Bradman is incomparable. Despite Smith's elevated Test average, Bradman still heads him by almost 40. A 40 average is a very solid Test career.
There is a certain ruthlessness about Smith's clinical dismantling of a bowling attack that must resemble the way Bradman drove bowlers to distraction. But here again Bradman has the edge; Smith hasn't scored 300 in a day of Test cricket as the knight did at Headingley in 1930.
However, there is some similarity in the way Smith has driven the English crazy with his run accumulation. English commentator David Lloyd related how he alighted at St John's Wood station for what was the first day's play at Lord's, to a PA announcement: "Anyone who knows how to dismiss Steve Smith, please report to the England dressing room."
So exasperated were the English in 1930 that when Bradman was finally dismissed in the last Test, at The Oval, the Star newspaper banner headline simply said: "He's out."
Not an unsurprising reaction, since Bradman's series aggregate was a world-record 974 at the mountainous average of 139, with four centuries, including a triple and two doubles.
Nevertheless, Smith's performance of scoring a century in both innings in the first Test of this series is a feat Bradman never achieved against England.
Comparisons with Bradman are pointless. It's no use asking how Bradman would cope with Jimmy Anderson's swing, any more than it is someone contemplating what Smith's reaction would have been to Harold Larwood's Bodyline attack.
There is, though, the question of where Smith ranks among modern-day Australian batsmen. The best three I have seen are Neil Harvey, Greg Chappell and Ricky Ponting. If he retains his form, by the end of his career Smith's name will be added to that list.
As for who is the best, in the words of British philosopher AC Grayling: Mt Parnassus, the mountain of achievement, has a plateau not a peak. There's room for many.
I'm often asked, "What made Bradman so great?"
I have concluded it was his ability to bat in a match as though he were in the nets. Many batsmen are at ease in the nets, where there's no pressure from being dismissed or to keep the scoreboard ticking over, but it's hard to replicate that approach in the middle.
In most of the footage I saw - apart from the Bodyline series - Bradman is carving up the bowling as though he's up against a school attack. Then I came across some footage from the 1938 Test at Trent Bridge. This is the match where Bradman told his team-mates to come out on the balcony and watch Stan McCabe's batting, because "You may never see the like of it again."
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Despite McCabe's swashbuckling 232, Australia were forced to follow-on.
In Australia's second innings Bradman's footwork was suddenly shuffling rather than fluid, as he battled to save the Test. This time the scoreboard had an effect on his approach. Bradman said in an interview: "I didn't want Stan's wonderful innings to be played in a losing cause."
There is a statistical similarity. Leading in to Lord's, Smith had scored 973 in his last six Tests against England, at an average of 108. That's eerily similar to Bradman's 1930 output.
In achieving this supremacy over the England attack, Smith has completely bamboozled their bowlers. They have been unable to thwart his incredible patience, and consequently he has destroyed their attempts to maintain line and length.
My answer to the PA announcement at St John's Wood station would be: "Bowl the perfect length, where driving is difficult and playing back is dangerous. You must threaten Smith's stumps all the time to exert maximum pressure."
Oh, and by the way, I would add: "You might have to do that for hours on end and it still may not be successful."
That's what it takes to get top-class batsmen out: prolonged, exceptionally good bowling.
Former Australia captain Ian Chappell is a a columnist