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Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.
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On mistaking pseudorandom number generators for being truly "random" — this quote is often erroneously interpreted to mean that von Neumann was against the use of pseudorandom numbers, when in reality he was cautioning about misunderstanding their true nature while advocating their use. From "Various techniques used in connection with random digits" by John von Neumann in Monte Carlo Method (1951) edited by A.S. Householder, G.E. Forsythe, and H.H. Germond

 

John von Neumann

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It was the random element that baffled investigation. Even that was a matter of semantics. For Holloway was convince that it wasn't really random. There just weren't enough known factors. No adult could work the abacus, for example. And Holloway thoughtfully refrained from letting a child play with the thing.
The crystal cube was similarly cryptic. It showed a mad pattern of colors, which sometimes moved. In this it resembled a kaleidoscope. But the shifting of balance and gravity didn't affect it. Again the random factor.
Or, rather, the unknown. The x pattern.

 

Lewis Padgett

 

There is no effective difference between guessing a variable that is not random, but for which information is partial or deficient (...), and a random one (...). In this sense, guessing (what I don't know, but what someone else may know) and predicting (what has not taken place yet) are the same thing.

 

Nassim Nicholas Taleb

 

O! many a shaft at random sent
Finds mark the archer little meant!
And many a word, at random spoken,
May soothe or wound a heart that's broken!

 

Walter Scott

 

Mutation is random; natural selection is the very opposite of random.

 

Richard Dawkins

 

My old suggestion that public offices be filled by drawing lots, as a jury box is filled, was probably more intelligent than I suspected. It has been criticized on the ground that selecting a man at random would probably produce some extremely bad State governors. [...] But I incline to believe that it would be best to choose members of the Legislature quite at random. No matter how stupid they were, they could not be more stupid than the average legislator under the present system. Certainly, they'd be measurably more honest, taking one with another. Finally, there would be the great advantage that all of them had got their jobs unwillingly, and were eager, not to spin out their sessions endlessly, but to get home as soon as possible.

 

H. L. Mencken