responses to opportunities—as if this were just what anyone would have done in the same situation. This is what the use of equations so often does: make it seem perfectly natural to assume that, if the price of silver in China is twice what it is in Seville, and inhabitants of Seville are capable of getting their hands on large quantities of silver and transporting it to China, then clearly they will, even if doing so requires the destruction of entire civilizations. Or if there is a demand for sugar in England, and enslaving millions is the easiest way to acquire labor to produce it, then it is inevitable that some will enslave them.”

David Graeber (1961) American anthropologist and anarchist

Source: Debt: The First 5,000 Years (2011), Chapter Eleven, "Age of the Great Capitalist Empires", p. 314

World , Way , Behavior , Nature

“The object of this paper is fivefold. The first objective is to derive a practical system of demand equations which possess properties usually considered desirable from the standpoint of elementary economic theory. The second is to consider the statistical problems involved in applying the system of equations. The third is to analyse the pattern of demand for consumers' goods in terms of this system on the basis of annual data relating to the United Kingdom over the years 1920-38. The fourth is to compare the results of this system, and systems like it, with the actual state of demand in 1900. Finally, the fifth is to compare the post-war structure of demand with what might be expected from the inter-war relationshipp under free-market condition.”

Richard Stone (1913–1991) British economist, Nobel Memorial Prize winner

Stone, Richard. " Linear expenditure systems and demand analysis: an application to the pattern of British demand http://www.jstor.org/discover/10.2307/2227743?uid=3738736&uid=2&uid=4&sid=21104302232953." The Economic Journal (1954): 511-527.

War , Problem

“These organizational processes result in our perceptions being structured into units corresponding to objects and properties of objects. It is these larger units that may be stored and later assembled into images that are experienced as quasi-pictorial, spatial entities resembling those evoked during perception itself…. It is erroneous to equate image representations with mental photographs, since this would overlook the fact that images are composed from highly processed perceptual encodings.”

Stephen Kosslyn (1948) American psychologist

Source: Image and Mind. 1980, p. 19

“Now, of course, one of the difficulties in speaking out today grows the fact that there are those who are seeking to equate dissent with disloyalty. It's a dark day in our nation when high-level authorities will seek to use every method to silence dissent. But something is happening, and people are not going to be silenced. The truth must be told, and I say that those who are seeking to make it appear that anyone who opposes the war in Vietnam is a fool or a traitor or an enemy of our soldiers is a person that has taken a stand against the best in our tradition.”

Martin Luther King, Jr. (1929–1968) American clergyman, activist, and leader in the American Civil Rights Movement

1960s, Why I Am Opposed to the War in Vietnam (1967)

War , People , Truth , Fools

“Avant-garde artistes such as respondents remain entirely free to é pater les bourgeois [shock the middle classes]; they are merely deprived of the additional satisfaction of having the bourgeoisie taxed to pay for it. It is preposterous to equate the denial of taxpayer subsidy with measures 'aimed at the suppression of dangerous ideas.”

Antonin Scalia (1936–2016) former Associate Justice of the Supreme Court of the United States

On tax-funded art: National Endowment for the Arts v. Finley (1998) (concurring).
1990s

Idea

“In the abstract world of American economists, equations run both ways; they believe that by changing the sign of a variable from plus to minus or from minus to plus or the price and quantity of x or y, the direction of historical movement can be reversed.”

Robert Gilpin (1930–2018) Political scientist

Source: The Political Economy of International Relations (1987), Chapter Eight, International Finance, p. 336

World , Way , Change

“Science is a differential equation. Religion is a boundary condition.”

Alan Turing (1912–1954) British mathematician, logician, cryptanalyst, and computer scientist

Epigram to Robin Gandy (1954); reprinted in Andrew Hodges, Alan Turing: the Enigma (Vintage edition 1992), p. 513.

Religion , Science

“As for negative numbers… most mathematicians of the sixteenth and seventeenth centuries did not accept them… In the fifteenth century Nicolas Chuquet and, in the sixteenth, Stifel both spoke of negative numbers as absurd numbers. …Descartes accepted them, in part. …he had shown that, given an equation, one can obtain another whose roots are larger than the original one by any given quantity. Thus an equation with negative roots could be transformed into one with positive roots. Since we can turn false roots into real roots, Descartes was willing to accept negative numbers. Pascal regarded the subtraction of 4 from zero as utter nonsense.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 252.

Parting , Falseness

“The field equation may… be given a geometrical foundation, at least to a first approximation, by replacing it with the requirement that the mean curvature of the space vanish at any point at which no heat is being applied to the medium—in complete analogy with… the general theory of relativity by which classical field equations are replaced by the requirement that the Ricci contracted curvature tensor vanish.”

Howard P. Robertson (1903–1961) American mathematician and physicist

Footnote
Geometry as a Branch of Physics (1949)

“The impressions received by the two observers A0 and A would be alike in all respects. It would be impossible to decide which of them moves or stands still with respect to the ether, and there would be no reason for preferring the times and lengths measured by the one to those determined by the other, nor for saying that either of them is in possession of the "true" times or the "true" lengths. This is a point which Einstein has laid particular stress on, in a theory in which he starts from what he calls the principle of relativity, i. e., the principle that the equations by means of which physical phenomena may be described are not altered in form when we change the axes of coordinates for others having a uniform motion of translation relatively to the original system.
I cannot speak here of the many highly interesting applications which Einstein has made of this principle. His results concerning electromagnetic and optical phenomena …agree in the main with those which we have obtained… the chief difference being that Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects, but the manifestation of a general and fundamental principle.
Yet, I think, something may also be claimed in favour of the form in which I have presented the theory. I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. …it seems natural not to assume at starting that it can never make any difference whether a body moves through the ether or not, and to measure distances and lengths of time by means of rods and clocks having a fixed position relatively to the ether.
It would be unjust not to add that, besides the fascinating boldness of its starting point, Einstein's theory has another marked advantage over mine. Whereas I have not been able to obtain for the equations referred to moving axes exactly the same form as for those which apply to a stationary system, Einstein has accomplished this by means of a system of new variables slightly different from those which I have introduced.”

Hendrik Lorentz (1853–1928) Dutch physicist

Source: The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat (1916), Ch. V Optical Phenomena in Moving Bodies.

