The fight was made possible by the President of Zaire, Mobutu Sese Seko, a deeply corrupt human rights abuser, who systematically exploited the nation formerly known as the Congo for more than 30 years. Mobutu paid more than $10 million to promote his own image. It was then an unimaginable sum, far more than fighters had ever commanded. But then, he was hiring the very best.
Ali was 32 years old and was attempting to regain the title he had lost to Ken Norton more than a year earlier.
Muhammad Ali appearing at a celebrity fight night in 2013. Photo / Getty
Although many shared his own opinion that he was the greatest 'of ahhhhhl tahm!', they also suspected that he was past his peak, that after 46 fights his talents were eroding.
Above and beyond all this lay a widespread conviction that the 25-year-old Foreman was genuinely invincible, a monster, one of the most terrifying punchers the sport had known. He had won the title with a murderous dismantling of Joe Frazier, and he saw Ali as his lucrative victim.
'My opponents don't worry about losing,' he said. 'They worry about getting hurt.' It was as near as this malevolent, taciturn presence ever came to humour.
By dazzling contrast, Ali was a force of nature; bright, funny, endlessly personable and dauntingly handsome.
Somebody once wrote of a fabled heavyweight: 'Joe Louis was a newspaperman's champion. He always finished in time for the first edition, so the guys could get to the bar before closing.'
Perhaps so. But when Ali started to paint his word-pictures, he made the bar seem a poor alternative. Before the Foreman fight, he ran through his repertoire.
He was contemptuous: 'Foreman's a big old bully from Texas who used to beat up people on the streets.'
He was dismissive: 'Foreman hits hard, sure. But hitting power don't mean nothing if you can't find nothing to hit.'
He spouted yards of his terrible poetry: 'You think the world was shocked when Nixon resigned?/Wait till I whup George Foreman's behind.' And, right across the world, the public lapped it up.
There was a false start when a sparring partner's elbow cut Foreman's eye and both fighters were required to remain in Zaire for a month while Foreman recovered.
Ali spent much of the time storming around town and leading the locals in chants of 'Ali, bomaye!' (Ali, kill him!).
Finally, on October 30, 1974, in the Stade du 20 Mai, before 60,000 people, a bell sounded and a fight began.
The legend has grown, these past 40 years, that Ali offered himself as a target, that he simply lay on the ropes and allowed Foreman to punch himself out.
Well, up to a point. Watching the fight through once again this week, it could be seen that for calculated spells, Ali encouraged Foreman to throw those scything punches, most of which were deflected by arms and gloves. But time and again he would cut loose from the ropes with bewildering combinations to the head.
Foreman grew increasingly confused, unbearably weary. And all the time, Ali talked to him: 'You was sp'osed to be bad, George! Show me something! That all you got, sucker? An' you gettin' tired, George. Ain't no place to get tired ...' And then, in the dying seconds of round eight, Ali found the energy and strength to throw the conclusive combination, and Foreman simply crumpled, exhausted, to the floor.
I recall the London cinema erupting in joy and relief as the count finished and the aisles were awash with dancing, jostling figures.
Ali had that effect; neutrality was not an option. I remember walking out into the Leicester Square dawn, and thinking I should never see anything quite like that again. And I never did.
He would have a third fight with Frazier, a vicious battle in which both men inflicted enduring mental and physical damage.
Then, as his resistance began to dissolve, every contest became an ordeal.
On October 2, 1980, in a casino car park in Las Vegas, I squirmed at ringside as Ali, old beyond his 38 years, was cruelly punished by Larry Holmes.
He took punch after pounding punch to his unprotected head, but his perverse pride would not allow him to fall. So he stood and accepted his punishment, and the odious leeches who had taken his money and bathed in his glory simply shrugged and moved on.
The illness which would ultimately devour him took hold. The speech grew slower and thicker, the reactions ponderous, the decline precipitous.
As his condition became more distressing, it provoked serious moral questions about our readiness to condone such licensed barbarity. After all, if the very best of them could suffer such an excruciating fate, how can boxing hope to protect those who have only their courage to commend them? For many of us, the answer was all too obvious.
Ali left a tangled legacy. Effectively, he legitimised boasting and strident self-praise. Before Ali, sporting modesty was mandatory; you were diffident in victory, gracious in defeat.
After Ali, across all our major sports, the old rules fell into disuse.
We now see an ordinary footballer celebrate a goal, or a journeyman cricketer a wicket, and all too easily we summon up a vision of a brash young man from Louisville, Kentucky.
But the fact that routinely escapes the capering imposters is that the young man happened to be a genius. For once, it is not too inflated a term to describe what he did and how he did it.
In this anniversary week, as Ali's condition grows increasingly hazardous, I shall recall the words of George Foreman, when he made a visit to London two or three years ago.
Foreman had escaped the fate which befell Ali. He was in robust health, and he was enjoying unprecedented riches, having lent his name to a hugely successful fat-free grill.
But he remembered his old opponent, warmly and without rancour.
'People think they know about him, but they don't appreciate just what a fighter he was', he said. 'I mean, I was pretty good. But Muhammad, he was something else.'
Foolishly, I asked if he could imagine another Ali emerging in this generation or the next.
'You mean, will we ever see anybody like that guy again? he asked.
He gave a small, pitying smile and said nothing. Some questions really don't deserve an answer.
- Mail on Sunday