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If you had to guess the most indecipherable object in an exhibition about mathematics, codes, linguistics and archaeology, what would it be?

The keyboard, plugboard and rotors of the 1940s Enigma electromechanical cipher machine used by German U-boat commanders?

Or maybe it鈥檚 one of the ancient Linear B clay tablets excavated at Knossos in Crete, inscribed with recognisable numerals and part-pictographic signs such as animal heads, handled cups and chariot wheels?

No, the most mysterious mystery object at the Fitzwilliam Museum鈥檚 unprecedented pairing, , has no symbols.

It is a plain, slightly battered, silver teaspoon belonging to one of the two stars of the show, Alan Turing. Pictured below, the teaspoon was lent by the archives of King鈥檚 College, Cambridge, where the computer pioneer was a student and fellow in mathematics before becoming the UK鈥檚 best-known wartime codebreaker at Bletchley Park.

It was his teaspoon, never before seen in public, and it carries a paper label handwritten and signed by Turing鈥檚 mother. Sara Turing writes that 鈥淭his is the spoon which I found in Alan鈥檚 laboratory鈥�, soon after her son鈥檚 untimely death. Then she adds: 鈥淚t is similar to the one which he gold-plated himself. It seems quite probable he was intending to gold-plate this one using cyanide of potassium of his own manufacture.鈥�

Turing unquestionably died from cyanide poisoning in Manchester, UK, in 1954, aged just 41. But to this day, despite informed speculation, including that of his biographer, mathematician Andrew Hodges, and of the 2014 Turing biopic, The Imitation Game, no one knows how he really died.

Was it a home-lab accident, as his mother maintained? Or suicide, as the inquest concluded, perhaps provoked by Turing鈥檚 1952 conviction for 鈥済ross indecency鈥� at a time when homosexual acts were still illegal, and the disturbing effects of hormonal treatment with oestrogen. These led Turing to tell a male mathematician friend: 鈥淚鈥檓 growing breasts!鈥�

By strange coincidence, a comparable doubt obscures the death of the show鈥檚 other star 鈥� the man who deciphered Linear B in 1952, Michael Ventris. He died in 1956, aged 34, in a car crash, while driving alone late at night near London.

Although Ventris had depression 鈥� provoked by disappointment with his lack of artistic ability as a professional architect 鈥� the inquest declared the crash an accident. Again, what really happened remains unclear, again despite, despite a 2002 BBC TV docu-drama, A Very English Genius.

Codes versus scripts

As for their research, Ventris and Turing were both working on scripts: Linear B and codes such as Enigma are both forms of writing, though separated by more than three millennia. 鈥淭here is an obvious resemblance between an unreadable script and a secret code; similar methods can be employed to break both,鈥� wrote Ventris鈥檚 close collaborator John Chadwick, a classicist at the University of Cambridge, in The Decipherment of Linear B, published soon after Ventris鈥檚 death. Chadwick once confessed to Ventris that he was 鈥渢he pedestrian Dr Watson鈥� to the master decipherer鈥檚 Sherlock Holmes.

Chadwick could not say so in The Decipherment of Linear B in 1958, but he had an inside track on Enigma: he had been a wartime codebreaker (one of a group of classicists at Bletchley) who broke Italian and Japanese codes.

Yet there are important differences between scripts and codes, even though the term 鈥渃ode鈥� is sometimes loosely used for scripts such as Linear B (and its still-undeciphered predecessor, Linear A). The most important is that scripts are in principle readable by anyone trained in writing the underlying language, while codes are designed to conceal their meaning from anyone who does not know the code鈥檚 key, however well trained in the underlying language.

Moreover, decipherers of a script have the advantage of being able to analyse the repeated patterns that inevitably occur in writing a natural language, but codebreakers cannot rely on such giveaway patterns, which are intentionally distorted during encryption.

Inspired guess

Ventris鈥檚 breakthrough was based on an inspired guess about such a pattern, on display in one of his fascinating letters 鈥� to a senior University of Oxford scholar in February 1952. This is immaculately written in English and Linear B.

In it, he guesses that a pattern of three similar, but not identical, Linear B sign-groups 鈥� spotted by a US classicist, Alice Kober, and dubbed 鈥淜ober鈥檚 triplets鈥� by Ventris 鈥� might represent Cretan towns and their inhabitants. For instance, one triplet might translate as 鈥淜nossos鈥� + 鈥渕en of Knossos鈥� + 鈥渨omen of Knossos鈥�.

On the other hand, decipherers are at a disadvantage because, unlike the majority of codebreakers, they usually do not know a script鈥檚 underlying language. This explains why no one knew that Linear B was written in an archaic dialect of ancient Greek. Until his breakthrough in 1952, Ventris had backed a non-Indo-European language, Etruscan.

By contrast, Enigma messages could be safely assumed to encrypt German 鈥� although not necessarily the repeated signoff 鈥淗eil Hitler!鈥�, as The Imitation Game implies with full dramatic license.

Turing and Ventris never met, nor were they aware of each other鈥檚 achievements in codebreaking and deciphering. Bletchley鈥檚 secrets, including Turing鈥檚 role, remained classified long after the founding in 1966 of the A. M. Turing Award. Equally, Turing showed no interest in script decipherment. As for Linear B, Turing showed no interest in script decipherment, notwithstanding worldwide publicity for Ventris after 1952.

Turing was a specialist, dedicated to mathematics and its applications from his teenage years, as the displays of his school report and pre-war papers on computing show.

Ventris, on the other hand, did not shine academically and never went to university. But he had a wider range of knowledge than Turing, not only in ancient and modern European languages, but also in architecture, art and archaeology.

Shared attributes

What the two men shared was intellectual unconventionality, personal modesty, an unusual willingness to collaborate with others 鈥� and general agreement about their respective status as geniuses.

Genius was surely at work in Ventris鈥檚 guess about the Cretan place names. In that letter to the Oxford scholar, he admits that 鈥淭his is one of those guesses it鈥檚 best to keep up one鈥檚 sleeve, because there鈥檚 an extremely good chance of it being completely wrong.鈥�

The wide-ranging catalogue of this exhibition complements engaging interactive displays of wartime codes and Linear B inscriptions, designed to appeal to all ages. It contains 10 contributions by experts in Linear B, the history of cryptography and current methods of encryption, including Turing Award winner Tony Hoare at Microsoft Research.

And in the epilogue, there is a tribute to Turing and Ventris by Cambridge philologist . He says that in the popular imagination both men have become for the 20th century what Jean-Fran莽ois Champollion, decipherer of Egyptian hieroglyphs, was for the 19th.

Indeed, Ventris鈥檚 achievement exceeds that of Champollion, who had the invaluable assistance of the Rosetta Stone, that world-famous chunk of dark grey granite-like stone which provided the key to deciphering ancient Egyptian writing. It was the first Ancient Egyptian/Greek bilingual text analysed in modern times, generating great public interest because of its potential to decipher an untranslated hieroglyphic language.

As Ventris noted in 1951 in one of the 20 work notes he circulated to would-be decipherers (the last of which is in the exhibition): 鈥淭o wait for a bilingual to help us solve our problem is to cry for the moon.鈥�

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