Nature , Thinking , Change , Time

“It seems to me that in understanding MOND and its fundamentals we have only scratched the surface. If the developments of quantum mechanics and relativity are any lesson here, departures of such magnitude from long- and well-tested physics may bring with them completely new concepts, not summarized by mere modifications of the governing actions or the equations of motion. MOND may also turn out to bring in concepts that are presently beyond our ken”

Mordehai Milgrom (1946) Israeli physicist

as hinted perhaps by the cosmological connotations of a<sub>0</sub>
MOND Theory, p. 5, Mordehai Milgrom, 30 Apr 2014, updated 31 Aug 2014 http://arxiv.org/abs/1404.7661,

Departure , Understanding

“The management science approach to organizational decision making is the analog to the rational approach by individual managers. Management science came into being during World War II. At that time, mathematical and statistical techniques were applied to urgent, large-scale military problems that were beyond the ability of individual decision makers. Mathematicians, physicists, and operations researchers used systems analysis to develop artillery trajectories, antisubmarine strategies, and bombing strategies such as salvoing (discharging multiple shells simultaneously). Consider the problem of a battleship trying to sink an enemy ship several miles away. The calculation for aiming the battleship's guns should consider distance, wind speed, shell size, speed and direction of both ships, pitch and roll of the firing ship, and curvature of the earth. Methods for performing such calculations using trial and error and intuition are not accurate, take far too long, and may never achieve success.
This is where management science came in. Analysts were able to identify the relevant variables involved in aiming a ship's guns and could model them with the use of mathematical equations. Distance, speed, pitch, roll, shell size, and so on could be calculated and entered into the equations. The answer was immediate, and the guns could begin firing. Factors such as pitch and roll were soon measured mechanically and fed directly into the targeting mechanism. Today, the human element is completely removed from the targeting process. Radar picks up the target, and the entire sequence is computed automatically.”

Richard L. Daft (1964) American sociologist

Source: Organization Theory and Design, 2007-2010, p. 500

War , World , Error , Mathematics

“Most fortunate Prince, we have known and seen how in the third year of your reign in the year of Our Lord 1498, in which your Highness ordered us to discover the Western region, a very large landmass with many large islands adjacent, extending 700 North of the Equator, and located beyond the greatness of the Ocean, has been discovered and navigated; this distant land is densely populated and extends 28º degrees on the other side of the Equator towards the Antarctic Pole. Such is its greatness and length that on either side its end has not been seen or known, so that it is certain that it goes round the whole globe.”

Duarte Pacheco Pereira (1460–1533) Portuguese explorer

Bemauenturado Príncipe, temos sabido e visto como no terceiro anno de vosso Reinado do hanno de nosso senhor de 1498, donde nos vossa alteza mandou descobrir a parte oucidental, passando alem ha grandeza do mar oceano, onde he achada a navegada hûa tão grande terra firme, com muitas e grandes ilhas ajacentes a ella, que se estende a setente graaos de ladeza da linha equinoçial contra ho pollo artico e posto que seja asaz fora, he grandemente pouorada, e do mesmo circulo equinocial torna outra vez e vay alem em vinte e oito graaos e meo de ladeza contra ho pollo antartico, e tanto se dilata sua grandeza e corre com muita longura, que de hûa parte nem da outra foy visto nem sabido ho fim e cabo della; pello qual segundo ha hordem que leua, he certo que vay en cercoyto por toda a Redondeza.
Esmeraldo de situ orbis [published between 1506 and 1508], Part I, ch. I, translated and edited by George Herbert Tinley Kimble, London: 1937, p. 12; Duarte Pacheco Pereira was most likely referring to the coast of Brazil.
Variant translations:
Your Highness sent us to discover towards the west, across the broad expansion of the ocean sea where there is found and sailed a very large mainland with many and large adjacent islands, which extends to 70°N of the equator to … 28º 50S.
As quoted in Diffie, Davison, Winius, Foundations of the Portuguese Empire (1977), p. 451
In the third year of your reign, in the year of grace of 1498, Your Highness ordered me that I went on a discovery expedition, in the areas of the west, crossing the entire extension of the ocean sea, where there was found and rounded a great firm land...
As quoted in Silva Pinto Sagres (2002), p. 313

Distant

“In the social equation, the value of a single life is nil; in the cosmic equation, it is infinite… Not only communism, but any political movement which implicitly relies on purely utilitarian ethics, must become a victim to the same fatal error. It is a fallacy as naïve as a mathematical teaser, and yet its consequences lead straight to Goya's Disasters, to the reign of the guillotine, the torture chambers of the Inquisition, or the cellars of the Lubianka.”

Arthur Koestler book The Invisible Writing

The Invisible Writing (1954).

Life , Error , Communication , Mathematics

“The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the impossibility of it. However, if I am not mistaken, they have not as yet succeeded. I therefore dare hope that the mathematicians will receive this memoir with good will, for its purpose is to fill this gap in the theory of algebraic equations.”

Niels Henrik Abel (1802–1829) Norwegian mathematician

A Memoir on Algebraic Equations, Proving the Impossibility of a Solution of the General Equation of the Fifth Degree (1824) Tr. W. H. Langdon, as quote in A Source Book in Mathematics (1929) ed. David Eugene Smith

Hope

“Aside from the equation it draws between making money and being good, the modern ideal of a successful life posits a further linkage between making money and being happy. This latter association rests on … assumptions. First, it is presumed that identifying what will make us happy is not an inordinately difficult task. Just as our bodies typically know what they need in order to be healthy… so, too, the theory goes, can our minds to be relied upon to understand what we should aim for so as to flourish as whole human beings. … Second, it is taken for granted that the enormous range of … consumer goods available to modern civilization is not merely a gaudy, enervating show responsible for stoking desires bearing little relevance to our welfare, but is, rather, a helpful array of potentialities and products, capable of satisfying some of our most important needs.”

Alain de Botton book Status Anxiety

Source: Status Anxiety (2004), Chapter 5 (pt.6 27:39).

Life , Money , Understanding , Success

“There are only four Hindu writers on algebra whose names are particularly noteworthy. These are Āryabhata, whose Āryabhatiyam (c. 510) included problems in series, permutations, and linear and quadratic equations; Brahmagupta, whose Brahmasiddhānta (c. 628) contains a satisfactory rule for solving the quadratic… Mahāvīra, whose Ganita-Sāra Sangraha (c. 850) contains a large number of problems involving series, radicals, and equations; and Bhāskara, whose Bija Ganita (c. 1150)… extends the work through quadratic equations.”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, Ch. 6: Algebra

Problem

“It sounds rather strange to talk of an infinite universe still expanding. If we were certain that the curvature was negative, we might still, as in the case of positive curvature, replace the phrase "the universe expands" by the equivalent one "the curvature of the universe decreases." But if the curvature is zero, and remains zero throughout, what sort of meaning are we to attach to the "expansion"? The real meaning is, of course, that the mutual distances between the galactic systems, measured in so-called natural measure, increase proportionally to a certain quantity R appearing in the equations, and varying with the time. The interpretation of R as the "radius of curvature" of the universe, though still possible if the universe has a curvature, evidently does not go down to the fundamental meaning of it.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

Nature , Universe , Appearance , Time

“We completely agree that description by differential equations is not only a clumsy but, in principle, inadequate way to deal with many problems of organization.”

