He told you he was stubborn. On a sweltering day at the MCG, Alastair Cook made his belated entrance to the 2017-18 Ashes series, with an unbeaten century that was characteristically resilient and uncharacteristically fluent. Cook’s fifth Ashes century was his quickest of the lot, giving England a strong position in the fourth Test, offering genuine hope of reducing their series deficit to 3-1.

Throughout this tour, Cook has brushed off questions about his desire, shrugged off his lack of form, blithely ignored the pundits - paid and armchair - who have speculated that he might already be dreaming of the quiet farmer’s life. All of which may still be true, of course. But while you may question Cook’s ability or question his hunger, there is one trait he has never lost: the cold satisfaction he takes from doing the one thing you say he can’t.

With Joe Root (49 not out) in tow, Cook became the first Englishman to score centuries at each of the five main Australian Test grounds. It was his first century against Australia since that halcyon winter of 2010-11, and coming after Stuart Broad’s four wickets in sticky conditions inspired a very English-style collapse by Australia, England’s chances of emerging from this series with more than a suntan are looking better than they were 24 hours ago.

Ashes fourth Test in pictures Show all 40 1 /40 Ashes fourth Test in pictures Ashes fourth Test in pictures mcg.jpg Over 88,000 people attended the first day's play at the Melbourne Cricket Ground. Getty Ashes fourth Test in pictures tom-curran.jpg Tom Curran reacts to his near-miss after dismissing David Warner on a no ball. Getty Ashes fourth Test in pictures chris-woakes.jpg Chris Woakes celebrates taking the wicket of Cameron Bancroft. Getty Ashes fourth Test in pictures david-warner1.jpg David Warner celebrates reaching his century. Getty Ashes fourth Test in pictures ashes-1.jpg David Warner celebrates scoring a century against England. Getty Ashes fourth Test in pictures david-warner.jpg Warner salutes the crowd as he leaves the field having made 103. Getty Ashes fourth Test in pictures usman-khawaja.jpg Stuart Broad celebrates after dismissing Usman Khawaja. Getty Ashes fourth Test in pictures steve-smith.jpg Steve Smith took little time to race to his half-century. Getty Ashes fourth Test in pictures stuart-broad1.jpg Stuart Broad appeals for the wicket of Shaun Marsh on his very first ball. Getty Ashes fourth Test in pictures stuart-broad.jpg Marsh was saved on review by an umpire's call. Getty Ashes fourth Test in pictures pictures-of-the-day-3.jpg TOPSHOT - Australia's Steve Smith drops a catch from England batsman Alastair Cook on the second day of the fourth Ashes cricket Test match at the MCG in Melbourne on December 27, 2017. / AFP PHOTO / WILLIAM WEST / --IMAGE RESTRICTED TO EDITORIAL USE - STRICTLY NO COMMERCIAL USE--WILLIAM WEST/AFP/Getty Images AFP/Getty Ashes fourth Test in pictures stuart-broad.jpg Stuart Broad successfully appeals for lbw against Jackson Bird. Getty Ashes fourth Test in pictures alastair-cook.jpg Alastair Cook registered his highest score of the Ashes tour at the MCG. Getty Ashes fourth Test in pictures alastair-cook-3.jpg Alaistair Cook celebrates reaching his century on the second day of the fourth Test against Australia. Getty Ashes fourth Test in pictures josh-hazlewood.jpg Josh Hazlewood celebrates dismissing Joe Root for 61. Getty Ashes fourth Test in pictures joe-root.jpg Joe Root hooks Josh Hazlewood to Nathan Lyon. Getty Ashes fourth Test in pictures dawid-malan.jpg Dawid Malan made just 14 before being trapped LBW by Josh Hazlewood. Getty Ashes fourth Test in pictures jonny-bairstow.jpg Jonny Bairstow is caught behind by Tim Paine off Nathan Lyon. Getty Ashes fourth Test in pictures moeen-ali.jpg Moeen Ali edges Nathan Lyon to Shaun Marsh for 20. Getty Ashes fourth Test in pictures pat-cummins.jpg Pat Cummins celebrates dismissing Chris Woakes for 26. Getty Ashes fourth Test in pictures tom-curran1.jpg Tom Curran is struck by the first ball he faces before getting out four just 4. Getty Ashes fourth Test in pictures stuart-broad2.jpg Stuart Broad provided strong support for Alastair Cook to help him reach his double century. Getty Ashes fourth Test in pictures stuart-broad3.jpg Stuart Broad celebrates reaching his half-century. Getty Ashes fourth Test in pictures steve-smith1.jpg Steve Smith dropped Alastair Cook twice during the first