Knowledge and belief – they are like chalk and cheese.

Richard Gasquet knows that he is a stunningly gifted tennis player with one of the best backhands in the world; Stan Wawrinka believes that, as a stunningly gifted tennis player with one of the best backhands in the world, he belongs with the big boys at the very top of the game. He knows that because he has two Grand Slam titles to prove it. But maybe, just maybe, Gasquet is beginning to believe now.

His 6-4, 4-6, 3-6, 6-4, 11-9 win over the French Open champion Wawrinka was the sort of battling, gutsy, determined victory that the French have been hoping to see from their man since he first picked up a racket. And it is the sort of battling, determined, gutsy performances he has so rarely managed to produce on the Grand Slam stages around the world.

This was only Wawrinka’s second quarter-final in SW19 in a lifetime of trying. But, as a new member of the Multiple Grand Slam Club, he was loving every moment on the slick, green turf. Even if his game is not specifically designed to succeed on grass, he was on a roll and he was having a blast.

Gasquet, on the other hand, had reached the semi-finals here back in 2007. He had come from two sets down to beat Andy Roddick in the quarter-finals and, fair enough, he lost to Roger Federer in the next round, but in those days, everybody lost to Federer in the next round. Federer had won every round he had played at Wimbledon since 2003. This was it, then: Gasquet was ready to make the big breakthrough. But it never happened.

There was one, brief glimmer of hope a couple of years ago when the world No.20 reached the last four at the US Open but once there, he was clobbered in straight sets by Rafael Nadal. Since then, he had not got beyond the fourth round in any of the major championships – until now.

For a while there, too, it did seem as if the quarter-finals was as far as he was going in SW19 this year. From taking the first set, he blinked at just the wrong moment, throwing in a couple of double faults as he served to stay in the second set. In a couple of minutes, he had been ousted from the driving seat and was now been relegated to the back of the bus as Wawrinka bludgeoned that backhand and served his way to a 2-1 lead. And then he double-faulted on set point in the fourth set and Gasquet breathed again.

Now as he got stuck into the fifth set, it all came down to belief. Gasquet thought he had it as he broke the Swiss and went to serve for the match at 5-3. Wawrinka appeared to have it in bucketloads when he broke straight back, turned to his box and tapped his temple. The message was clear: I’ve got it sorted between the ears. Don’t worry.

It could have been a real body blow to Gasquet’s ambitions. What could he do to stop his confidence evaporating? What he did was pour every ounce of strength into every point. He ran himself ragged as he chased down every ball – and Wawrinka was trying to pull him all over the court – and he stuck to his plan: serve smart, hit that backhand and, if you can possibly manage it, attack the net.

His coach, Sebastien Grosjean (one of the finest grass court exponents of his generation), has been trying to get Gasquet to come forward for years, ever since they started working together at the Australian Open in 2011. Then again, every coach Gasquet has ever had has told him to attack.