Ludwig von Bertalanffy (1901–1972) austrian biologist and philosopher

Source: General System Theory (1968), 4. Advances in General Systems Theory, p. 97

Way , Problem

“Many physicists these days sound like the Delphic oracle - with equations.”

John Twelve Hawks American writer

Fourth Realm Trilogy (2005-2009), The Dark River (2007)

“One can see clearly some ambivalence in Dirac's attitudes… On the one hand, he has repeated many, many times his conviction that beauty in the fundamental equations of physics has priority… On the other hand… we see Dirac deeply involved with approximate calculations whose only purpose was to obtain an answer which the experimenters could rely upon.”

Richard Dalitz (1925–2006) Australian physicist

R. H. Dalitz, Another side to Paul Dirac, in Paul Adrien Maurice Dirac (Cambridge University, Cambridge, 1987) Chapter 10.

Beauty , Time

“The actual heart of quantum mechanics is that the objects in its equations are connected to the observations very differently than the classical counterparts have been.”

Luboš Motl (1973) Czech physicist and translator

https://motls.blogspot.com/2018/09/why-string-theory-is-quantum-mechanics.html
The Reference Frame http://motls.blogspot.com/

Heart

“General systems theory deals with the most fundamental concepts and aspects of systems. Many theories dealing with more specific types of systems (e. g., dynamical systems, automata, control systems, game-theoretic systems, among many others) have been under development for quite some time. General systems theory is concerned with the basic issues common to all these specialized treatments. Also, for truly complex phenomena, such as those found predominantly in the social and biological sciences, the specialized descriptions used in classical theories (which are based on special mathematical structures such as differential or difference equations, numerical or abstract algebras, etc.) do not adequately and properly represent the actual events. Either because of this inadequate match between the events and types of descriptions available or because of the pure lack of knowledge, for many truly complex problems one can give only the most general statements, which are qualitative and too often even only verbal. General systems theory is aimed at providing a description and explanation for such complex phenomena.”

Mihajlo D. Mesarovic (1928) Serbian academic

Mihajlo D. Mesarovic and Y. Takahare (1975) General Systems Theory, Mathematical foundations. Academic Press. Cited in: Franz Pichler, Roberto Moreno Diaz (1993. Computer Aided Systems Theory. p. 134

Game , Mathematics , Knowledge , Problem

“Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i. e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

Mathematics , Reality , Sense , Study

“The problem of the biquadratic equation was laid prominently before Italian mathematicians by Zuanne de Tonini da Coi, who in 1540 proposed the problem, "Divide 10 parts into three parts such that they shall be continued in proportion and that the product of the first two shall be 6." He gave this to Cardan with the statement that it could not be solved, but Cardan denied the assertion, although himself unable to solve it. He gave it to Ferrari, his pupil, and the latter, although then a mere youth, succeeded where the master had failed. …This method soon became known to algebraists through Cardan's Ars Magna, and in 1567 we find it used by Nicolas Petri”

David Eugene Smith (1860–1944) American mathematician

of Deventer
Source: History of Mathematics (1925) Vol.2, pp.467-468

Youth , Problem , Parting

“An ideological movement is a collection of people many of whom could hardly bake a cake, fix a car, sustain a friendship or a marriage, or even do a quadratic equation, yet they believe they know how to rule the world. The university, in which it is possible to combine theoretical pretension with comprehensive ineptitude, has become the natural habitat of the ideological enthusiast. A kind of adventure playground, carefully insulated from reality in order to prevent absent-minded professors from bumping into things as they explore transcendental realms, has become the institutional base for civilizational self-hatred.”

Kenneth Minogue (1930–2013) Australian political theorist

Kenneth Minogue in National Review, November 18, 1991, cited in: fortnightlyreview.co.uk http://fortnightlyreview.co.uk/2013/07/quick-define-quadratic-equation/, 2013/07

Friendship , Marriage , People , World

“I was dealing with a political story where much of the action took place on the floor of the U. S. Senate, and one of the edicts that came down from the Mt. Sinai of advertisers row was that at no time in a political drama must a speech or a character be equated with an existing political party or current political problems. So several million viewers were treated to an incredible display of senators shouting, gesticulating and talking in hieroglyphics, saying not a single thing germaine to the current political scene.”

Rod Serling (1924–1975) American screenwriter

Rod Serling on Arena, American Masters.
Other

Problem , Time

“In the work of Vieta the analytic methods replaced the geometric, and his solutions of the quadratic equation were therefore a distinct advance upon those of his predecessors. For example, to solve the equation x^2 + ax + b = 0 he placed u + z for x. He then hadu^2 + (2z + a)u +(z^2 + az + b) = 0.He now let 2z + a = 0, whence z = -\frac{1}{2}a,and this gaveu^2 - \frac{1}{4}(a^2 - 4b) = 0.
u = \pm \frac{1}{2} \sqrt{a^2 - 4b}.andx = u + z = -\frac{1}{2}a \pm \sqrt{a^2 - 4b}.</center”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, p.449

“And the fact that John Kerry would not support a federal marriage amendment [prohibiting gay marriage], it equates in our minds as someone 150 years ago saying I'm personally opposed to slavery, but if my neighbor wants to own one or two that's OK. We don't buy that.”

Jerry Falwell (1933–2007) American evangelical pastor, televangelist, and conservative political commentator

CNN : Anderson Cooper 360 Degrees http://transcripts.cnn.com/TRANSCRIPTS/0411/03/acd.01.html (3 November 2004)

Marriage , Support , Personality

“The field equations, in their most general form, contain a term multiplied by a constant, which is denoted by the Greek letter λ… sometimes called the "cosmical constant." This is a name without any meaning… We have, in fact, not the slightest inkling of what its real significance is. It is put in the equations in order to give them the greatest possible degree of mathematical generality, but, so far as its mathematical function is concerned, it is entirely undetermined: it may be positive or negative, it might also be zero.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

Mathematics

“Eventually, I'd like one monitor at the North Pole, one at the South, and two at the equator, big monitors switching images back and forth.”

Ira Schneider (1939) American artist

Ira Schneider (1969), Arts Magazine, Vol. 44, p. 22

“You could never teach other people anything that mattered. The important things they had to learn for themselves, almost always by making mistakes, so that the lessons arrived too late to help. Experience was in that sense useless. It was precisely what could not be passed along in a lesson or an equation.”

Kim Stanley Robinson book Galileo's Dream

Source: Galileo's Dream (2009), Ch. 20, p. 513–514

People , Sense , Learning , Help

“In 1929 Oskar Klein stumbled into an apparent paradox when trying to describe the scattering of a relativistic electron by a square potential using Dirac’s wave equation. … In order to capture the essence of the problem without entering into unnecessary complication we will study Klein’s paradox in the context of the Klein– Gordon equation.”

