Quotes about solution
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Wilhelm Von Humboldt photo
Évariste Galois photo

“It seems there is no fruit to be drawn from the solution we offer.”

Évariste Galois (1811–1832) French mathematician, founder of group theory

citation needed
Il parait après cela qu'il n'y a aucun fruit à tirer de la solution que nous proposons.

Phil Donahue photo

“Suicide is a permanent solution to a temporary problem.”

Phil Donahue (1935) American talk show host, film producer and writer

Attributed to Phil Donahue in: Dennis Coon, ‎John Mitterer (2008), Psychology: Modules for Active Learning. p. 553

Frédéric Bastiat photo
Bjarne Stroustrup photo

“The connection between the language in which we think/program and the problems and solutions we can imagine is very close. For this reason restricting language features with the intent of eliminating programmer errors is at best dangerous.”

Bjarne Stroustrup (1950) Danish computer scientist, creator of C++

Bjarne Stroustrup's The C++ Programming Language (Third Edition and Special Edition) Notes to the Reader page 9, 2012-04-28, http://web.archive.org/web/20091128074415/http://www2.research.att.com/~bs/3rd_notes.pdf#page=7, 2009-11-28 http://www2.research.att.com/~bs/3rd_notes.pdf#page=7,

Aga Khan IV photo

“What students know is no longer the most important measure of an education. The true test is the ability of students and graduates to engage with what they do not know, and to work out a solution.”

Aga Khan IV (1936) 49th and current Imam of Nizari Ismailism

Context: What students know is no longer the most important measure of an education. The true test is the ability of students and graduates to engage with what they do not know, and to work out a solution. They must also be able to reach conclusions that constitute the basis for informed judgements. The ability to make judgements that are grounded in solid information, and employ careful analysis, should be one of the most important goals for any educational endeavor. As students develop this capability, they can begin to grapple with the most important and difficult step: to learn to place such judgements in an ethical framework. For all these reasons, there is no better investment that individuals, parents and the nation can make than an investment in education of the highest possible quality. Such investments are reflected, and endure, in the formation of the kind of social conscience that our world so desperately needs.

Foreword to Excellence in Education (2003) http://www.agakhanacademies.org/general/vision<!-- Aga Khan Academy, Mombasa brochure p. 3 http://www.akdn.org/publications/case_study_academies_mombasa.pdf, also quoted at The Aga Khan Academies http://www.agakhanacademies.org/mombasa/student-projects -->

Carl Friedrich Gauss photo

“Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in General Investigations of Curved Surfaces of 1827 and 1825 http://books.google.com/books?id=SYJsAAAAMAAJ& (1902)
Context: In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere, which are the end points of the radii drawn parallel to the lines. The centre and the radius of this auxiliary sphere are here quite arbitrary. The radius may be taken equal to unity. This procedure agrees fundamentally with that which is constantly employed in astronomy, where all directions are referred to a fictitious celestial sphere of infinite radius. Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.

Karl Marx photo

“Therefore, mankind always sets itself only such tasks as it can solve; since, looking at the matter more closely, we will always find that the task itself arises only when the material conditions necessary for its solution already exist or are at least in the process of formation”

Karl Marx (1818–1883) German philosopher, economist, sociologist, journalist and revolutionary socialist

Preface to ' (1859).
Context: In the social production of their life, men enter into definite relations that are indispensable and independent of their will; these relations of production correspond to a definite stage of development of their material forces of production. The sum total of these relations of production constitutes the economic structure of society — the real foundation, on which rises a legal and political superstructure and to which correspond definite forms of social consciousness. The mode of production of material life determines the social, political and intellectual life process in general. It is not the consciousness of men that determines their being, but, on the contrary, their social being that determines their consciousness. [Es ist nicht das Bewußtsein der Menschen, das ihr Sein, sondern umgekehrt ihr gesellschaftliches Sein, das ihr Bewusstsein bestimmt. ] At a certain stage of their development, the material productive forces in society come in conflict with the existing relations of production, or — what is but a legal expression for the same thing — with the property relations within which they have been at work before. From forms of development of the productive forces these relations turn into fetters. Then begins an epoch of social revolution. With the change of the economic foundation the entire immense superstructure is more or less rapidly transformed. In considering such transformations a distinction should always be made between the material transformation of the economic conditions of production, which can be determined with the precision of natural science, and the legal, political, religious, aesthetic or philosophic — in short, ideological forms in which men become conscious of this conflict and fight it out. Just as our opinion of an individual is not based on what he thinks of himself, so we can not judge of such a period of transformation by its own consciousness; on the contrary, this consciousness must be explained rather from the contradictions of material life, from the existing conflict between the social productive forces and the relations of production. No social order ever disappears before all the productive forces for which there is room in it have been developed; and new, higher relations of production never appear before the material conditions of their existence have matured in the womb of the old society itself. Therefore, mankind always sets itself only such tasks as it can solve; since, looking at the matter more closely, we will always find that the task itself arises only when the material conditions necessary for its solution already exist or are at least in the process of formation. In broad outlines we can designate the Asiatic, the ancient, the feudal, and the modern bourgeois modes of production as so many progressive epochs in the economic formation of society. The bourgeois relations of production are the last antagonistic form of the social process of production — antagonistic not in the sense of individual antagonism, but of one arising from the social conditions of life of the individuals; at the same time the productive forces developing in the womb of bourgeois society create the material conditions for the solution of that antagonism. This social formation constitutes, therefore, the closing chapter of the prehistoric stage of human society.

