The mystery of how a mute boy aged 12 became the first deaf-born person to be taught to speak has been solved after more than 300 years with the discovery of his school book.

The cure of Alexander Popham, a descendant of the judge who sentenced Guy Fawkes to death, was so controversial in the 17th century that the scientific establishment was split over who should be given credit for it.

The Royal Society was riven by competing claims made by William Holder, a musician and ear expert who counted Sir Christopher Wren among his allies, and John Wallis, a code-breaking mathematician and linguist who had on his side Lord Brouncker, the Royal Society's founding president.

The pair engaged in a decade-long battle of claim and counter-claim that remained unresolved until this week, when a small, leather-bound notebook was discovered at a country house hotel. It contains the only surviving evidence of the practical methods used to teach Alexander.

The book, which features diagrams of how Alexander should control his throat and mouth to make certain sounds, carries an inscription in the front that reads: “Alexander Popham, his book, Oxford, November 8, 1662.”

The writing, which has been authenticated by a linguistics researcher at Oxford University, is in the hand of John Wallis, the mathematician credited with cracking the code used by Charles I during the English Civil War, allowing the Parliamentarians to read his letters to the Queen.

Philip Beeley, of the faculty of linguistics and philology at Oxford, believes that the book is the “smoking gun” that will prove that Wallis deserves the credit. Holder's claim that Alexander had spoken “plainly and distinctly, and with a good and graceful tone” under his tuition and was merely suffering a relapse when Wallis later took him on would cease to be credible, Dr Beeley believes.

The book, the size of a pocket diary, was found at Littlecote House, the Pophams' ancestral home and now a hotel run by Warner Leisure. Barry Levy, who entertains guests at the hotel as a jester, said that he first saw the book when he dropped a juggling ball on the floor of the butler's pantry, which is now used as a store room.

“We had been moving things in and out from some of the rooms — portraits and things like that,” he said. “The book was just on the floor. I didn't know what it was. It just looked old.”

The book begins with instructions on how Alexander should place his tongue on his palate and how wide his mouth and throat should be to make different sounds. It then lists vocabulary considered essential to a young aristocrat, beginning with “God, spirit, angel, Devil” and moving on to parts of the body: “Back, breast, belly, buttock, thigh.”

The book is divided into sections, which show progression from simple vocabulary to more complicated phrases, including one that gives a clue as to the incentives Wallis used in his tuition. One sentence reads: “If you will not speak, then you must not eat.”

Alexander's mother first sought help for her son's muteness in 1659 by commissioning Holder, who investigated the boy's ears and the way they reacted to loud noises. He found that Alexander reacted to very loud drumbeats and claimed that the boy's eardrums tautened, allowing him to hear his own name.

On September 30, 1662, his mother turned to Wallis, who had taught speech to a boy who had lost his hearing at the age of 5, and offered him £100 (the equivalent of £9,600 today) a year to instruct her son.

Dr Beeley, visibly excited upon seeing Wallis's instructions for the first time, said that until now the only evidence of how Alexander had learnt to speak were theoretical accounts published by Holder and Wallis, but no evidence of actual tuition.

“Up until now I'd say that the issue has not been resolved. Most recently the opponents of Wallis had the upper hand. Now that we have concrete evidence of the approach that Wallis took we may be able to solve this. It is something every historian dreams of. It is the smoking gun.”

Janet Corbin, Alexander's direct descendant nine generations removed, and her sister Bea Salter, wondered whether they would exist if their forebear, who married and had four children, had not learnt to speak.

Ms Corbin said: “It's absolutely magical. It's exciting because it's physical. People keep pieces of furniture, but this is very personal. You think: it contains his sweat.”

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