Carrying positive momentum into Dubai is important to Williams, who reclaimed the No 1 spot on the women's tour despite her Qatar Open final loss to Victoria Azarenka.
New world number one Serena Williams out to break Dubai duck
As you walk through the narrow corridors of the Dubai Tennis Stadium, it is impossible to miss the images of the former champions on the walls. Roger Federer, Rafael Nadal and Novak Djokovic are among them, proud as they are pictured holding aloft the trophy or photographed in celebration.
On the women's side are Martina Hingis and the four-time champion Justine Henin. Amelie Mauresmo, Lindsay Davenport, Elena Dementieva, Caroline Wozniacki and Agnieszka Radwanska also feature on the stadium's wall of fame.
One leading player is notable by her absence: Serena Williams.
The younger of the Williams sisters will certainly notice that when she arrives in Dubai from Doha, where she won back the No 1 ranking for a fifth time and after an absence of around two years and four months.
Her elder sister, Venus, has triumphed in Dubai twice, in 2009 and 2010, but Serena has not done better than the semi-finals in three previous visits here. The elder sister had been here in 2002 and 2004, but Serena did not make her Dubai debut until 2005 when she reached the semi-finals before retiring at 4-6, 3-4 against Jelena Jankovic. She came back in 2008, but withdrew before hitting a ball, citing a bout of flu. The next year, both sisters were here, together for the first time, and they met in the semi-finals, where Venus prevailed 6-4, 6-4.
Venus is not here this time, but Serena is. Officially, she is the oldest No 1 in the history of the Women's Tennis Association, but this is a brand new Serena, one determined to make up for lost time, an athlete who experienced a competitive rebirth after injury and illness threatened to end her career.
"Since I didn't do the youngest, I figure I'll do the oldest," Williams, 31, said on Thursday when asked about her possible return to the world No 1 rankings for the first time since October 2010.
A day later she was overcome by emotion and broke down in tears after defeating Petra Kvitova to make sure she will replace Victoria Azarenka when the new rankings are released today.
"I didn't expect that reaction at all," Williams said. "I did not expect to not be able to stop crying. I didn't expect to feel that way at all. I just thought I would be happy and just move on to the next round.
"It was completely surprising to me, but it was nice. It was really genuine, and it felt good and completely unexpected.
"There's often times that - I mean, in my particular situation - I never thought I'd play again. Then I thought I'd never be able to win tournaments or grand slams. No 1 was so far off. I mean, it was always a dream, but, I was No 1 when tragedy struck, and it was just an awful thing to happen. So I'm happy that I'm back."
Just four days after winning her fourth Wimbledon crown in 2010, she was celebrating with friends at a restaurant in Munich when she stepped on broken glass. The American had to receive 18 stitches for the cuts, but the injury was much more serious. It required surgery and kept her out of the game for 11 months.
During that period, Williams also confirmed she had suffered a hematoma and a pulmonary embolism, which, in simpler terms, means a potentially fatal blockage of the main artery of the lungs.
"I had a tube in my stomach and it was draining constantly," Williams said. "Gosh, I mean, right before that I had the blood clot. I had lung problems. I had two foot surgeries ... I felt like I didn't do anything to bring that on. I just felt down. It was just the lowest of lows."
Recovery was slow, but she was determined and announced her return with a run to the final of the 2011 US Open, where she lost to Samantha Stosur. But it was the 2012 French Open that really jolted her out of her slumber, if you could call it that. For the first time in her career, Williams suffered a first-round defeat at a grand slam, losing to Virginie Razzano.
"As much as I hate to lose, sometimes it's good for my game and my motivation," she said. "So I think for sure that loss helped me. I have never been so miserable after a loss."
Her determination soon became evident. She won Wimbledon, the 2012 Olympic gold and the US Open before signing off with victory in the 2012 WTA Championships Finals.
Given those successes, the world No 1 was bound to come sooner or later. And now, one of her sponsors is celebrating the achievement with an advert saying: "Age is Just a Number".
At 31 years, four months, 24 days, Williams is the oldest women's world No 1, replacing Chris Evert (30 years, 11 months, three days, in 1985) from the top of that list.
But she is not feeling that old.
"Honestly, I have been saying I feel really young, like I'm 22 or something," she said. "I don't know if it's because I don't play every week, I don't know, but I feel great. Hopefully I can keep it going."
And that is why doing well in Dubai this week is "very important" for her.
Then, of course, she will be really keen to see herself on that wall of champions as well.
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