David Ben-Gurion photo

“Everybody sees a difficulty in the question of relations between Arabs and Jews. But not everybody sees that there is no solution to this question.”

David Ben-Gurion (1886–1973) Israeli politician, Zionist leader, prime minister of Israel

Written statement (June 1919), as quoted in Time magazine (24 July 2006)
Context: Everybody sees a difficulty in the question of relations between Arabs and Jews. But not everybody sees that there is no solution to this question. No solution! There is a gulf, and nothing can bridge it… We, as a nation, want this country to be ours; the Arabs, as a nation, want this country to be theirs.

John Nash photo

“One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other.”

John Nash (1928–2015) American mathematician and Nobel Prize laureate

"Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->
1950s
Context: We give two independent derivations of our solution of the two-person cooperative game. In the first, the cooperative game is reduced to a non-cooperative game. To do this, one makes the players’ steps of negotiation in the cooperative game become moves in the noncooperative model. Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game. The negotiation process must be formalized and restricted, but in such a way that each participant is still able to utilize all the essential strengths of his position. The second approach is by the axiomatic method. One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other.

Paulo Coelho photo

“If you rely only on experience, you’ll simply keep applying old solutions to new problems.”

I know a lot of people who feel they have an identity only when they’re talking about their problems. That way, they exist, because their problems are linked to what they judge to be their history.
Aleph (2011)

Malcolm X photo

“The only true world solution today is governments guided by true religion — of the spirit.”

Malcolm X (1925–1965) American human rights activist

The Autobiography of Malcolm X (1965)

Joseph Campbell photo

“But in the dream the forms are quirked by the peculiar troubles of the dreamer, whereas in myth the problem and solutions shown are directly valid for all mankind.”

Source: The Hero with a Thousand Faces (1949), Chapter 1
Context: Dream is personalized myth, myth is depersonalized dream; both myth and dream are symbolic in the same general way of the dynamics of the psyche. But in the dream the forms are quirked by the peculiar troubles of the dreamer, whereas in myth the problem and solutions shown are directly valid for all mankind.

Jacque Fresco photo
Etty Hillesum photo
Greta Thunberg photo
Jawaharlal Nehru photo
Jawaharlal Nehru photo
Nikola Tesla photo

“For every person who perishes from the effects of a stimulant, at least a thousand die from the consequences of drinking impure water. This precious fluid, which daily infuses new life into us, is likewise the chief vehicle through which disease and death enter our bodies. The germs of destruction it conveys are enemies all the more terrible as they perform their fatal work unperceived. They seal our doom while we live and enjoy. The majority of people are so ignorant or careless in drinking water, and the consequences of this are so disastrous, that a philanthropist can scarcely use his efforts better than by endeavoring to enlighten those who are thus injuring themselves. By systematic purification and sterilization of the drinking water the human mass would be very considerably increased. It should be made a rigid rule which might be enforced by law to boil or to sterilize otherwise the drinking water in every household and public place. The mere filtering does not afford sufficient security against infection. All ice for internal uses should be artificially prepared from water thoroughly sterilized. The importance of eliminating germs of disease from the city water is generally recognized, but little is being done to improve the existing conditions, as no satisfactory method of sterilizing great quantities of water has yet been brought forward. By improved electrical appliances we are now enabled to produce ozone cheaply and in large amounts, and this ideal disinfectant seems to offer a happy solution of the important question.”