Luis Álvarez-Gaumé Spanish physicist

Source: An Invitation to Quantum Field Theory (2012), Ch. 1 : Why Do We Need Quantum Field Theory After All?

Problem , Study

“Each technology equated to some human value or set of values, she saw. She’d known that. But on Earth, in the Archipelago and everywhere else, technologies came first, and values changed to accommodate them. Under the locks, values were the keys to access or shut away technologies…
The locks proclaimed that there were no neutral technologies. The devices and methods people used didn’t just represent certain values—they were those values, in some way.”

Karl Schroeder (1962) Author. Technology consultant

Source: Lady of Mazes (2005), Chapter 23 (pp. 255-256).

People , Way , Change

“Symmetrical equations are good in their place, but 'vector' is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.”

William Thomson (1824–1907) British physicist and engineer

Letter to G. F. FitzGerald (1896) as quoted in A History of Vector Analysis : The Evolution of the Idea of a Vectorial System (1994) by Michael J. Crowe, p. 120

“Von Neumann languages do not have useful properties for reasoning about programs. Axiomatic and denotational semantics are precise tools for describing and understanding conventional programs, but they only talk about them and cannot alter their ungainly properties. Unlike von Neumann languages, the language of ordinary algebra is suitable both for stating its laws and for transforming an equation into its solution, all within the "language."”

John Backus (1924–2007) American computer scientist

"Can Programming Be Liberated From the von Neumann Style?" http://dl.acm.org/ft_gateway.cfm?id=1283933&type=pdf, 1977 Turing Award Lecture, Communications of the ACM 21 (8), (August 1978): pp. 639-640

Law , Understanding

“The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration ofjkbni semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.”

Leonid Kantorovich (1912–1986) Russian mathematician

"On one class of functional equations" (1936), as cited in: O'Connor, John J.; Robertson, Edmund F., " Leonid Kantorovich http://www-history.mcs.st-andrews.ac.uk/Biographies/Kantorovich.html", MacTutor History of Mathematics archive, University of St Andrews

Study , Success

“The equation state = politics becomes erroneous and deceptive at exactly the moment when state and society penetrate each other.”

Carl Schmitt book The Concept of the Political

The Concept of the Political (1927)

“Elegance requires that the number of defining equations be small. Five is better than ten, and one is better than five. On this score, one might facetiously say that String Theory is the ultimate epitome of elegance. With all the years that String Theory has been studied, no one has found even a single defining equation! The number at present count is zero. We know neither what the fundamental equations of the theory are nor even if it has any.”

Leonard Susskind book The Cosmic Landscape

[The Cosmic Landscape: String Theory and the Illusion of Intelligent Design, 2008, Little, Brown, https://books.google.com/books?id=RIW9E1sOyxUC&q=epitome#v=snippet&q=epitome&f=false]

Study

“Our "society" is not a community, but merely a collection of isolated family units. Desperately insecure, fearing his woman will leave him if she's exposed to other men or to anything remotely resembling life, the male seeks to isolate her from other men and from what little civilization there is, so he moves her out to the suburbs, a collection of self-absorbed couples and their kids. Isolation, further, enables him to try to maintain his pretense of being an individual by being a "rugged individualist", a loner, equating non-co-operation and solitariness with individuality.”

Valerie Solanas (1936–1988) American radical feminist and writer. Attempted to assassinate Andy Warhol.

Source: SCUM MANIFESTO (1967), p. 7 (line break in "non-"/"co-operation").

Life , Men , Fear , Family

“One can find meaning in poetry as well as in science in the contemplations of a flower as well as in the grasp of an equation. We can be filled with wonder as we stand under the majestic dome of the night sky and see the myriad lights that twinkle and shine in its seemingly infinite depths. We can also be filled wit awe as we behold the meaning of the formulae that define the propagation of light in space, the formation of galaxies, the synthesis of chemical elements, and the relation of energy, mass and velocity in the physical universe. The mystical perception of oneness and the religious intuition of a Divine intelligence are as much a construction of meaning as the postulation of the universal law of gravitation.”

Ervin László (1932) Hungarian musician and philosopher

Source: Evolution: the general theory (1996), p. 3.

Law , Intelligence , Flowers , Light

“Menæchmus, a pupil of Eudoxus, and a contemporary of Plato, found the two mean proportionals by means of conic sections, in two ways, (α) by the intersection of two parabolas, the equations of which in Cartesian co-ordinates would be x2=ay, y2=bx, and (β) by the intersection of a parabola and a rectangular hyperbola, the corresponding equations being x2=ay, and xy=ab respectively. It would appear that it was in the effort to solve this problem that Menæchmus discovered the conic sections, which are called, in an epigram by Eratosthenes, "the triads of Menæchmus."”

Thomas Little Heath (1861–1940) British civil servant and academic

Achimedes (1920)

Way , Problem , Effort , Appearance

“[Einstein's cosmological constant] is a name without any meaning. …We have, in fact, not the slightest inkling of what it's real significance is. It is put in the equations in order to give the greatest possible degree of mathematical generality.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932)

Mathematics

“An international system consists of a group of interacting behavior units called "nations" or "countries," to which may sometimes be added certain supra-national organizations, such as the United Nations. Each of the behavior units in the system can be described in terms of a set of "relevant variables." Just what is relevant and what is not is a matter of judgment of the system-builder, but we think of such things as states of war or peace, degrees of hostility or friendliness, alliance or enmity, arms budgets, geographic extent, friendly or hostile communications, and so on. Having defined our variables, we can then proceed to postulate certain relationships between them, sufficient to define a path for all the variables through time. Thus we might suppose, with Lewis Richardson that the rate of change of hostility of one nation toward a second depends on the level of hostility in the second and that the rate of change of hostility of the second toward the first depends on the level of hostility of the first. Then, if we start from given levels of hostility in each nation, these equations are sufficient to spell out what happens to these levels in succeeding time periods.”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1950s, National images and international systems, 1959, p. 120-121

Hostility , War , Peace , Behavior

“Moreover, the lie that the film propagates claiming that I would equate Israel with Nazi Germany is abhorrent. I have never made such a reprehensible equation.”

Joseph Massad (1963) Associate Professor of Arab Studies

Massad, in "Intimidating Columbia University" in the Egyptian newspaper Al-Ahram, on the short film Columbia Unbecoming concerning claims of mistreatment of students with opposing viewpoints. (2004)
On Comparisons of Israel to Nazi Germany

Lie

“L. Walras first formulated the state of the economic system at any point of time as the solution of a system of simultaneous equations representing the demand for goods by consumers, the supply of goods by producers and the equilibrium condition that supply equal demand on every market.”

