TURIN, Italy -- It turns out Cristiano Ronaldo is not enough. The Portuguese scored in both legs of Juventus' Champions League quarterfinal against Ajax. He put the Bianconeri in front at the Allianz Stadium on Tuesday. They wouldn't even be here without his face-saving hat trick against Atletico Madrid in the round of 16. The 34-year-old kept up his side of the bargain. Ultimately, though, Juventus came up short.

What Ajax have achieved is stunning. As Erik ten Hag noted on the eve of the game, "it's already a big deal to still be in Europe after winter." Ajax had not reached the competition's knockout stages in 13 years. They began the campaign in the second qualifying round. When Ajax played Sturm Graz at the end of July, they couldn't have imagined they would be the first Eredivisie side to reach the Champions League semifinals since PSV in 2005. The game has become so economically stratified since then.

Consider the wealth gap. The €112 million Juventus spent on acquiring Ronaldo is €20m more than Ajax's annual revenues. The team's wage bill is €4m short of what the five-time Ballon d'Or winner makes before tax.

But sometimes ideas trump investment. Ajax deserved to win in Amsterdam a week ago and outplayed Juventus in the second half Tuesday for a 2-1 win and 3-2 aggregate edge. They remain unbeaten on the road in Europe despite going to Bayern Munich, Real Madrid and now Juventus. The feat of coming back from behind in the backyard of a team who are about to become the first in Europe's top five leagues to win the title for eight straight years is jaw-dropping.

Not least because Ajax did not look themselves in the first half. Six fouls in the first 15 minutes stopped either team getting into a rhythm. Frenkie De Jong's influence was initially more limited than it had been in the first leg, perhaps because of the muscle injury he sustained at the weekend, and the early loss of Noussair Mazraoui to injury meant Ajax were without either of their first-choice full-backs with Nicolas Tagliafico also missing the game through suspension.

Ronaldo's goal came just as Ajax were beginning to build some pressure, too. Teams of lesser character would have resigned themselves to their fate, thinking this is just the way it is. Ronaldo has scored 65 goals in 78 knockout games. He has won this trophy four times in the past five years. This is what Madrid were missing when Ajax dumped the holders out of the competition last month.

But Ten Hag's players never let any doubt creep into their minds. That in itself is astonishing. Ajax are the youngest side in the competition. Legs are supposed to tremble under this kind of pressure. But this team didn't waver an inch. Before kickoff, Juventus' vice president Pavel Nedved was asked what stood out to him about their opponents in Amsterdam. "I was surprised by the composure with which they play," he said.

That composure came to the fore again Tuesday. Ajax got back level within six minutes of going behind. A deflected Hakim Ziyech shot found its way to Donny van de Beek, who didn't look up to check whether he was onside or not, focusing solely on beating Wojciech Szczesny. The flag stayed down, as it should in today's VAR era, correctly too because Federico Bernardeschi, late to step up, played the Dutchman onside.

A different Ajax emerged after the interval, the one we've become accustomed to over the course of this season. It was as if they'd overcome whatever had been inhibiting them in the first half. It was as if they realised there was nothing to be afraid of.

They proceeded to cut Juventus to shreds. Were it not for Szczesny, the Old Lady's man of the match, the defeat would have been heavier. The Poland international needed a strong left hand to repel a Ziyech shot and then tipped a Van der Beek curler over the bar with his right. Like Ronaldo, he cannot be blamed for Juventus' elimination.

In the moments before Matthijs de Ligt's towering header, it looked as if Ajax might be found guilty of attempting to walk it in. Dusan Tadic and Ziyech both passed when they had ample time to shoot, letting Juventus' defenders off the hook. But their 19-year-old captain -- just let that sink in for a moment -- ensured Ajax left with no regrets, emulating Gerrie Muhren, who scored the decisive goal in the Dutch side's last win over Juventus 45 years ago.

And so the dream lives on. Ajax are in the semis for the first time since 1997.

This wasn't supposed to happen. The best team they'd had in years was picked apart two seasons ago. Just the Europa League final in Stockholm felt like a fairy tale in the modern game. No one thought Ajax would be back and do even better. Davinson Sanchez and Davy Klaassen left for the Premier League. Last summer, Justin Kluivert decided it was time for him to go to Serie A.

The rest made a pact to stay together one more year, curious to see what might happen if they realised their potential. It's fair to say they have exceeded all expectations. In the next round Ajax will play Spurs -- a team consisting of alumni like Toby Alderweireld, Jan Vertonghen, Sanchez and Christian Eriksen -- or Manchester City, whose coach Pep Guardiola learned everything he knows under Johan Cruyff.

Whatever happens, we can safely Ajax will win. It is the triumph of their idea.