While taking a bath, he noticed that the water rose as he got in and realised that this effect could be used to determine the volume of the crown, and therefore its density. The story goes that Archimedes took to the streets naked crying "Eureka!" ("I have found it!").

Into a bowl filled with water to the brim, Archimedes placed a weight of silver and then the same weight of gold, both equal to the crown. He measured how much water was spilled in the two cases, then immersed the crown and found that the water collected in this case was between the two previous measures.

Psychologists have been interested for more than a century in learning what thought processes are involved in such "Aha!" moments - those moments of clarity when the solution to a vexing problem falls into place with a blinding flash.

Now a study published in the journal PLoS ONE by a team led by Dr Joydeep Bhattacharya at Goldsmiths College, London, and the Austian Academy of Sciences, Vienna, reveals how relaxing the brain, and not being too focused, is the key to creativity.

The team studied brain rhythms while 21 volunteers solved verbal problems. Each problem consisted of three test words (for example, head, shade, post) and they needed to generate a solution word (lamp), which would form a valid compound word or phrase with each of the three test words.

Often, the participants reached a state of mental block and could not progress further, marked by excessive amount of gamma brain rhythm (one linked with focused attention). "Focusing or attending too much on a topic might have a detrimental deadlock effect," he says.

This was confirmed when the team gave the subjects hints and found that it was possible, from the brain rhythms, to predict the success or failure three or four seconds later. Those showing higher alpha brain rhythm (one linked with a relaxed brain with free floating ideas) in the right side of the brain would lead to the correct solution. Those showing gamma rhythms and stuck in one particular way of thinking were less successful. "The brain does not lie," he says.

A Eureka! sensation involves minimal monitoring of one's own thoughts and builds on the sentiment expressed than a century ago, when the great scientist Louis Pasteur declared that "Chance favours only the prepared mind."

Sudden flashes of insight don't just happen, but are the product of preparation a when the brain is relaxed and receptive to "free floating ideas," Dr Bhattacharya says, adding that it may be possible one day to reveal when the brain is in a more receptive state by monitoring the electrical signals he studied.

Other work has pinpointed the role of one brain region that influences the "aha" or Eureka moment, called the anterior cingulate cortex, the focus of a new monkey study by Dr Emmanuel Procyk of the Stem Cell and Brain Research Institute in Bron, France, and Université de Lyon in Lyon, France, and colleagues in the journal Neuron.

The team studied how this centre shapes behaviour to get rewards. In this case, the Eureka moment came when they discovered the right targets on a computer screen to get more orange juice. The ACC not only helps evaluate feedback but shapes behaviour to ensure there are more Eureka moments to come.

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