Gérard Debreu (1921–2004) French economist and mathematician

Arrow, Kenneth J., and Gerard Debreu. " Existence of an equilibrium for a competitive economy http://cowles.econ.yale.edu/P/cp/p00b/p0087.pdf." Econometrica: Journal of the Econometric Society (1954): p. 265

Time

“We notice the movement of automobiles and other beings in the street, but we do not notice that the turning of the earth. We believe that automobiles go at a great speed on a fixed ground; yet the speed of the earth's rotation at the equator is 40,000 km every 24 hours.
As truly serious art must follow the greater laws, and not only appearance, I try to put all the elements in motion in my mobile sculptures. It is a matter of harmonizing these movements, thus arriving at a new possibility for beauty.”

Alexander Calder (1898–1976) American artist

Quote of Calder (8 March 1932), in text 'That which moves - On mobile sculptures', unpubl. MS https://web.archive.org/web/20110222045901/http://calder.org:80/historicaltexts/text/5.html, 1932, Calder Foundation Archives, New York
1930s - 1950s

Law , Beauty , Art , Appearance

“It is a common myth that idlers are incapable of working. The term “idler” is used as a pejorative by the forces of dullness and authority as they like the idea that idleness equates to evil, and they want society at large to despise the idler. The non-idler cannot understand the paradox of the working idler. He likes things to be simple: you are either working, or not working.”

Tom Hodgkinson (1968) British writer

“Idleness and Industry,” The Idler.

Idea , Understanding , Evil

“Simulators set up the required system of interdependences, usually between electrical potentials or voltages as variables, by means of valve-amplifiers and electrical networks. Since the voltage across a capacitance is proportional to the integral of a current, that across an inductance to the first derivative of a current, and that across a resistor to the current itself, it is possible to arrange a network of electrical elements, with amplifiers and feeds-back where necessary, so that a given linear differential equation is caused to relate an ’output’ voltage to an ’input’ voltage. Thus a given linear system of interdependences can be simulated, either directly or in any convenient transformation. If non-linear relationships are required there is no universally applicable simple device, but there do exist a great variety of non-linear elements with non-linear characteristics that are known and to some extent; adjustable. These include non-linear resistors… and the characteristic curves of thermionic valves, of rectifiers and discharge vessels and of magnetic materials. Limits may be set by the use of neon tubes that become conducting when a certain voltage is exceeded, or by relays, and so on”

Arnold Tustin (1899–1994) British engineer

Source: The Mechanism of Economic Systems (1953), p. 128; As cited in: Prices Revalued as Information: Circuit Elements, online document 2013

Universe

“The critical element in this equation is developing inclusiveness that envelopes all these competing priorities (of the different ethnic groups) in a manner that is fair to all. Without it we risk remaining a divided society all the more tragic for having unfulfilled our potential.”

Joni Madraiwiwi (1957–2016) Fijian politician

Opening address to the Commonwealth Parliamentary Association conference in Nadi, 6 September 2005.

“Ideas and techniques known in quantum electrodynamics have been applied to the Bardeen-Cooper-Schrieffer theory of superconductivity. In an approximation which corresponds to a generalization of the Hartree-Fock fields, one can write down an integral equation defining the self-energy of an electron in an electron gas with phonon and Coulomb interaction. The form of the equation implies the existence of a particular solution which does not follow from perturbation theory, and which leads to the energy gap equation and the quasi-particle picture analogous to Bogolyubov's.”

Yoichiro Nambu (1921–2015) American physicist

[Quasi-particles and gauge invariance in the theory of superconductivity, Physical Review, 117, 3, February 1960, 648–663, 10.1103/PhysRev.117.648]

Idea

“Disarmament has become the urgent imperative of our time. I do not say this because I equate the absence of arms to peace, or because I believe that bringing an end to the nuclear arms race automatically guarantees the peace, or because the elimination of nuclear warheads from the arsenals of the world will bring in its wake that change in attitude requisite to the peaceful settlement of disputes between nations. Disarmament is vital today, quite simply, because of the immense destructive capacity of which men dispose.”

Haile Selassie (1892–1975) Emperor of Ethiopia

Address to the United Nations (1963)

Men , World , Peace , Change

“Different ways of writing the same equation can suggest very different things, even if they are logically equivalent…. In Einstein's original 1905 paper, you do not find the equation E = mc2. What you find is m = E/c2…. the title of the paper is a question: "Does the Inertia of a Body Depend on Its Energy Content?" …If we can explain mass in terms of energy, we'll be improving our description of the world. We'll need fewer ingrediants in our world-recipe.”

Frank Wilczek (1951) physicist

Source: The Lightness of Being – Mass, Ether and the Unification of Forces (2008), Ch. 3, p. 19.

World , Way , Question , Dependency

“Resistants were on the right side, Salò Republic's combatants on the wrong one. (…) One cannot equate who was fighting for a right cause of equality and freedom, and who, apart of goodfaith, was on the wrong side. (…) The judgement of the Right [on Fascism] have to be negative, due to freedom limitation. (…) We cannot deny ourselves history, and Fascism was a dictatorship that denied some fundamental freedoms.”

Gianfranco Fini (1952) Italian politician

cited in «La destra si riconosca nell'antifascismo» http://www.corriere.it/politica/08_settembre_13/fini_antifascismo_ccb8bcec-8175-11dd-95db-00144f02aabc.shtml, Il Corriere della Sera, 13 September 2008).

History , Freedom , Fight

“The inevitable lack of objectivity in political decisions, which is only the reflex to suppress the politically inherent friend-enemy antithesis, manifests itself in the regrettable forms and aspects of the scramble for office and the politics of patronage. The demand for depoliticalization which arises in this context means only the rejection of party politics, etc. The equation politics = party politics is possible whenever antagonisms among domestic political parties succeed in weakening the all-embracing political unit, the state.”

Carl Schmitt book The Concept of the Political

The Concept of the Political (1927)

Decision

“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.”

Ezra Pound book The Spirit of Romance

The Spirit of Romance (1910), p. 5

Mathematics , Science

“Algebra in the Renaissance period received its first serious consideration in Pacioli's Sūma (1494)… which characterized in a careless way the knowledge… thus far accumulated. By the aid of the crude symbolism then in use it gave a considerable amount of work in equations.
The noteworthy work… and the first to be devoted entirely to the subject, was Rudolff's Coss (1525). This work made no decided advance in the theory, but it improved the symbolism for radicals and made the science better known in Germany. Stiffel's edition of this work (1553-1554) gave the subject still more prominence.
The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). The next great work… to appear in print was the General Trattato of Tartaglia…”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, p. 384; Ch. 6: Algebra

Way , Knowledge , Appearance , Science

“The manner in which time and space are bound up with each other in the four-dimensional continuum is variable. It is difficult to express this variability of the cross-connections between space and time in simple language, and different interpretations of it are possible, corresponding to different mathematical transformations of the fundamental line-element, e. g. a different choice of the variable which we interpret as "time." Perhaps the best way we can express it is by saying that the solution of the field-equations of the theory of relativity shows that there is in the universe a tendency to change its scale, which at the present time results in an expansion, but may perhaps at other times become, or have been, a shrinking. This is true of the grand scale model of the universe.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

Way , Mathematics , Universe , Change

“There was a comfort in the thought, a strange sort of personal comfort in being able to believe that some intelligence might have solved the riddle of that mysterious equation of the universe. And how, perhaps, that mysterious equation might tie in with the spiritual force that was idealistic brother to time and space and all those other elemental factors that held the universe together.”

