It is one of Australia's greatest mysteries. On December 1, 1948, an unknown man was found dead on Somerton Beach in Adelaide.

Nobody knew who he was or how he died. But as the days went on, the case proved to be anything but straightforward.

Seventy years later, it remains unsolved.

It's a mystery that has captivated sleuths for decades.

But none more so than Derek Abbott, an engineering professor from the University of Adelaide, with an interest in mathematics, cryptography and forensic engineering, who is still trying to solve the case today.

Derek Abbott, a University of Adelaide professor, is fascinated by the Somerton Man case. ( ABC News: Malcolm Sutton )

In a twist akin to something you'd find in a detective novel, Derek is married to a woman he believes holds the answer to the man's identity — and a recent breakthrough involving DNA means he might finally be able to prove it.

"Here is a man who has passed away and we don't know what his name is. And giving someone their name back is perhaps the most important thing we can do," Derek said.

Who was the Somerton Man?

In 1948, the deceased man found on Somerton Beach quickly became known as "the Somerton Man".

He was well-built, clean shaven, and found nicely dressed in a suit and tie. He had no real belongings on him, no identification, and the tags on his clothes had been removed.

But police later discovered a secret pocket in the waistband of the man's pants.

Inside they found a piece of paper rolled tightly, bearing the words "Tamam Shud". This phrase appears at the end of the Rubaiyat of Omar Khayyam, an 11th century book of Persian poems.

And when translated, the words mean "the end", or "finished".

In the weeks following this discovery, a businessman came forward with a copy of the Rubaiyat. He claimed it had been thrown into his car through an open window. And when police turned to the back of the book they found the final page, where the words Taman Shud should have been, torn out.

More intriguing though was the writing on the back cover of the book — five lines of letters and at least one phone number.

A police scan of the handwritten letters and numbers found in the back of the book. ( Supplied: Australian Police )

The letters couldn't be decoded, but the telephone number led police to the doorstep of a young nurse.

Did she know who the Somerton Man was?

Despite now being buried, a plaster cast of the Somerton Man's body had been made. When the nurse was asked to identify it, she looked like she was going to faint.

But she denied ever knowing the man.

At the time, police felt sure the nurse knew more. But without evidence of motive, no more leads, and no real suspects in the frame, his death was declared a suicide and the case went cold.

The nurse asked for her name to be scratched from the case file — and with murder ruled out, the police had no choice but to comply.

Entwined in a cold case

For several decades, many people worked hard to solve the Somerton Man mystery.

Most gave up — but not Derek.

Derek Abbott spent years examining the letters in the abandoned copy of the Rubaiyat. ( ABC News: Malcolm Sutton )

First, he tried cracking the code on the back cover of the book thrown into the businessman's car.

But six years of exhaustive research led him to a dead end.

"We came to the conclusion that it's simply just the first few letters of words of the English language, rather like a memory aide for a shopping list," Derek said.

Next, he reached out to Gerry Feltus, an Adelaide detective with over 40 years of experience in solving crimes, who for the last decade had been looking into the Somerton Man case.

"He had the actual original piece of paper that was found in the Somerton Man's pocket," Derek said.

After meeting Gerry, Derek became interested in finding out the name of the nurse, whose phone number was found on the back of the book.

But by the time he discovered her name — Jo Thomson — she had passed away.

So he turned his attention towards the nurse's son, Robin, who was born the year before the Somerton Man died.

And at this point, Derek discovered a very important clue.

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"One fine day, [his mum] just took him by the hand and took him to dance classes — and he stuck with it and became a professional ballet dancer," he said.

Derek thought back to the notes the coroner made in 1948 and remembered the Somerton man had some identifying features, like well-defined calf muscles.

"Trained dancers will tend to have pronounced calf muscles, much higher up the calf than a runner or a cycler," he said.

But by the time Derek tracked Robin down, he had also passed away.

Luckily, because the man had been a professional ballet dancer, Derek was easily able to dig up old photos of him.

"I found a fantastic newspaper photo of him that had a close up of his ear, and lo and behold, I found he has the same strange ear feature as the Somerton Man," he said.

He also found a close-up photo of Robin's smile, showing he shared another genetically-inherited trait with the Somerton Man — his incisor teeth were missing.

"Coupling this information together with the fact that Jo Thomson was unmarried in '47, and the Somerton Man had her number ... it seemed to me [they] had a liaison together and she had Robin," he said.

After spending almost five years trying to crack the case, Derek felt like he was finally on to something.

So he set out to find out if Robin had any children, which is how he met Rachel Egan — a woman who now plays a major role in his life.

An affair of the heart

Rachel is Robin's daughter, which means if Derek's theory is correct, she is the Somerton Man's granddaughter.

Not that Rachel knew anything about this while she was growing up. As a baby she'd been put up for adoption by her parents, Robin and Roma.

Derek Abbott and Rachel Egan hope the Somerton Man's DNA will provide answers. ( Supplied: Derek Abbott )

"I grew up not knowing I was adopted, however, there were many aspects of me and my adoptive family that were very different ... I always had a passion for ballet, and dance, and theatre and I always wondered where that came from," she said.

Then, when Rachel was in her early 20s, her mother Roma made contact with her.

She explained she had been a dancer with the Australian Ballet and had fallen pregnant with Rachel while dancing in New Zealand.

Once re-connected, Rachel moved to Brisbane to be closer to her mother, which is where Derek found her.

He sent her a letter about the Somerton Man, and while at first they discussed the case, they soon started talking about their own lives.

"[It] turned out that we'd had a lot of similarities with our upbringings ... like me he wasn't planned, his parents were quite young and they were students," Rachel said.

Derek and Rachel arranged to meet.

"We collected him from the airport and spent a few days together, looking at photos and sharing information," Rachel said.

But it wasn't all business — by the end of the weekend, Derek had proposed to Rachel.

To everyone around them, their engagement seemed extremely odd — especially Gerry, the detective who'd been looking into the cold case.

"I just couldn't believe it, and I thought 'What the hell is going on here, has this guy married this girl, to just try and pursue his DNA subject?'" Gerry said.

The couple have since made a family together, and for this reason Derek prefers to keep his personal life separate from his work.

He and Rachel now have three children — a four-year-old daughter and three-year-old twins — who are potentially the Somerton Man's great-grandchildren.

"The fact that my family is now entwined with the Somerton Man makes things perhaps a bit more complicated … [but] as a scientist, when I do my work and my scientific research I have to be neutral about things, I have to be dispassionate," Derek said.

Breakthrough in 70-year-old case

To prove his wife is, in fact, the Somerton Man's granddaughter, Derek needs a sample of the dead man's DNA. Twice he's petitioned the South Australian government to have the body exhumed, and twice his request has been denied.

But he recently had a huge breakthrough with the case.

Professor Jeremy Austin is helping Derek Abbott examine the Somerton Man's DNA. ( ABC News: Malcolm Sutton )

"I have found three excellent hairs on the [plaster] bust that have their roots at the right development stage for extracting DNA and I have given these to Jeremy Austin at the Australian Centre for Ancient DNA at the University of Adelaide," Derek said.

But the results could take up to a year to process.

So, in the meantime, he is preparing his third petition to exhume the Somerton Man's body.

And in a strange way, Derek feels he owes quite a lot to that nameless man, found on an Adelaide beach so many years ago.

"The Somerton Man has brought me to the place I am today," Derek says.

"I have the children I love, and might not have existed ... if it wasn't for him."