Nikola Tesla (1856–1943) Serbian American inventor

The Problem of Increasing Human Energy (1900)

Philip Kotler photo
Steve Jobs photo
Wendell Berry photo
Max Planck photo

“I also knew the formula that expresses the energy distribution in the normal spectrum. A theoretical interpretation therefore had to be found at any cost, no matter how high. It was clear to me that classical physics could offer no solution to this problem, and would have meant that all energy would eventually transfer from matter to radiation. ...This approach was opened to me by maintaining the two laws of thermodynamics. The two laws, it seems to me, must be upheld under all circumstances. For the rest, I was ready to sacrifice every one of my previous convictions about physical laws. ...[One] finds that the continuous loss of energy into radiation can be prevented by assuming that energy is forced at the outset to remain together in certain quanta. This was purely a formal assumption and I really did not give it much thought except that no matter what the cost, I must bring about a positive result.”

Max Planck (1858–1947) German theoretical physicist

Letter to Robert W. Wood (October 7, 1931) in Archive for the History of Quantum Physics, Microfilm 66, 5, as cited in Thomas S. Kuhn, Black-Body Theory and the Quantum Discontinuity, 1894–1912 (1978) pp. 132, 288. Translation of the entire letter, which is follow above is in Armin Hermann, Frühgeschiche der Quantentheorie (1899–1913) Mosbach/Baden: Physik Verlag (1969), transl. Claude W. Nash, p. 23 of the translation; and also in M. S. Longair,Theoretical Concepts in Physics(Cambridge and NewYork: Cambridge University Press, 1984), ch. 6–12, p. 222. All as quoted/cited by Clayton A. Gearhart, "Planck, the Quantum, and the Historians" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.613.4262&rep=rep1&type=pdf, Physics in Perspective, 4 (2002) 170-215.

Bahá'u'lláh photo

“...for each day there is a new problem and for every problem an expedient solution.”

Bahá'u'lláh (1817–1892) founder of the Bahá'í Faith

The Kitáb-i-Aqdas

Mwanandeke Kindembo photo
Guy P. Harrison photo
Neale Donald Walsch photo
Prevale photo

“It is fascinating the intellect of a person who always has a resource, who instead of getting down about a problem look for a solution. The mind remains the most interesting and engaging place of a human being.”

Prevale (1983) Italian DJ and producer

Original: È affascinante l'intelletto di una persona che ha sempre una risorsa, che invece di abbattersi per un problema cerca una soluzione. La mente rimane il posto più interessante e coinvolgente di un essere umano.
Source: prevale.net

Isaac Asimov photo

“Science fiction writers foresee the inevitable, and although problems and catastrophes may be inevitable, solutions are not.”

Isaac Asimov (1920–1992) American writer and professor of biochemistry at Boston University, known for his works of science fiction …

"How Easy to See the Future", Natural History magazine (April 1975);
General sources

Edward R. Murrow photo
Thomas Merton photo
Kazuo Ishiguro photo

“Complex problems do not demand complex solutions.”

Solution-Focused Pastoral Counseling: An Effective Short-Term Approach for Getting People Back on Track

Robert Anton Wilson photo

“… an optimistic mind-set finds dozens of possible solutions for every problem that the pessimist regards as incurable.”

Robert Anton Wilson (1932–2007) American author and polymath

Source: Cosmic Trigger: Die letzten Geheimnisse der Illuminaten oder An den Grenzen des erweiterten Bewusstseins

Leo Tolstoy photo
Anne McCaffrey photo

“Necessity breeds solution.”

Source: Dragonsinger

Orson Scott Card photo
Julian Barnes photo
Anthony Kiedis photo
Terry Goodkind photo
Martin Luther King, Jr. photo

“Rarely do we find men who willingly engage in hard, solid thinking. There is an almost universal quest for easy answers and half-baked solutions. Nothing pains some people more than having to think.”

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

Source: 1960s, Strength to Love (1963), Ch. 1 : A tough mind and a tender heart
Context: The tough mind is sharp and penetrating, breaking through the crust of legends and myths and sifting the true from the false. The tough-minded individual is astute and discerning. He has a strong austere quality that makes for firmness of purpose and solidness of commitment.
Who doubts that this toughness is one of man's greatest needs? Rarely do we find men who willingly engage in hard, solid thinking. There is an almost universal quest for easy answers and half-baked solutions. Nothing pains some people more than having to think.