Clifford D. Simak book Way Station

Source: Way Station (1963), Ch. 30

Intelligence , Universe , Time , Personality

“The astonishing thing about Einstein's equations is that they appear to have come out of nothing.”

Ernest Barnes (1874–1953) English mathematician and clergyman

As quoted by Gerald James Whitrow, The Structure of the Universe: An Introduction to Cosmology (1949)

Appearance

“When virtue is pictured as innocence and innocence equated with childlikeness, the implication is obviously that knowledge and experience are no longer media of goodness, but have become in themselves contaminating. This is a very despairing outlook, in its way as black as Augustine's original sin, for it supposes that original goodness will in all likelihood be defiled…It surrenders the attempt to represent virtue in a mature phase.”

Marina Warner (1946) writer and mythographer

Joan of Arc (Harmondsworth, Penguin, [1981] 1983) p. 262.

Way , Knowledge , Despair

“The term system has a number of meanings. There are systems of numbers and of equations, systems of value and of thought, systems of law, solar systems, organic systems, management systems, command and control systems, electronic systems, even the Union Pacific Railroad system. The meanings of "system" are often confused. The most general, however, is: A system is a set of interacting units with relationships among them. The word "set" implies that the units have some common properties. These common properties are essential if the units are to interact or have relationships. The state of each unit is constrained by, conditioned by, or dependent on the state of other units. The units are coupled. Moreover, there is at least one measure of the sum of its units which is larger than the sum of that measure of its units.”

James Grier Miller (1916–2002) biologist

Source: Living systems, 1978, p. 16; As cited in: Sven Rasegård (2002) Man and Science: A Web of Systems and Social Conventions. p. 29

Law , Dependency

“When investigating theories at the tiniest conceivable scales in nature, almost all researchers today revert to the quantum language, accepting the verdict from the Copenhagen doctrine that the only way to describe what is going on will always involve states in HIlbert space, controlled by operator equations.”

Gerardus 't Hooft (1946) Dutch theoretical physicist and Nobel Prize winner

The Cellular Automaton Interpretation of Quantum Mechanics, 21 December 2015, arXiv:1405.1548v3 https://arxiv.org/abs/1405.1548,

Way , Nature

“The conservation of matter in a chemical change is represented in a balanced chemical equation for that process. The study of the relationships between the numbers of reactant and product molecules is called stoichiometry. Stoichiometry is fundamental to all aspects of chemistry.”

David W. Oxtoby (1951) President of Pomona college

Principles of Modern Chemistry (7th ed., 2012), Ch. 2 : Chemical Formulas, Equations, and Reaction Yields

Study , Change

“I have endeavoured, in the following treatise, to convey as complete an account of the present state of knowledge on the subject of Differential Equations, as was consistent with the idea of a work intended, primarily, for elementary instruction. It was my object, first of all, to meet the wants of those who had no previous acquaintance with the subject, but I also desired not quite to disappoint others who might seek for more v advanced information. These distinct, but not inconsistent - aims determined the plan of composition.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, A treatise on differential equations (1859), p. v; Lead paragraph of the preface

Disappointment , Idea , Knowledge

“It may be in some measure due to the defects of notation in his time that Diophantos will have in his solutions no numbers whatever except rational numbers, in [the non-numbers of] which, in addition to surds and imaginary quantities, he includes negative quantities. …Such equations then as lead to surd, imaginary, or negative roots he regards as useless for his purpose: the solution is in these cases ὰδοπος, impossible. So we find him describing the equation 4=4x+20 as ᾰτοπος because it would give x=-4. Diophantos makes it throughout his object to obtain solutions in rational numbers, and we find him frequently giving, as a preliminary, conditions which must be satisfied, which are the conditions of a result rational in Diophantos' sense. In the great majority of cases when Diophantos arrives in the course of a solution at an equation which would give an irrational result he retraces his steps and finds out how his equation has arisen, and how he may by altering the previous work substitute for it another which shall give a rational result. This gives rise, in general, to a subsidiary problem the solution of which ensures a rational result for the problem itself. Though, however, Diophantos has no notation for a surd, and does not admit surd results, it is scarcely true to say that he makes no use of quadratic equations which lead to such results. Thus, for example, in v. 33 he solves such an equation so far as to be able to see to what integers the solution would approximate most nearly.”

Thomas Little Heath (1861–1940) British civil servant and academic

Diophantos of Alexandria: A Study in the History of Greek Algebra (1885)

Problem , Sense , Time

“Though acts of reception and of understanding are in some measure fictions of ordered intuition, myths of reason, this truth does not justify the denial of intentional conduct. It is as absurd to discard as mendacious, as anarchically opaque, the bearing of contextual probability and suggestion, as it is to invest in such probability any blind trust. The negations of post-structuralism and of certain varieties of deconstruction are precisely as dogmatic, as political as were the positivist equations of archival historicism. The "emptiness of meaning" postulate is no less a priori, no less a case of despotic reductionism than were, say, the axioms of economic and psycho-sociological causality in regard to the generation of meaning in literature and the arts in turn-of-the-century pragmatism and scientism.”

George Steiner (1929–2020) American writer

Source: Real Presences (1989), III: Presences, Ch. 3 (pp. 174-175).

Truth , Art , Literature , Understanding

“Deciding to avoid other people does not necessarily equate with having no desire whatsoever for company; it may simply reflect a dissatisfaction with what—or who—is available. Cynics are, in the end, only idealists with awkwardly high standards. In Chamfort’s words, “It is sometimes said of a man who lives alone that he does not like society. This is like saying of a man he does not like going for walks because he is not fond of walking at night in the forêt de Bondy.””

Alain de Botton book Status Anxiety

Source: Status Anxiety (2004), p. 119.

