“The solution of the higher indeterminates depends almost entirely on very favourable numerical conditions and his methods are defective. But the extraordinary ability of Diophantus appears rather in the other department of his art, namely the ingenuity with which he reduces every problem to an equation which he is competent to solve.”

— James Gow (scholar)

p, 125
A Short History of Greek Mathematics (1884)

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James Gow (scholar) 22

scholar 1854–1923

James Gow (scholar) (1854–1923) scholar

p, 125
A Short History of Greek Mathematics (1884)

“Though the defects in Diophantus' proofs are in general due to the limitation of his symbolism, it is not so always. Very frequently indeed Diophantus introduces into a solution arbitrary conditions and determinations which are not in the problem. Of such "fudged" solutions, as a schoolboy would call them, two particular kinds are very frequent. Sometimes an unknown is assumed at a determinate value… Sometimes a new condition is introduced.”

James Gow (scholar) (1854–1923) scholar

A Short History of Greek Mathematics (1884)

“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)

“When an equation…clearly leads to two negative or imaginary roots, [Diophantus] retraces his steps and shows by how by altering the equation, he can get a new one that has rational roots. …Diophantus is a pure algebraist; and since algebra in his time did not recognize irrational, negative, and complex numbers, he rejected equations with such solutions.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 143.

“Art is this: art is the solution of a problem which cannot be expressed explicitly until it is solved.”

Piet Hein (1905–1996) Danish puzzle designer, mathematician, author, poet

As quoted in Man Creates Art Creates Man (1973) by Duane Preble, p. 14
Variant translation: Art is solving problems that cannot be formulated before they have been solved. The shaping of the question is part of the answer.
As quoted in Architecture: form, space, and order (2007) by Francis D.K. Ching, p. ix
Context: After all, what is art? Art is the creative process and it goes through all fields. Einstein’s theory of relativity — now that is a work of art! Einstein was more of an artist in physics than on his violin.
Art is this: art is the solution of a problem which cannot be expressed explicitly until it is solved.

“Bertolucci is extraordinary in his ability to perceive, he's a poet…he is very easy to work for.”

Marlon Brando (1924–2004) American screen and stage actor

Rolling Stone Issue No. 213 (May 20, 1976) on Bernardo Bertolucci.

“Man is the only animal for whom his own existence is a problem which he has to solve and from which he cannot escape.”

Erich Fromm (1900–1980) German social psychologist and psychoanalyst

Source: Man for Himself (1947), Ch. 3 "Human Nature and Character

“We leave the question whether a man shall be a brain or hand worker entirely to him to settle. At the end of the term of three years as a common laborer, which every man must serve, it is for him to choose, in accordance to his natural tastes, whether he will fit himself for an art or profession, or be a farmer or mechanic. If he feels that he can do better work with his brains than his muscles, he finds every facility provided for testing the reality of his supposed bent, of cultivating it, and if fit of pursuing it as his avocation. The schools of technology, of medicine, of art, of music, of histrionics, and of higher liberal learning are always open to aspirants without condition.”

Edward Bellamy (1850–1898) American author and socialist

Source: Looking Backward, 2000-1887 http://www.gutenberg.org/ebooks/25439 (1888), Ch. 7.

“A defect, as such, does not imply determinations in any direction. The individual's happiness is in the continuous unfolding of his experience, and also in the fruitfulness of his suffering. The criterion of his happiness is his power and permission to grow into his own self, with all that this involves. This, in turn, depends on other circumstances; the reality or mere ostensibility of his reception; the degree to which he is allowed, together with his defects and inherited birth constellations, to be integrated into his community; and the degree to which the community is permitted to become integrated into what he, the individual, represents.”

Martti Siirala (1889–1948) Finnish philosopher

Medicine in Metamorphosis (2003).

“A master in the art of living draws no sharp distinction between his work and his play; his labor and his leisure; his mind and his body; his education and his recreation. He hardly knows which is which. He simply pursues his vision of excellence through whatever he is doing, and leaves others to determine whether he is working or playing. To himself, he always appears to be doing both.”

L. P. Jacks (1860–1955) British educator, philosopher, and Unitarian minister

Misattributed to Chateaubriand on the internet and even some recently published books, this statement actually originated with L. P. Jacks in Education through Recreation (1932)
Misattributed

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