“… I would rather have questions that I can't answer than answers that I can't question. (variation of a remark by Richard Feynman)”
(quote at 42:11 of 1:56:02)
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Max Tegmark 24
Swedish-American cosmologist 1967Related quotes

“When I lay these questions before God I get no answer. But a rather special sort of 'No answer.”
It is not the locked door. It is more like a silent, certainly not uncompassionate, gaze. As though He shook His head not in refusal but waiving the question. Like, 'Peace, child; you don't understand.'
A Grief Observed (1961)

Quoted in an article, "Why Is There Something Rather Than Nothing?" http://www.csicop.org/sb/show/why_is_there_something_rather_than_nothing, by Victor Stenger (June 2006).

“I am more content with questions than answers.”
Source: Life Itself : A Memoir (2011), Ch. 54 : How I Believe In God
Context: Quantum theory is now discussing instantaneous connections between two entangled quantum objects such as electrons. This phenomenon has been observed in laboratory experiments and scientists believe they have proven it takes place. They’re not talking about faster than the speed of light. Speed has nothing to do with it. The entangled objects somehow communicate instantaneously at a distance. If that is true, distance has no meaning. Light-years have no meaning. Space has no meaning. In a sense, the entangled objects are not even communicating. They are the same thing. At the “quantum level” (and I don’t know what that means), everything may be actually or theoretically linked. All is one. Sun, moon, stars, rain, you, me, everything. All one. If this is so, then Buddhism must have been a quantum theory all along. No, I am not a Buddhist. I am not a believer, not an atheist, not an agnostic. I am more content with questions than answers.

“Judge a man by his questions rather than by his answers.”
Il est encore plus facile de juger de l'esprit d'un homme par ses questions que par ses réponses. (It is easier to judge the mind of a man by his questions rather than his answers) — Pierre-Marc-Gaston, duc de Lévis (1764-1830), Maximes et réflexions sur différents sujets de morale et de politique (Paris, 1808): Maxim xviii
Misattributed

“I refuse to answer that question on the grounds that I don't know the answer”

“I wish I had an answer to that because I'm tired of answering that question.”