innings. Getty Ashes fourth Test in pictures alastair-cook.jpg Alastair Cook celebrates reaching his double century on day three of the fourth Test Getty Ashes fourth Test in pictures alastair-cook1.jpg The Barmy Army applaud Alastair Cook's double-century at the MCG. Getty Ashes fourth Test in pictures james-anderson2.jpg Pat Cummins dismissed James Anderson with the first ball of the day to end England's innings. Getty Ashes fourth Test in pictures alastair-cook2.jpg Alastair Cook was left stranded on 244 after batting for the entire England innings. Getty Ashes fourth Test in pictures cameron-bancroft.jpg Cameron Bancroft is dismissed by Chris Woakes. Getty Ashes fourth Test in pictures usman-khawaja1.jpg James Anderson celebrates dismissing Usman Khawaja. Getty Ashes fourth Test in pictures james-anderson-joe-root.jpg James Anderson and Joe Root spent the most time looking after the ball Getty Ashes fourth Test in pictures james-anderson1.jpg Australian media accused James Anderson of ball tampering during the fourth day of the fourth Test Getty Ashes fourth Test in pictures james-anderson.jpg James Anderson will not face any action over the allegations Getty Ashes fourth Test in pictures england-australia.jpg MELBOURNE, AUSTRALIA - DECEMBER 30: Joe Root, captain of England celebrates after dismissing David Warner of Australia during day one of the Fourth Test Match in the 2017/18 Ashes series between Australia and England at Melbourne Cricket Ground on December 30, 2017 in Melbourne, Australia. (Photo by Scott Barbour/Getty Images) Getty Images Ashes fourth Test in pictures england-australia-2.jpg MELBOURNE, AUSTRALIA - DECEMBER 30: Jonny Bairstow of England celebrates after dismissing Shaun Marsh of Australia with Joe Root and his teammates during day one of the Fourth Test Match in the 2017/18 Ashes series between Australia and England at Melbourne Cricket Ground on December 30, 2017 in Melbourne, Australia. (Photo by Scott Barbour/Getty Images) Getty Images Ashes fourth Test in pictures england-australia-3.jpg MELBOURNE, AUSTRALIA - DECEMBER 30: Steve Smith of Australia hits the ball to make his century during day one of the Fourth Test Match in the 2017/18 Ashes series between Australia and England at Melbourne Cricket Ground on December 30, 2017 in Melbourne, Australia. (Photo by Michael Dodge/Getty Images) Getty Images Ashes fourth Test in pictures england-australia-4.jpg Australia's captain Steve Smith celebrates scoring his century against England on the final day of the fourth Ashes cricket Test match at the MCG in Melbourne on December 30, 2017. / AFP PHOTO / William WEST / -- IMAGE RESTRICTED TO EDITORIAL USE - STRICTLY NO COMMERCIAL USE -- (Photo credit should read WILLIAM WEST/AFP/Getty Images) AFP/Getty Images Ashes fourth Test in pictures england-australia-5.jpg MELBOURNE, AUSTRALIA - DECEMBER 30: Steve Smith of Australia (L) and Joe Root of England shake hands after the drawn result during day one of the Fourth Test Match in the 2017/18 Ashes series between Australia and England at Melbourne Cricket Ground on December 30, 2017 in Melbourne, Australia. (Photo by Michael Dodge/Getty Images) Getty Images Ashes fourth Test in pictures england-australia-6.jpg MELBOURNE, AUSTRALIA - DECEMBER 30: England players thank the Barmy Army for their support after the dran result during day one of the Fourth Test Match in the 2017/18 Ashes series between Australia and England at Melbourne Cricket Ground on December 30, 2017 in Melbourne, Australia. (Photo by Michael Dodge/Getty Images) Getty Images Ashes fourth Test in pictures england-australia-7.jpg MELBOURNE, AUSTRALIA - DECEMBER 30: Steve Smith of Australia (R) and Joe Root of England shake hands after the drawn result during day one of the Fourth Test Match in the 2017/18 Ashes series between Australia and England at Melbourne Cricket Ground on December 30, 2017 in Melbourne, Australia. (Photo by Michael Dodge/Getty Images) Getty Images

Caution is still advised, of course. Four years ago, England were well on top in Melbourne for most of the first three days, effectively 137-1 in their second innings, and still managed to lose by eight wickets. This winter, they were ahead of the game in Brisbane and Perth, and invariably managed to find a rake to step on. For a side that has found all sorts of colourful and creative ways to squander winning positions over the last couple of years, the situation remains uncertain at best.

