
The Lazio Speeches (1936), as quoted in The Book of Italian Wisdom by Antonio Santi, Citadel Press, (2003) p. 87.
1930s
As discussed in this entry from Quote Investigator http://quoteinvestigator.com/2011/11/05/computers-useless/#more-2932, the origin seems to be the article "Pablo Picasso: A Composite Interview" by William Fifield which appeared in The Paris Review 32, Summer-Fall 1964, and collected a number of interviews Fifield had done with Picasso.
Common later variant: "Computers are useless. They can only give you answers." This variant seems to have arisen in the 1980s, the earliest known appearance in a book is Herman Feshbach, "Reflections on the Microprocessor Revolution: A Physicist's Viewpoint", in Man and Technology (1983), ed. Bruce M. Adkins, where the attribution is described as "rumoured". http://books.google.com/books?id=9EohAQAAIAAJ&q=Picasso
1960s
The Lazio Speeches (1936), as quoted in The Book of Italian Wisdom by Antonio Santi, Citadel Press, (2003) p. 87.
1930s
Cameron Country, broadcast on BBC TV, July 12, 1969.
“Pose your questions to people and you will get countless useless answers.”
“A Question for the Sun,” p. 123
The Sun Watches the Sun (1999), Sequence: “Hopelessness”
“I am not some kind of computer. Only machines have glib answers for everything.”
Source: A Swiftly Tilting Planet
[Undecidability and intractability in theoretical physics, Physical Review Letters, 54, 8, 1985, 735–738, 10.1103/PhysRevLett.54.735, https://www.stephenwolfram.com/publications/academic/undecidability-intractability-theoretical-physics.pdf]
An Amiable Icicle https://thegreatbaz.wordpress.com/2013/11/08/an-amiable-icicle-1929/ (August 1929)
“We need to ask ourselves not only what computers can do, but what computers should do.”
The Seattle Times: " Microsoft Build: Data privacy must be protected, CEO Satya Nadella tells technologists https://www.seattletimes.com/business/microsoft/microsoft-build-data-privacy-must-be-protected-ceo-satya-nadella-tells-technologists/" (7 May 2018)
“I ain’t up on sillygisms, but I can give you some arguments that nobody can answer. p. 13”
Plunkitt of Tammany Hall, Chapter 3, The Curse of Civil Service Reform