To borrow from the language of American tennis, Serena Williams is the GOAT (the Greatest of All Time).

Hyperbole tends to follows every Grand Slam tournament, with the sport's global chattering classes getting carried away and making big, bold claims about the champion's future and her place in history. But this time it isn't hyperbole. Even those of a calm, measured nature are making the argument that Williams - whose Australian Open victory brought her a 19th Grand Slam title - is the greatest. Of course, there will never be total agreement on this, but post-Melbourne it's difficult to hear any other name being pushed as the GOAT.

To be considered the greatest player of all generations, you have to dominate your own time, and there's absolutely no doubt that Williams is the alpha female on the scene today (to mount a counter-argument would be to make yourself sound completely absurd). Maria Sharapova is the world number two, and one of the most successful women of modern times, but Williams now has 16 successive victories against the Siberian, having not lost to her since 2004. That's an astonishing run of results, which tells you more about Williams than almost any other number or statistic. I say almost because the one figure that matters most, the number that will define how people see her, and how she sees herself, is the American's tally of majors.

Williams maintained her dominant winning streak over Maria Sharapova in Oz

Williams' dominant winning streak against Sharapova continued in Oz

At the end of an intense, wildly entertaining final on the Rod Laver Arena, Williams had propelled herself into outright second place in the list of the most successful women of the professional era, one ahead of Martina Navratilova and Chris Evert, and three behind Steffi Graf, who won 22 majors.

She also trails Margaret Court, who won 24 slams, but those tournaments were won in both the amateur and professional eras, and almost half of them - 11 - came at the Australian Open at a time when many of the elite players didn't always travel to the bottom of the tennis earth. No, the 'true' record is Graf's. Williams has said that true greatness comes from holding that record, that she "goes by the numbers and what's written down". But I don't think you should agree with Williams, especially as you have to wonder if Graf would have won quite so many slams if Monica Seles hadn't been stabbed in the back with a boning knife while playing a tournament in Hamburg. Of course, you need to be high up that list to be considered as the GOAT, but I don't believe you necessarily have to be on the top line. In the extraordinary event that Williams never wins another Grand Slam title - it would take illness or injury to derail her - she has already done enough.

This is a player who won her first Grand Slam title at the 1999 US Open, when she was 17, and who is still such a force at the age of 33. She hasn't just fended off Sharapova, she's also beaten several generations of opponents. Only two players have defeated Williams in Grand Slam finals - Sharapova and her older sister Venus.

There's no greater shot in tennis than her serve - there was evidence of that during her victory over Sharapova."

Mark Hodgkinson

Consider how she has taken the sport to new heights with her power and athleticism (there are those who suggest that she is much more than the greatest female tennis player of all time, that she is also the greatest female athlete in history). Another point in Williams' favour: there's no greater shot in tennis than her serve - there was evidence of that during her victory over Sharapova. In her mid-thirties, she is still improving, with her coach Patrick Mouratoglou suggesting that her delivery is more potent now than it has ever been.

Ponder, too, the aura that Williams has built up, and how she terrifies most of the locker-room (though Sharapova isn't among that number, despite that run of losses). Whether Williams wins or loses, it's generally on her terms. She's capable of defeating herself - as despite all her achievements, she is still badly affected by nerves. But when she's firing, when she's healthy, motivated and hitting everything out of the middle of her racket, it's almost impossible to stop her. Tracy Austin once told me that she had never seen another player who has such control of her own destiny.

Together, Serena and Venus have done much to inspire the younger generation of black female players. Taylor Townsend, an African-American teenager, recently broke into the Top 100, while Sloane Stephens has already shown her class at the highest level - she defeated Serena on the way to the semi-finals of the 2013 Australian Open.

But Serena's real legacy to the sport is her own greatness.

Mark Hodgkinson is the author of 'Game, Set and Match: Secret Weapons of the World's Top Tennis Players' (Bloomsbury, May 2015).