People , Night

“When we speak of the early history of algebra it is necessary to consider… the meaning of the term. If… we mean the science that allows us to solve the equation ax^2 + bx + c = 0, expressed in these symbols, then the history begins in the 17th century; if we remove the restriction as to these particular signs, and allow for other and less convenient symbols, we might properly begin the history in the 3rd century; if we allow for the solution of the above equation by geometric methods, without algebraic symbols of any kind, we might say that algebra begins with the Alexandrian School or a little earlier; and if we say that we should class as algebra any problem that we should now solve with algebra (even though it was as first solved by mere guessing or by some cumbersome arithmetic process), the the science was known about 1800 B. C., and probably still earlier.<”

David Eugene Smith (1860–1944) American mathematician

Source: History of Mathematics (1925) Vol.2, Ch. 6: Algebra, p. 378

History , Problem , Science

“The result of my work has been the most extraordinary, the most unforeseen, and the happiest, that ever was; for, after having performed all the equations, multiplications, antitheses, and other operations of my method, and having finally finished the problem, I have found that my principle gives exactly and precisely the same proportion for the refractions which Monsieur Descartes has established.”

Pierre de Fermat (1601–1665) French mathematician and lawyer

Epist. XLII, written at Toulouse (Jan. 1, 1662) and reprinted in Œvres de Fermat, ii, p. 457; i, pp. 170, 173, as quoted by E. T. Whittaker, A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century (1910) p. 10. https://books.google.com/books?id=CGJDAAAAIAAJ&pg=PA10

Problem

“By 1700 all of the familiar members of the [number] system… were known. However, opposition to the newer types of numbers was expressed throughout the century. Typical are the objections of… Baron Francis Masères… in 1759 his Dissertation on the Use of the Negative Sign in Algebra… shows how to avoid negative numbers… and especially negative roots, by carefully segregating the types of quadratic equations so that those with negative roots are considered separately; and… the negative roots are to be rejected.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 592.

“On notable classmate was Dan Friedan. Friedan stunned me, and I think everyone else, at his Ph. D. seminar, when he showed that Einstein's equation, the basic equation of general relativity, could be interpreted in terms of one of the basic objects in QFT, the β function that governs the energy scale. I did not see what this could possibly mean, but a few years later it showed up as one of the key ideas in string theory.”

Joseph Polchinski Memories of a Theoretical Physicist

Memories of a Theoretical Physicist, arXiv preprint arXiv:1708.09093, 2017 https://arxiv.org/abs/1708.09093, (pp. 30–31)

Idea , Thinking

“What appear to be the most valuable aspects of the theoretical physics we have are the mathematical descriptions which enable us to predict events. These equations are, we would argue, the only realities we can be certain of in physics; any other ways we have of thinking about the situation are visual aids or mnemonics which make it easier for beings with our sort of macroscopic experience to use and remember the equations.”

Celia Green (1935) British philosopher

The Lost Cause (2003)

Way , Mathematics , Thinking , Reality

“Of course that's Bud and Laurindo. I liked Laurindo very much, and I love some of the tunes he does. In fact, I've been doing some piano transcriptions of some guitar things of his, and we recently recorded a tune of his. This particular thing again—how are you going to equate it? As jazz? As Brazilioan music or what? I wiould much rather hear Laurindo in his native habitat. I know he and Bud have been associated this way before, yet I don't feel that a real good rapport goes on between them. The constant mixing—half-jazz, half-Brazillian—I don't think it's good. You lose certain features of the one when you try to come out with the other. Let's give that three stars.”

Clare Fischer (1928–2012) American keyboardist, composer, arranger, and bandleader

Reviewing "Tocata" https://www.youtube.com/watch?v=a940h3-1NV0 from Brazilliance; as quoted in "Clare Fischer: Blindfold Test" http://www.mediafire.com/view/fix6ane8h54gx/Clare_Fischer#rjvay58eo774rhe

Love , Music , Way , Feeling

“The deepest problems of modern life derive from the claim of the individual to preserve the autonomy and individuality of his existence in the face of overwhelming social forces, of historical heritage, of external culture, and of the technique of life. The fight with nature which primitive man has to wage for his bodily existence attains in this modern form its latest transformation. The eighteenth century called upon man to free himself of all the historical bonds in the state and in religion, in morals and in economics. Man’s nature, originally good and common to all, should develop unhampered. In addition to more liberty, the nineteenth century demanded the functional specialization of man and his work; this specialization makes one individual incomparable to another, and each of them indispensable to the highest possible extent. However, this specialization makes each man the more directly dependent upon the supplementary activities of all others. Nietzsche sees the full development of the individual conditioned by the most ruthless struggle of individuals; socialism believes in the suppression of all competition for the same reason. Be that as it may, in all these positions the same basic motive is at work: the person resists to being leveled down and worn out by a social technological mechanism. An inquiry into the inner meaning of specifically modern life and its products, into the soul of the cultural body, so to speak, must seek to solve the equation which structures like the metropolis set up between the individual and the super-individual contents of life. Such an inquiry must answer the question of how the personality accommodates itself in the adjustments to external forces.”

Georg Simmel (1858–1918) German sociologist, philosopher, and critic

Source: The Metropolis and Modern Life (1903), p. 409

Life , Religion , Soul , Motivation

“It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. …The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake.”

Frank Wilczek (1951) physicist

Longing for the Harmonies: Themes and Variations from Modern Physics (1987)

Way , Motivation , Understanding , Universe

“The historical associations of the word algebra almost substantiate the sordid character of the subject. The word comes from the title of a book written by… Al Khowarizmi. In this title, al-jebr w' almuqabala, the word al-jebr meant transposing a quantity from one side of an equation to another and muqabala meant simplification of the resulting expressions. Figuratively, al-jebr meant restoring the balance of an equation… When the Moors reached Spain… algebrista… came to mean a bonesetter… and signs reading Algebrista y Sangrador (bonesetter and bloodletter) were found over Spanish barber shops. Thus it might be said that there is a good historical basis for the fact that the word algebra stirs up disagreeable thoughts.”

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 69

Books , Reading

“Three distinct geometries on S7 arise as solutions of the classical equations of motion in eleven dimensions. In addition to the conventional riemannian geometry, one can also obtain the two exceptional Cartan-Schouten compact flat geometries with torsion.”

François Englert (1932) Belgian theoretical physicist

[10.1016/0370-2693(82)90684-0, 1982, Spontaneous compactification of eleven-dimensional supergravity, Physics Letters B, 119, 4–6, 339–342]

“Thus, the way Romila Thapar equates Mahmud Ghaznavi with Harsha of Kashmir (twelfth century) as being both temple plunderers, can be shown up to be in gross conflict with the contemporary testimonies about the two….. Romila Thapar's explanation that Ghaznavi's behaviour was essentially the same as Harsha's, can only rest on an utter incompetence in reading the source material, or in a deliberate attempt to distort history. What is more, if at all one wants to compare Harsha's behaviour with that of the Muslim rulers, one should face the connection that the contemporary historian Kalhan explicitly makes. Commenting on Harsha's temple plundering, he writes :"Prompted by the Turks in his employ, he behaved like a Turk"…. Kalhan is simply saying that the very idea that a temple need not be respected, was borrowed by Harsha from the Muslim Turks. These already had a well-established reputation for temple desecration, and that is a fact to which the Nehruvian historians prefer not to draw the readers' attention….. So, here we have a case of a history professor who does not realize that the proofs he cites have hardly any logical connection with the thesis he proposes; or who is so assured about his eminence that he doesn't expect readers to notice the faulty reasoning.”

