What do these three men - all comfortably beyond the age of retirement - have in common: Sean Connery, Alfred Brendel, George Steiner?

There may seem little to link a Hollywood star, a consummate concert pianist and a maverick intellectual, but in the past few days, in their different ways, all have been tending to their legacy, determined that the world should remember them, not through the hit-or-miss judgments of the internet or the viperous comments of their critics, but from the stamp they put on their own lives. Not for them the dependency culture which this week's report on our ageing population complains about: on the contrary, they depended on nothing but their own determination to tell things their way.

It may seem odd to worry about your reputation, just near the point where it really is not going to matter much any more, but, listening to these three in Edinburgh as they rounded the final bend, I found the sheer energy they put into their final performances as impressive in its way as Britain's coxless rowing four in Beijing going for the finishing line as if life itself depended on it.

The analogy is not as absurd as it might seem. Professor Steiner talked of exercising the brain in the same way as you exercise a muscle, and said that his greatest fear was losing his powers of recollection. He had set himself the task every morning of picking a random passage from a book and then translating it into each of the four languages he speaks, in order to ensure that his compendious mind was still in working order.

“If you let memory slip, then you run the risk of losing all the treasures of time,” he told his rapt audience at the Book Festival. Approaching 80, Steiner has gathered together in My Unwritten Books some of the subjects he feels he will not have time to address properly, and has devoted an essay to each as “a kind of good-bye to what may not be”: such things as intellectual envy, comparative education, Judaism - and sex, to which he devotes an eye-popping chapter; he is less embarrassed about his discourse on the language of eroticism than some of his readers have been, not least because it allows him to claim to have made love to women of several nationalities and to have remembered precisely what each of them said at the climactic moment. No loss of potency there.

What Steiner seemed keen to demonstrate was a refusal to conform. He has never been loved by the academic Establishment (even in my days at Cambridge his lectures were held in some distant hall, well away from the cloistered premises of the English faculty), and though he has been subjected to mockery and disdain at the hands of those less well read than he is, he has never played it safe by going along with the latest literary trends. His range is extraordinary, and he does little to conceal it; at the same time he is more honest about himself, his failures and his triumphs, than most of his rivals could bear to be.

A few days later, in the Usher Hall, the audience rose, emotionally, to applaud Alfred Brendel's farewell concert - his penultimate solo performance in Britain (the last was given at Aldeburgh on Saturday; there will be three more orchestral concerts on these shores, then that's it.) At 77, he may feel that those pyretic fingers are beginning to stiffen, but no one listening to the Mozart, Beethoven and Schubert sonatas he gave us would ever have suspected it.

For Brendel, unlike Steiner, striving for perfection is a case of narrowing the focus, seeking ever deeper levels as he grows older, rather than broadening the range, Steiner-style. His mantra has been to play the works of these three composers as they intended for them to be played, keeping the interpretation simple. “If I belong to a tradition it is a tradition that makes the masterpiece tell the performer what he should do and not the performer telling the piece what it should be like, or the composer what he ought to have composed,” is the Brendel dictum.

The three encores he gave last week's audience, ending with a Schubert impromptu, were greeted by a sustained standing ovation, the audience saluting a lifetime's achievement with wave after wave of unbridled ecstasy. What they were applauding was Brendel's single-minded dedication to perfection - and it is for this that he will wish to be remembered.

Sean Connery's approach to securing his legacy is rather different. While most movie celebrities opt for the confessional mode, throwing open their hearts and spreading out their linen, however dirty, for all to see, in order to elicit our sympathy, he has taken a very different route. He has dispensed with the services of conventional biographers, and chosen instead to write about himself and his country - Scotland. A self-taught man, he has collaborated on a book that examines his nation's history, characters and idiosyncrasies.

In the course of it he has shown that he is widely read, holds strong and unconventional views and is not afraid to speak his mind. He wants to be remembered, not as a star, but as a serious individual who has a life beyond the fripperies of the movie world - in short, a hinterland.

The result may be unexpected, but it tells us more about the man behind James Bond than any number of warts-and-all disclosures.

What all three of these men demonstrate is that old age is an opportunity for self-expression rather than simply the final coda to a working life - and that is a useful lesson to the rest of us as we contemplate the challenges of old age; those retirement years could be every be every bit as important in defining our lives as youth and middle age do. It might even be an unexpected pleasure. As George Burns the comedian so aptly put it at the age of 100: “I'm very pleased to be here. Let's face it, at my age I'm very pleased to be anywhere.”

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