intractable

What it means

1. Not tractable; not able to be managed, controlled, governed or directed.

   And I cannot but expect that this will repeatedly lead to the discovery that an initially intractable problem can be factored after all.

   1972, Edsger W. Dijkstra, The Humble Programmer (EWD340)

2. mathematicsNot able to be solved in polynomial time; too difficult to attempt to solve.
3. Difficult to deal with, solve, or manage. (of a problem)

   Working with many nations in this room, we are solving decades of intractable challenges, and we are settling years of unfinished business.

   2026 September 22, Donald Trump, speech at United Nations

   1 more example

   Work—bureaucratic work in particular—poses a series of intractable dilemmas that often demand compromises with traditional moral beliefs.

   1988, Robert Jackall, “Chapter 1: Moral Probations, Old and New”, in Moral Mazes: The World of Corporate Managers, Twentieth Anniversary edition, →ISBN, page 12

In a sentence

And I cannot but expect that this will repeatedly lead to the discovery that an initially intractable problem can be factored after all.

1972, Edsger W. Dijkstra, The Humble Programmer (EWD340)

Where it comes from

1. Proto-Indo-European*né
2. Proto-Indo-European*n̥-
3. Proto-Italic*n̥-
4. Latinin-
5. Middle Englishin-
6. Englishin-
7. Englishtractable
8. Englishintractable

From in- + tractable.