Thomas Szasz photo
Carl Sagan photo
Robin S. Sharma photo

“Victims recite problems, leaders provide solutions.”

Robin S. Sharma (1965) Canadian self help writer

The Leader Who Had No Title: A Modern Fable on Real Success in Business and in Life
Variant: Victims recite problems. Leaders present solutions.

“I've concluded that genius is as common as dirt. We suppress genius because we haven't yet figured out how to manage a population of educated men and women. The solution, I think, is simple and glorious. Let them manage themselves.”

John Taylor Gatto (1935–2018) American teacher, book author

Source: Weapons of Mass Instruction: A Schoolteacher's Journey Through the Dark World of Compulsory Schooling, New Society Publishers (2013) p. xxii

Anthony Doerr photo

“Every outcome has its cause, and every predicament has its solution.”

Source: All the Light We Cannot See

Michael Crichton photo
Zadie Smith photo
Maya Angelou photo
Tori Amos photo

“Never was a cornflake girl;
Thought it was a good solution: hanging with the raisin girls.”

Tori Amos (1963) American singer

Source: Under the Pink

Albert Einstein photo

“When the solution is simple, God is answering.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity
Alice Hoffman photo
Stephen R. Covey photo
Patricia C. Wrede photo
Lawrence Durrell photo
Albert Einstein photo
Paulo Coelho photo
Maya Angelou photo
Raymond E. Feist photo
Maureen Johnson photo
Simone de Beauvoir photo
Anaïs Nin photo

“Do not seek the because - in love there is no because, no reason, no explanation, no solutions.”

Anaïs Nin (1903–1977) writer of novels, short stories, and erotica

Source: Henry And June

Sarah Dessen photo
Cheryl Strayed photo
Jonathan Franzen photo
Cassandra Clare photo
Ellen DeGeneres photo
Richard Bach photo
Albert Einstein photo
Sigmund Freud photo
Umberto Eco photo
H.L. Mencken photo

“Explanations exist; they have existed for all time; there is always a well-known solution to every human problem — neat, plausible, and wrong.”

H.L. Mencken (1880–1956) American journalist and writer

The portion after the second semicolon is widely paraphrased or misquoted. Two examples are "For every complex problem there is an answer that is clear, simple, and wrong" and "There is always an easy solution to every human problem -- neat, plausible, and wrong."
1910s
Source: "The Divine Afflatus" in New York Evening Mail (16 November 1917); later published in Prejudices: Second Series (1920) and A Mencken Chrestomathy (1949)

Dave Barry photo
Colin Powell photo
Albert Einstein photo
Isaac Asimov photo
Hazrat Inayat Khan photo
Margaret Atwood photo

“Mathematics because of its nature and structure is peculiarly fitted for high school instruction [Gymnasiallehrfach]. Especially the higher mathematics, even if presented only in its elements, combines within itself all those qualities which are demanded of a secondary subject. It engages, it fructifies, it quickens, compels attention, is as circumspect as inventive, induces courage and self-confidence as well as modesty and submission to truth. It yields the essence and kernel of all things, is brief in form and overflows with its wealth of content. It discloses the depth and breadth of the law and spiritual element behind the surface of phenomena; it impels from point to point and carries within itself the incentive toward progress; it stimulates the artistic perception, good taste in judgment and execution, as well as the scientific comprehension of things. Mathematics, therefore, above all other subjects, makes the student lust after knowledge, fills him, as it were, with a longing to fathom the cause of things and to employ his own powers independently; it collects his mental forces and concentrates them on a single point and thus awakens the spirit of individual inquiry, self-confidence and the joy of doing; it fascinates because of the view-points which it offers and creates certainty and assurance, owing to the universal validity of its methods. Thus, both what he receives and what he himself contributes toward the proper conception and solution of a problem, combine to mature the student and to make him skillful, to lead him away from the surface of things and to exercise him in the perception of their essence. A student thus prepared thirsts after knowledge and is ready for the university and its sciences. Thus it appears, that higher mathematics is the best guide to philosophy and to the philosophic conception of the world (considered as a self-contained whole) and of one’s own being.”

Christian Heinrich von Dillmann (1829–1899) German educationist

Source: Die Mathematik die Fackelträgerin einer neuen Zeit (Stuttgart, 1889), p. 40.

David Brin photo