Is Michael Phelps the greatest Olympian of all time? The US swimmer's 21 gold medals would appear to end the argument, for no-one else has even half as many.

But that would be to underestimate the wonders the past 120 years have brought…

The numbers: Get your medals out

If you want to turn it into a pure numbers game, here are some of the other leading contenders for the podium: Ukrainian-born gymnast Larisa Latynina (18 medals, nine of them golds); Soviet gymnast Nikolai Andrianov (15 medals, seven golds); and moustachioed US swimmer Mark Spitz (nine golds, a silver and a bronze).

But the same opportunities are not available to all athletes in all sports.

Athlete Jesse Owens, winner of those four glorious golds in Berlin in 1936, was denied another chance by global conflict and the discrimination the black American suffered when he returned to the US from Hitler's Germany.

In the same way, distance runner Paavo Nurmi (nine golds and three silvers between 1920 and 1928) might also have won more, had the Finn not been excluded by officials from the 10,000m in Paris for health reasons, and then banned from the 1932 Olympics for breaking the strict rules governing amateur status after once receiving travel expenses to attend a meet.

There are also those who won plenty but, because of when they competed, might not have faced the most arduous of challenges.

US athlete Ray Ewry overcame childhood polio and long spells confined to a wheelchair to win three golds in Paris in 1900, three again in St Louis four years later and then two more in 1908, but comparing his deeds to those of 21st Century heroes when his triumphs came in the standing long jump and standing triple jump is an inexact science at best.

And what of those who mastered more than one event but could win only a solitary gold?

Britain's Daley Thompson twice proved himself the greatest decathlete in the world, first at the 1980 Moscow Games aged just 22 and then again in Los Angeles four years later, overcoming bigger and stronger rivals across 10 disciplines and two days.

Not all medals are equal. Not all Olympians can race over the same distance in different styles. Only a few can compete in relays.

We need more than arithmetic.

The competition: Dominating across eras

Nurmi's record on the track may never be matched, not least because he was running in an era before East African competition.

That's not to belittle his achievements - he had just 26 minutes to rest between winning the finals of the 1500m and 5,000m in 1924 - but it was a smaller and less diverse field than Hicham El Guerrouj would face when pulling off the same double in 2004.

Then there is Carl Lewis, with his nine golds spread across four events over 12 years, seven of them coming in individual events.

When the American sprinter and jumper dominated at the Los Angeles Olympics in 1984, the Eastern Bloc boycott decimated the fields he would face.

But he had been ranked number one in the world over 100m for the previous three seasons, and had won the 100m, 4x100m and long jump at the inaugural World Championships the previous year against the best from across the globe.

Those who span the eras, who maintain their superiority across Olympiads and against different generations of rivals, are deserving of their own glories: British rower Sir Steve Redgrave, with five golds in five Games; German kayaker Birgit Fischer winning eight, over six Olympic Games, despite having missed those LA Games as part of the boycott; Hungarian fencer Aladar Gerevich, who won medals in the same event six times, 28 years separating his first and final gold.

Owens is famed not only for the number of his golds but for the message they sent out, at an Olympics hijacked to promote the twisted ideals of National Socialism and Hitler's abhorrent doctrines of Aryan supremacy.

Dutch track athlete Fanny Blankers-Koen had got Owens' autograph when she competed in Berlin as a callow 18-year-old. That she came back to the first post-war Olympics in London in 1948 to win four golds, as a mother of two, not only underplayed her athletic gifts (she was prevented from entering the high jump and long jump because athletes were allowed a maximum of four events) but did an incalculable amount to advance the cause of women's sport.

And what of Jamaican sprint legend Usain Bolt, who would win his first Olympic gold at the same Beijing Games where Phelps won eight?

No-one had ever run like Bolt before, and no-one could dream of the times he has run. In an era beset by doping scandals, when the other four fastest men of all time have all been sanctioned for drugs offences, he has sometimes carried his sport and at other times redefined it.

Bolt, like that other most charismatic of Olympians before him, Muhammad Ali, has had an impact across the world unmatched by anyone else.

By the end of these Rio Games he may be up to nine golds. But that number fails to encapsulate either his brilliance or the inspiration he has wrought.

The style: It's the way that you do it

It's not just what you win, but the style you show in winning.

Romanian gymnast Nadia Comaneci's fame stems not just from her tally of five golds, three silvers and a bronze, but the perfect 10s that took the teenager to those titles.

Under today's judging they would not receive the same score. What American Simone Biles can do on the beam, for example, exceeds in difficulty Comaneci's routines but without the same numerical reward, which highlights another flaw with comparisons across the generations.

But it shows how critical flair can be in informing our admiration of great Olympians.

There is insouciance: Czech distance runner Emil Zatopek winning his third gold at the 1952 Olympics in the marathon, an event he had never run before, and doing so by jogging alongside flat-out favourite Jim Peters and asking the Briton whether they were running fast enough.

There is guts, a determination that is almost madness - the USA's Al Oerter, winner of discus gold at four successive Games despite a car crash that nearly killed him, replying to a doctor who told him to retire on medical grounds by saying: "This is the Olympics. You die before you quit."

And there is making the impossible seem humdrum.

Bolt has shattered world records after a lunch of chicken nuggets, with his shoelaces undone, and by running the last 10 metres with his arms spread wide and a huge grin on his face. There has been no-one else like him.

The legacy: Greatness that endures

To truly care about an Olympian's deeds, to push them ahead of so many others who have achieved so much else, we have not only to relish the moment but to let that golden glow linger.

Lewis tested positive for banned substances three times before the 1988 US Olympic trials, initially being banned from the Seoul Olympics before being let off with a warning. For some, those retrospective revelations dulled the lustre of all those medals.

Phelps, at his fifth Olympics, is a markedly different man to the one who left London 2012 to retire. He is more open, more sociable, clearly much happier in his skin.

That may make you warm to him all the more. For the only way to settle on the greatest Olympian is to make your own choice for your own reasons. Greatness may come from public deeds, but it is secured by private affections.

(BBC)