Calculus Maple

HAMBURG, Germany -- Cristiano Ronaldo and Kylian Mbappé met for the first time 12 years ago; Ronaldo the Real Madrid galáctico and Mbappé the unknown kid from Paris on a scouting trip.

There's a picture from the day in December 2012, taken at Madrid's Valdebebas training centre. Ronaldo is smiling and giving a thumbs up while Mbappé looks every bit the starstruck teenager.

On Friday in Hamburg they will meet again. Now it's Mbappé, the new face of Real Madrid and Ronaldo, the man coming to the end of his era of greatness which includes success at the Bernabéu that Mbappé can only hope to match. At 39 years old, Ronaldo is playing out his last days as European football's pre-eminent global superstar. Mbappé is one of those in line to take over.

As a 14-year-old, Mbappé's bedroom at his home in the northeastern Paris suburb of Bondy was covered in pictures of Ronaldo. He would watch videos of his goals on YouTube. When his free transfer from Paris Saint-Germain to Real Madrid was confirmed in June -- following in the footsteps of his boyhood idol -- Ronaldo posted a comment on the France international's announcement on Instagram saying it was "my turn to watch." The comment received more than five million 'likes' on the social media platform.

It's a twist of fate perhaps that Mbappé, who has been so open about the inspiration he has taken from Ronaldo, could end up playing a part in ending a portion of his hero's career. Ronaldo has said that if Portugal lose to France in their Euro 2024 quarterfinal it will be his last appearance at a European Championship.

"It is, without doubt, my last Euros," he said after an emotional night against Slovenia in the round of 16.

Ronaldo scored his first international goal at Euro 2004 as a teenager 20 years ago and won his first and only international trophy at Euro 2016. It says everything about his longevity that when he confirmed that he won't play in another tournament there was still an element of surprise, despite the fact that he will be 43 by the time Euro 2028 kicks off. He has been around so long that on Friday he will likely share the pitch with France forward Marcus Thuram, whose father Lilian played against Ronaldo in a World Cup semifinal 18 years ago this week.

After two decades and more than 1,000 professional games, people have stopped trying to guess when he might call it quits. He could yet carry on until the 2026 World Cup in Canada, Mexico and the United States in two years' time.

Ronaldo's career (895 goals in 1,230 games) has been so remarkable that the 24-year-old Mbappé, considered one of the best strikers in the world, would need to score 40 goals a season for the next 14 years to match his astonishing numbers (he currently has 336 goals in 455 games). Real Madrid can only hope he gets close, having finally got their man after a pursuit which began all the way back in 2012 and that trip to Valdebebas.

Mbappé made his name at Monaco and PSG, but moving to Madrid will catapult him to a different level of stardom, just like it did for Ronaldo in 2009. One of the best players in the world joining arguably the biggest club in the world was a match made in heaven when Ronaldo arrived from Manchester United for a then-world record fee of €94 million 15 years ago. There's a similar feeling with Mbappé now.

Ronaldo is perhaps the only player who will know what Mbappé will experience under the intense spotlight in the Spanish capital, but as they prepare to go head-to-head in Hamburg, they're facing very different pressures.

Mbappé is the star at the peak of his powers, expected to score the goals to help France win it. Ronaldo, meanwhile, is battling to show he still deserves his place with Portugal amid fierce debate at home about whether, now past his prime, he's a help or a hindrance to the team.

Both have had their ups and down in Germany. Mbappé scored a penalty against Poland in the group stage but, wearing a mask to protect a broken nose suffered in the first game against Austria, he has not looked at his scintillating best.

Ronaldo, playing at his sixth Euros, is yet to score and missed an extra-time penalty against Slovenia. He broke down in tears after catching a glimpse of his mother Dolores, visibly upset in the stands, but was still able to steady himself to score in the shootout and help send Portugal through.

Ronaldo was left on the bench for Portugal's World Cup quarterfinal in Qatar two years ago by former coach Fernando Santos, a decision which at the time looked to have ended his international career. Reinstated by Santos' predecessor Roberto Martínez, he scored 10 goals during an almost flawless qualifying campaign. Still, the questions won't go away.

Martínez has been asked at almost every news conference in Germany about whether Ronaldo should still start games at this level. Each time, however, he has come armed with numbers to back up his stance. Ronaldo scored 50 goals in 51 games for Al Nassr last season -- albeit in the Saudi Pro League, which is not considered to be at the same standard as those in Europe -- while potential replacements Gonçalo Ramos and João Félix got 12 and 10 for PSG and Barcelona, respectively.

Martínez's style of play -- with full-backs given licence to get forward and lots of crosses into the penalty area -- is designed to suit Ronaldo's predatory instincts and he's not going to change it now despite his captain's failure to score so far. At times against Slovenia there was a sense of desperation about Ronaldo; trying things his body will no longer let him do and demanding free kicks around the box before missing every time.

Mbappé hasn't had it his own way either and there have been suggestions in France that Didier Deschamps' pragmatic approach doesn't get the best out of one of the most thrilling attackers in the world. There's a nagging feeling that a squad which has the greatest depth of talent at the Euros is overly reliant on Mbappé having a magic moment, rather than winning games because of a slick attacking system.

France were one of the pre-tournament favourites, but have managed to reach the last eight without scoring from open play. They had 20 attempts against Belgium in the round of 16, but won thanks to a late Jan Vertonghen own goal. They remain favourites to beat Portugal and reach the semifinals, although it could yet come down to whether Ronaldo or Mbappé has the better day.

Nine years after their first picture together in Madrid, Ronaldo and Mbappé were pictured together again at the last Euros. This time it was in the tunnel at Puskás Arena in Budapest after a 2-2 draw between Portugal and France in the group stage. They walked off the pitch together, swapped shirts and shared a joke, knowing their campaigns would continue on separate paths in the knockout phase. This time it's make-or-break and only one will be left smiling.