To many, he is the greatest scientist who ever lived, but a unique collection of Albert Einstein's letters and papers reveals a history of struggle and failure made worse by an apparently shaky grasp of maths.

An archive which goes on sale in London next month with a price tag of US$1.5 million shows how after transforming physics and securing unprecedented celebrity status with his general theory of relativity in 1916, Einstein suffered years of frustration as he failed to top that with "a grand theory of everything."

The 15 manuscripts and 33 letters penned between 1933 and 1954 give a glimpse into a period in Einstein's life when he strayed away from mainstream physics and grappled with the most fundamental questions in the universe.

"At the time, a lot of his colleagues, the theoretical physicists, felt that he was completely off the beaten path and so they didn't really take him seriously," said Howard Rootenberg, of B&L Rootenberg Books in California, who is handling the sale.

Although manuscripts dealing with Einstein's earlier work and his social and political views are relatively common, the collection is unique in helping to document the latter half of his life, when he moved to Princeton University in New Jersey and embarked on a struggle to unite all branches of physics.

But his work in this period made very little impact on contemporaries and he never found his grand theory something physicists are still grappling with.

The archive was collected by Einstein's colleague Ernst Gabor Straus, a young mathematician whom the great physicist selected to help him during his Princeton years.

"A lot of people think of Einstein as a mathematical genius he wasn't," said David McMullan, a physicist at Plymouth University.

He said it was fascinating to see breakthroughs not coming easily to Einstein. "Here we see the greatest scientist who ever lived struggling and being honest about it."

In one sequence of 16 letters Straus criticizes a line of inquiry that Einstein is pursuing and eventually persuades him to abandon it. "It would take somebody with real balls to say to Einstein, 'look, this is wrong'," said Peter Coles, a physicist at Nottingham University.

The papers have never been studied because they have been held by Straus and his family since they were written. Einstein scholars were not even aware they existed until Straus's wife and son decided to put them on the market. They tell the story of the two men's evolving thought process in the vain search for the unified field theory, as the grand theory was called.

Einstein hoped to unite the forces of gravity and electromagnetism under one theoretical framework. But the search turned out to be a series of blind alleys.

"It's a part of Einstein's life that we know comparatively little about," said Tilman Sauer, a senior editor at the Einstein Papers Project at the California Institute of Technology.

"There is a general image of Einstein in Princeton that he was sitting in a kind of golden cage, having lost contact with mainstream physics and doing esoteric calculations. These documents paint a much more nuanced picture of Einstein's later life."