"Some are born great, some achieve greatness and some have greatness thrust upon them," according to the famous Shakespearean quote.

Muhammad Ali chose to brashly thrust greatness upon himself and then spent a lifetime living up to it.

It was the annotation to most of the three-time world heavyweight champion's towering exploits in the boxing ring.

"I'm the greatest thing that ever lived. I don't have a mark on my face, and I upset Sonny Liston, and I just turned twenty-two years old," the exuberant new king of boxing's glamour division said after his stunning triumph at Miami Beach Convention Center in 1964. "I must be the greatest. I shook up the world!"

A decade on and the other side of a three-and-a-half-year boxing exile that robbed the man born Cassius Marcellus Clay of a chunk of his prime, he was similarly unflinching when addressing the doubters having knocked out George Foreman after eight rounds of the Thrilla in Manila.

"I told you today I'm still the greatest of all time," he growled down the camera. "Never again make me the underdog until I'm about 50 years old.

"I told you I'm the real champion of the world. All of my critics crawl! All you suckers bow!"

In purely boxing terms, those suckers still tend to disagree slightly. The imperious Sugar Ray Robinson tends to edge Ali in all-time polls, such as ESPN.com's 50 Greatest Fighters in History from 2007.

But if Robinson is the man for the boxing purists, it is Ali who breaks out to the wider sports fan – a transcendent figure who continued to represent the celebrated glory of boxing's compelling brutality, while showing the bleak consequences of its inherent darkness through his long and dignified battle with Parkinson's disease.

You might not know football, but you will recognise Pele. Golf might bore you, but you will know the entertainment supplied by Tiger Woods. If basketball is not your sport, Michael Jordan will not have passed you by. You may loathe the spectacle of two men punching each other, but you will know Muhammad Ali.

A key ingredient for the transcendent sporting great is an irresistible narrative. Ali might not dominate boxing through sheer weight of statistics as, for example, Don Bradman does in cricket; in terms of narrative, he outdoes them all.

Pele and Brazil were kicked and fouled to an early exit at the 1966 World Cup before earning dazzling redemption with a third winners' medal at Mexico 1970.

Woods is yet to emerge from the fallow years precipitated by injury and revelations over his private life, remaining stuck on 14 career major championships. Even Jordan interrupted his mastery of the court for a forgettable stint in minor league baseball.

Ali's wilderness years were of an infinitely more serious nature – denied licenses to box in the United States for rejecting military service on the grounds of his religious beliefs and the fact he "ain't got no quarrel with them Viet Cong. No Viet Cong ever called me n*****".

By 1971, when the US Supreme Court unanimously overturned a conviction on charges of draft evasion, Ali was much more than a lion-hearted boxer who would rail against declining skills with success and unfathomable bravery to twice more regain the heavyweight title.

He was a proud Muslim, peace campaigner and black American who stood defiantly against the venomous abuse and discrimination such designations drew. Inside and outside the ring he was an unbowed inspiration.

Any attempted beatification of Ali should take into account his mercilessly nasty humiliation of Frazier around their epic contests. He was no saint.

However, he was a hostage negotiator - helping to secure the release of 15 US hostages in Iraq before the first Gulf War, the man who lit the 1996 Olympic cauldron in a moment of unforgettable poignancy, a recipient of the presidential medal and countless millenial "greatest sportsman" gongs.

Sport is never stronger than when its heroes are embedded in the popular consciousness. Everyone knew of Muhammad Ali's brilliance and beliefs, with each as unflinching as the other, and of his successes and struggles.

Greatest or not, he was an irreplaceable one-off.