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Prof Jack Copeland told the BBC:
"Turing was hounded, yet he remained cheerful and humorous. The thing is to tell the truth in so far as we know it, and not to speculate.
"In a way, we have in modern times been recreating the narrative of Turing's life, and we have recreated him as an unhappy young man who committed suicide. But the evidence is not there.
"The exact circumstances of Turing's death will probably always be unclear. Perhaps we should just shrug our shoulders, and focus on Turing's life and extraordinary work."
In the first, he follows the events leading up to Turing's design for a fully programmable computer (Ace) at the National Physical Laboratory. In the second episode, to be broadcast on Monday, he explores the life and legacy of Turing. Both programmes are presented by Standup Mathematician Matt Parker.