“There are things known
and there are things unknown
and in between are the doors.”

Aldous Huxley, using the term "the doors of perception" which originated with William Blake in The Marriage of Heaven and Hell. It is sometimes credited to Morrison because he cited it in interviews as the inspiration for the name The Doors and without always crediting Huxley as the source.
Misattributed

Quote in a letter to Sherwood Anderson, October 1923; as quoted in Georgia O'Keeffe: A Life, Roxana Robinson, University Press of New England, 1999
1917 - 1929
Context: I have been thinking of what you say about form... I feel that a real living form is the natural result of the individual’s effort to create the living thing out of the adventure of his spirit into the unknown.... and from that experience comes the desire to make the unknown known. By unknown I mean the thing that means so much to the person that he want to put it down - clarify something he feels but does not clearly understand... Making the unknown known.... if you stop to think of form as form you are lost.

(Cambridge: 2002), Book 9, Chapter 1, p. 24
On the Trinity (417)

Source: A Field Guide to Getting Lost

Department of Defense news briefing (12 February 2002)
Variant:
Now what is the message there? The message is that there are no "knowns." There are things we know that we know. There are known unknowns. That is to say there are things that we now know we don't know. But there are also unknown unknowns. There are things we do not know we don't know. So when we do the best we can and we pull all this information together, and we then say well that's basically what we see as the situation, that is really only the known knowns and the known unknowns. And each year, we discover a few more of those unknown unknowns.
:It sounds like a riddle. It isn't a riddle. It is a very serious, important matter.
:There's another way to phrase that and that is that the absence of evidence is not evidence of absence. It is basically saying the same thing in a different way. Simply because you do not have evidence that something exists does not mean that you have evidence that it doesn't exist. And yet almost always, when we make our threat assessments, when we look at the world, we end up basing it on the first two pieces of that puzzle, rather than all three.
:* Extending on his earlier comments in a press conference at NATO Headquarters, Brussels, Belgium (6 June 2002) http://www.nato.int/docu/speech/2002/s020606g.htm
2000s

Quote in a letter to Sherwood Anderson, October 1923; as quoted in Georgia O'Keeffe: A Life, Roxana Robinson, University Press of New England, 1999
1917 - 1929

Treatise on Demonstration of Problems of Algebra (1070).
Context: By the help of God and with His precious assistance, I say that Algebra is a scientific art. The objects with which it deals are absolute numbers and measurable quantities which, though themselves unknown, are related to "things" which are known, whereby the determination of the unknown quantities is possible. Such a thing is either a quantity or a unique relation, which is only determined by careful examination. What one searches for in the algebraic art are the relations which lead from the known to the unknown, to discover which is the object of Algebra as stated above. The perfection of this art consists in knowledge of the scientific method by which one determines numerical and geometric unknowns.

"Quoting an Also Private Thought" (this poem is a very slight reworking of an earlier poem "As Has Been Said")
The Poems of Marianne Moore (2003)