“Once I have gotten into a problem, I find it extremely helpful to get a complete perspective, to learn what earlier scientists thought about it. I want to see not only what lines of thought proved to be productive, but also where and why certain other directions proved to be unproductive.”

In Search of Memory (2006)

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Eric R. Kandel81

American neuropsychiatrist 1929

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“Understand the problem. What kind of problem is it? There are three main types of problems:
‘Show that …’ or ‘Evaluate …’ questions, in which a certain statement has to be proved true, or a certain expression has to be worked out;
‘Find a…’ or ‘Find all…’ questions, which requires one to find something (or everything) that satisfies certain requirements;
‘Is there a …’ questions, which either require you to prove a statement or provide a counterexample”

Terence Tao (1975) Australian mathematician

and thus is one of the previous two types of problem
Source: Solving Mathematical Problems (2nd ed., 2006), Ch. 1 : Strategies in problem solving

“Once I undertook the analysis of a problem, I often looked at it from a variety of perspectives. I approached the problem as a series of thought experiments — unlike many other sciences, we typically cannot do actual experiments.”

Joseph E. Stiglitz (1943) American economist and professor, born 1943.

Autobiographical Essay (2001)

“If only I knew what I wanted I could try to see about getting it.”

Sylvia Plath (1932–1963) American poet, novelist and short story writer

Source: The Unabridged Journals of Sylvia Plath

“The problem of induction is, roughly speaking, the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future.”

Alfred Jules Ayer book Language, Truth, and Logic

Source: Language, Truth, and Logic (1936), p. 49.
Context: The problem of induction is, roughly speaking, the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future. There are only two ways of approaching this problem on the assumption that it is a genuine problem, and it is easy to see that neither of them can lead to its solution.

“I have often thought since that there is sound sense in what was once said by the late Lord C. J. Eyre, that the sooner a bad precedent was gotten rid of, the better.”

Lloyd Kenyon, 1st Baron Kenyon (1732–1802) British Baron

King v. Stone (1800), 1 East, 648 n. (a).

“To prove cannot mean anything other than to bring the other person to my own conviction. The truth lies only in the unification of “I” and “You.” The Other of pure thought, however, is the sensuous intellect in general. In the field of philosophy, proof therefore consists only in the fact that the contradiction between sensuous intellect and pure thought is disposed, so that thought is true not only for itself but also for its opposite.”

Ludwig Feuerbach (1804–1872) German philosopher and anthropologist

Z. Hanfi, trans., in The Fiery Brook (1972), p. 75
Towards a Critique of Hegel’s Philosophy (1839)

“I cannot see why it is necessary that every deduction from algebra should be bound to certain conventions incident to an earlier stage of mathematical learning, even supposing them to have been consistently used up to the point in question. I should not care if any one thought this treatise unalgebraical, but should only ask whether the premises were admissible and the conclusions logical.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

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The Differential and Integral Calculus (1836)

“Some luck lies in not getting what you thought you wanted but getting what you have, which once you have got it you may be smart enough to see is what you would have wanted had you known.”

Garrison Keillor (1942) American radio host and writer

Lake Wobegon Days (1985), p. 337
Source: Lake Wobegon U.S.A.

“I am far from convinced that energy spent doing damage to life, limb and property is likely to prove more productive than properly thought-out and planned non-violent direct action.
More likely the opposite.”

Yakoub Islam

"Anarchism Against Riots" (7 August 2011). 
Captain Jul's Mission Blog (2011 - 2013)
Context: Riots may be symptoms of a deeper socio-political malaise: the product of unjust government policy and racist policing. I know from friends I have spoken to who were participants in the 1981 Brixton riots, that riots can engender a great deal of local solidarity against an oppressive State. But I am far from convinced that energy spent doing damage to life, limb and property is likely to prove more productive than properly thought-out and planned non-violent direct action.
More likely the opposite.

“We prove what we want to prove, and the real difficulty is to know what we want to prove.”

Alain (1868–1951) French philosopher

On prouve tout ce qu'on veut, et la vraie difficulté est de savoir ce qu'on veut prouver.
Système des Beaux-Arts (1920), as quoted in The Most Brilliant Thoughts of All Time (In Two Lines or Less) by John M. Shanahan, p. 34
Variant translation: We prove anything we want to prove, and the real difficulty is to know what we want to prove.

“Once I have gotten into a problem, I find it extremely helpful to get a complete perspective, to learn what earlier scientists thought about it. I want to see not only what lines of thought proved to be productive, but also where and why certain other directions proved to be unproductive.”

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Eric R. Kandel81

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