But on what has been a gruelling and grim tour, Root’s men will happily take it. They would certainly have taken it when David Warner was flaying them to pieces on Boxing Day morning, or when Steve Smith was patiently assembling his latest bone-crushing masterpiece. Instead, against all the odds, it was England’s senior players who stood tall. And on the 17th day of the series, with the Ashes already gone, it was their all-time leading run-scorer who finally graced us with a contribution worthy of his reputation.

On a surface that demanded patience, with the ball increasingly sticking in the pitch, who better to bat on it than a man who has seen off 14 opening partners during his England career? Cook no longer dominates series the way he did at his peak, but he is still good enough to play decisive innings - the 88 against South Africa at The Oval, the 243 under lights against the West Indies. You just have to wait a little longer for them these days.

Earlier, it was Broad who took centre stage, proving once again that he is an entirely different proposition when the ball is moving around. Encouraged by the reverse nip on offer, Broad pitched the ball full, bowled aggressively, and earned his rewards. In the same vein as Cook, he may no longer dominate Tests the way he did at his peak, but he is still good enough to deliver decisive spells. You just have to wait a little longer for them these days.

Cook finally found form in Melbourne (Getty)

Arguably, though, it was Tom Curran who delivered the decisive blow of the day. Before play, he speculated amusingly that having missed out on a first Test wicket when Warner was reprieved by a no-ball on day one, getting Smith instead would be a decent second prize. And just seven overs into the day, there he was: arms outspread, his second ball of the morning, tearing away towards backward point, scarcely believing. The wicket itself? A filthy long hop outside off-stump, dragged on. But nobody cared about that. Smith had departed for a meagre, derisory, insignificant 76. England celebrated like lottery winners.

Root was having a blessed morning. Woakes also struck in his first over, another cut dragged onto the stumps, this time off the bat of Mitchell Marsh. Remarkably Tim Paine went the same way, and in between Broad nipped out Shaun Marsh, who had clipped his way to 50 before being trapped stone dead by a Broad straightener from over the wicket.

Cook occasionally rode his luck but finally brought up three figures in the evening session (Getty)

The absence of Mitchell Starc gave Australia’s tail an elongated look, and without the cover provided by a senior batsman, it folded without too much fuss. Seven wickets in under two hours’ play, six of them bowled or LBW, and Australia had gone from 260-3 to 327 all out. It was England’s best bowling performance of the tour: tickled by fortune to an extent, but a glimpse of how this series might have panned out if England had played as well as they said they could.

This was the way they had intended things to go along: tight, disciplined bowling, Australian batsmen suckered by their own hubris, Australian bowlers gradually ground down into docility. Starc’s replacement Jackson Bird barely cleared 80mph at times. Pat Cummins was suffering from an upset stomach and well down on his usual pace. Josh Hazlewood is a far less threatening prospect when you can simply wait him out. England’s plan had finally come to fruition. Pity they were already 3-0 down.

They still had Nathan Lyon to contend with, of course. There wasn’t much turn for him out there, but his bounce discouraged the batsmen from sweeping, and his control of length offered little to drive. Eventually Mark Stoneman lost patience, tried to hit him back over his head, and was caught and bowler, an acrobatic leap and a right-handed grab. James Vince offered his customary James Vince contribution, an innings composed entirely of adjectives: a couple of exceptional cover drives and then the familiar misjudgment, an absence of footwork, LBW this time, 17 runs scored, another hour of everyone’s time wasted.

Cook left to a well deserved ovation (Getty)

Meanwhile, Cook was cooking: seeing the ball big, picking the gaps, even unfurling the straight drive, which Cook only really brings out these days as a special treat on Christmas and birthdays (and given his birthday is December 25, this was both). Occasionally he rode his luck - there was the odd outside edge for four, a sharp dropped catch off Marsh that Smith fumbled twice at slip, a couple that fell short. But by and large this was comfortable, almost relaxing stuff for England, the perfect antidote to a fraught tour.

With Cook on 93, Smith brought himself on for the final over the day. It felt like a cunning plan. Instead, it was his seasonal gift to England. Cook hewed a full toss to the boundary, nudged off his legs for two to reach 99. Then, with the field up, he pulled a long hop through backward square leg to bring up his 31st Test century: drawing level with Steve Waugh in a most Waugh-like fashion.