Harsha of Kashmir

Koenraad Elst 1991: Ayodhya and after: issues before Hindu society.

Way , History , Idea , Reading

“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”

Norman Mailer book The Naked and the Dead

Gen. Edward Cummings, in Pt. 1, Ch. 6
The Naked and the Dead (1948)

Men , Past , Fight

“Sculpture is, in the twentieth century, a wide field of experience, with many facets of symbol and material and individual calligraphy. But in all these varied and exciting extensions of our experience we always come back tot the fact that we are human beings of such and such a size, biologically the same as primitive man, and that it is through drawing and observing, or observing and drawing, that we equate our bodies with our landscape.”

Barbara Hepworth (1903–1975) English sculptor

Studio International 171 – June 1966, p. 280
1961 - 1975

Drawing

“Complexity has the propensity to overload systems, making the relevance of a particular piece of information not statistically significant. And when an array of mind-numbing factors is added into the equation, theory and models rarely conform to reality.”

L. K. Samuels (1951) American writer

Source: In Defense of Chaos: The Chaology of Politics, Economics and Human Action, (2013), p. 28.

Reality

“Since the 1950s, the key equation of quantum gravity has been called the Wheeler-DeWitt equation. Bryce DeWitt and John Wheeler wrote it down, but in all the time since then, no one had been able to solve it. We found we could solve it exactly, and in fact we found an infinite number of exact solutions.”

Lee Smolin (1955) American cosmologist

Describing work with Ted Jacobson
"Loop Quantum Gravity," The New Humanists: Science at the Edge (2003)

Time

“Differential equations won't help you much in the design of aeroplanes — not yet, anyhow.”

Nevil Shute book Stephen Morris

Rawdon, the aircraft designer, to Morris, his aspiring protege.
Stephen Morris, ch. 3, p. 41 (1923, published posthumously in 1961)

Help

“Money is indispensable to a long-circuit heavy load energy system. It must be used when a sufficient surplus is being produced to allow a margin for exchange, and cost of transport, over a considerable distance. Money represents a storage battery when idle, and a generalized mode of the conversion of energy when it is in motion, with a function of equating time and space.”

Isabel Paterson (1886–1961) author and editor

Source: The God of the Machine (1943), p. 32

Money , Time

“The sharpest peaks of the Ridge are the cluster of islets known as the Rocks of St. Paul, near the equator. The entire cluster of half a dozen islets is not more than a quarter of a mile across, and their rocky slopes drop off at so sheer an angle that water more than half a mile deep lies only a few feet off shore.”

Rachel Carson book The Sea Around Us

Chapter 5, Page 90 https://books.google.com/books?id=PvkDFTtW6f4C&&pg=PA90
The Sea Around Us (1951)

Water

“Great leaders recognize that companies must innovate to remain competitive, and they nurture environments that encourage creative thinking… Innovation is rarely accidental — it takes an organizational commitment that starts at the executive level. The idea is not enough. As Thomas Edison said, innovation is 1% inspiration and 99% perspiration. Too often companies forget the ‘perspiration’ or execution part of the equation.”

Gregory Balestrero (1947) American industrial engineer

Balestrero (2008) quoted in: "America the Innovator The New Rules for Global Market Growth" http://www.forbesspecialsections.com/SectionPDFs/PMIAmericaInnov.pdf By Karen A. Edelman. Forbes : A Special Advertising Section. Accessed 3 Dec 2008.
2000s

Idea , Thinking , Parting , Forgetting

“I cannot help but protest in the strongest possible terms against the cartoon on page 3 of your publication of the 30th of December equating the present governments of Poland and Chile. It can only be explained by complete ignorance of the facts or by the systematically promoted socialist calumnies of the present situation in Chile, which I had not expected the F. A. Z. to fall for. I believe that all the participants in the Mont Pelerin Society conference held a few weeks ago in Chile would agree with me that you owe the Chilean government a humble apology for such twisting of the facts. Any Pole lucky enough to escape to Chile could consider himself fortunate.”

Friedrich Hayek (1899–1992) Austrian and British economist and Nobel Prize for Economics laureate

Letter to the editor of Frankfurter Allgemeine Zeitung, on a cartoon comparing Pinochet's Chile to Jaruzelski's Poland, which was published on 6 January 1982
1980s and later

Help

“The moon blew up without warning and for no apparent reason. It was waxing, only one day short of full. The time was 05:03:12 UTC. Later it would be designated A+0.0.0, or simply Zero.
An amateur astronomer in Utah was the first person on Earth to realize that something unusual was happening. Moments earlier, he had noticed a blur flourishing in the vicinity of the Reiner Gamma formation, near the moon’s equator. He assumed it was a dust cloud thrown up by a meteor strike. He pulled out his phone and blogged the event.”

Neal Stephenson book Seveneves

Opening paragraphs of the novel; "The Age of the One Moon"
Seveneves (2015), Part One

Time , Personality

“No one minds what Jeffrey says:… it is not more than a week ago that I heard him speak disrespectfully of the equator.”

Sydney Smith (1771–1845) English writer and clergyman

Vol. I, p. 17
Lady Holland's Memoir (1855), Bartlett's Familiar Quotations, 10th ed. (1919)

“A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this 'variance equation' completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or non-stationary statistics.
The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field.
The duality principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side.
Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.”

Rudolf E. Kálmán (1930–2016) Hungarian-born American electrical engineer

Source: New results in linear filtering and prediction theory (1961), p. 95 Article summary; cited in: " Rudolf E. Kálmán http://www-history.mcs.st-andrews.ac.uk/Biographies/Kalman.html", MacTutor History of Mathematics archive, 2010

Error , Optimism , Problem

“The minimum principle that unified the knowledge of light, gravitation, and electricity of Hamilton's time no longer suffices to relate these fundamental branches of physics. Within fifty years of its creation, the belief that Hamilton's principle would outlive all other physical laws of physics was shattered. Minimum principles have since been created for separate branches of physics… but these are not only restricted… but seem to be contrived…
A single minimum principle, a universal law governing all processes in nature, is still the direction in which the search for simplicity is headed, with the price of simplicity now raised from a mastery of differential equations to a mastery of the calculus of variations.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 442.

Law , Search , Nature , Knowledge

“It is clear that the building of models is not a purely mechanical process but requires skill of a high order – not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1950s, The Skills of the Economist, 1958, p. 16-17 as cited in Andrew Mearman (2011).

Mathematics