Gordian Knot

When Zoe told the Second Doctor that "you just can't cut through hyperoxide", the Doctor remarked that "the Gordian Knot couldn't be untied, either". Zoe was immediately perplexed, and Jamie, trying to impress the newly-met girl genius, stumbled around for a definition, whereupon the Doctor revealed that it meant, "There's always a solution." (TV: The Wheel in Space)

Behind the scenes

Unremarked in the story is any sort of context for the phrase, which is based on a legendary knot. Prophecies were made of the great man who could untie this complex knot, which many had tried, and failed, to do. Alexander the Great (who was real) was once challenged to untie it. On being told it was impossible, he took his sword and sliced the knot in half.

While Alexander was a real person (born 20/21 July 356 BC), like most historical figures great enough, and old enough, there are many legends about him which didn't actually happen. The Gordian Knot is thought to be one of those.

While the knot was "impossible" to undo with conventional thinking, Alexander attacked it from a different point of view. An early example of what's called "lateral thinking", when one invokes the "Gordian Knot", one is essentially saying, "Think outside the box and you'll find a solution."