In the 3rd century B.C., a man named Archimedes steadily built a reputation as one of the greatest scientific minds of the era.

Archimedes, who lived in the powerful Greek city-state of Syracuse, on the island of Sicily, was known by all the region’s kings and generals for his pragmatic problem-solving that went far beyond mere theory.

Today, Archimedes is often mentioned as one of the greatest scientific minds in history.

But of all his discoveries, one moment stands out among the rest—not because of what he discovered, but how he discovered it.

The ruler of Syracuse commissioned the creation of a gold crown properly befitting his standing. But after it was delivered, suspicion arose that the goldsmith may have mixed silver into the crown to cut his costs in its creation.

The ruler brought the problem to Archimedes, who faced a difficult question:

How do you verify the purity of the crown without melting or damaging it?

He stewed over the problem day and night, turning it over again and again. One day, growing frustrated with his lack of progress, he decided to take a bath to calm his mind.

When he stepped into the bath, he noticed that some water overflowed over the edges. Suddenly, it hit him.

“Eureka!” He exclaimed, leaping from the bath and running half-naked through the streets to his workshop.

The insight itself was simple:

If the crown were pure gold, it should displace the exact same amount of water as a cube of pure gold of the same weight.

When he conducted the experiment, he found that the crown displaced more water than the cube of pure gold, meaning the goldsmith had mixed in other metals that took up more space.

(I can’t imagine the goldsmith met a particularly happy end…)

But the way Archimedes had uncovered the insight—during an “inactive moment” in his bathtub—is the point I want to talk about today.

You’ve undoubtedly experienced something similar in your own life:

Wrestling with a challenging problem. Making no progress. Then, you go on a walk, take a shower, or go for a drive. And suddenly. Bam! The creative insight strikes. It appears out of the blue, clear as day.

It can feel like a stroke of luck. Even divine intervention. But it’s far from it.

As it turns out, there’s real science that explains this phenomenon—and it’s fascinating to consider how you can use it to your advantage.

A neuroscientist named Dr. Nancy Andreasen spent years studying the patterns that emerged across the lives and careers of history’s most creative people.

She noticed a common trend: Disciplined, structured work followed by rituals of unstructured, undirected, free-floating thought.

Dr. Andreasen conducted ​a series of brain imaging studies​ to understand exactly what happens during these periods of active rest.

She found that the brain is actually highly active during this “rest”:

Regions of the association cortex light up. These are responsible for memory, abstraction, pattern recognition, and meaning-making. The activity allows people to link seemingly distant ideas, combine experiences in novel ways, and surface previously unexplored connections.

Dr. Andreasen wrote:

“We were not [seeing] a passive silent brain during the ‘resting state,’ but rather a brain that was actively connecting thoughts and experiences.”

She coined the term Random Episodic Silent Thinking (or REST) to refer to these periods where the brain defaults to creativity when given the space to do so.

Importantly, it’s the effort and active work leading up to the REST that gives your brain the raw material to work with.

That “lucky break” of creative insight is actually anything but…Your effort, energy, and inputs created it—whether you realize it or not.

I like to think of this as the Archimedes Principle:

Creative Insight = Active Work x Active Rest

Most people default to work or rest, but it’s the collision of the two where the magic is found.

So, as you think about your own work and life, consider this:

Work hard and create space for the work to breathe.

Your next insight may already be there, waiting patiently for you to stop crowding it out.