Rock star mathematician Cédric Villani says Nobel-Prize winning mathematician John Nash, who died in a car crash on 23 May, had made a startling discovery before his death.

Speaking at the Hay Festival, Villani said he had spoken to Nash about a "replacement" equation for Albert Einstein's theory of relativity at an event in Norway on 20 May.

Villani, 41, who won the prestigious Fields Medal in 2010, said Nash was "really inspirational" and came up with "ideas completely off stage," the Times reported on Saturday (30 May).

"I will certainly look into it," he said. "He explained it to me. He thought he had discovered a replacement for the equation."

"He qualifies as a genius," he said. "I had the honour of being the chairman at a lecture he was giving. He told about the equation he had tried to devise in his study of general relativity. He was summarising the problem with difficult equations. It was amazing."

John Forbes Nash Jr. died along with his wife of 60 years, Alicia, in a car crash in the US State of New Jersey. He was 86.

Several days before he died, he was awarded the prestigious £500,000 Abel Prize for mathematics along with his colleague Louis Nirenberg, for his work on non-linear partial differential equations.

Princeton University mathematician Nash also won the Nobel Prize for Economics in 1994 for his work in "game theory", developing "an equilibrium concept for non-cooperative games that now is called Nash equilibrium".

Among other awards, Nash also won the John von Neumann Theory Prize (1978) and American Mathematical Society's Steele Prize for a Seminal Contribution to Research (1999).

Although his theories are now used in everything from artificial intelligence to economics, Nash was also well-known for overcoming mental illness, as portrayed in the Academy Award-winning movie A Beautiful Mind (2001).