It turns out that the least remarkable thing about Alexander the Great was his sexuality. Having been admired to the point of veneration for more than 2,000 years, Alexander’s star began to fade in the 19th century so that there is now more passionate discussion about Colin Farrell’s sexually ambiguous performance in the Oliver Stone movie. But there are at least two noteworthy things about Alexander: first, he created a previously unimagined empire stretching from the Danube to the Indus and single-handedly changed the nature of the ancient world in little more than a decade out of a life of only 32 years which ended in 323 BC. And second, his life and achievements inspired artists and rulers for the next 2,200 years.

Now the Australian Museum on Sydney’s College Street is hosting (until 28 April) a truly remarkable exhibition, Alexander The Great: 2,000 Years of Treasures, drawn from the collection of the State Hermitage Museum of St Petersburg, which was founded to meet Catherine the Great’s interest in the man and the era. It is worth noting that the extraordinary Hermitage Museum will be celebrating its 250th anniversary next year; we are the hosts of an anniversary celebration in advance.

Given that Alexander was by all accounts and depictions extremely handsome, it is appropriate that Australian Museum director Frank Howarth and his team have created a very handsome exhibition, displaying hundreds of fascinating and beautiful objects. The refinement and delicacy of many of the earliest objects is amazing. The exhibition catalogue has a number of interesting essays pointing out the significance of Alexander’s continuing influence. Although his vast empire did not long survive his death, his lasting legacy was Greek culture in the form of Hellenism influencing the development of the arts from the Renaissance to the present: the absorption of the Greek discovery — art as an imitation of nature — as a basis of Western artistic language. To some extent the essays may overstate the case, but in summary, after Alexander everything was different.

Whatever Alexander did in his bedroom or tent is irrelevant, although not uninteresting in a gossipy way. It is said that his great loves were his mother, his horse Bucephalus and his general and life-long friend Herphaestion, yet he also had two wives and a son. All this while creating an extraordinary empire before an untimely death. This exhibition does him and his influence great honour.

There was never the slightest doubt about the sexuality of Francis Bacon. A major exhibition doesn’t let us forget it. Francis Bacon: Five Decades is at the Art Gallery of NSW until 24 February. Like the Alexander show it is very handsomely presented with beautiful wall colours, impressive gold frames around impressively large pictures under glass, and splendid lighting (especially important given the presence of the glass). This first exhibition dedicated to his work in Australia is curated by the gallery’s curatorial director, Anthony Bond, and contains more than 50 paintings drawn from 37 collections together with effectively displayed archival material from Bacon’s evidently chaotic London studio now recreated in Dublin.

The exhibition tells us that Francis Bacon is widely acknowledged as one of the most important figurative painters of the 20th century: ‘Gutsy, visceral and provocative, his paintings lay bare the struggles of the human condition.’ For evidence of the importance placed on Bacon’s work, we can turn to the market. Portrait, the attractive and informative magazine of the National Portrait Gallery, provides a list of the international top ten auction results for self-portraits. Francis Bacon takes five of the top ten positions. The numbers are staggering: ‘Self-Portrait 1978’ sold at Sotheby’s London in June 2007 for US$38,319,050 and then, post-GFC, ‘Study for Self-Portrait 1964’ sold at Christie’s London in June 2012 for US$33,578,272. It probably isn’t smart to argue with the market, so I won’t, but I’ve had a problem with Bacon. This undoubtedly says more about me than it does about the works themselves. The paintings are beautifully executed using lovely colours and beguiling shapes. It is not surprising that Brett Whiteley was so drawn to Bacon as evidenced in this show. Bacon’s pictures are astonishingly decorative but the treatment of his subject matter keeps me at a distance. Nevertheless this is a very important exhibition which will interest all who care about painting and its development.

Arriving at the gallery, we were struck by the curiously subdued atmosphere in a place that, in the past, I have described as making one feel better just by walking through the door. Not at the moment it doesn’t. On the other hand, the Australian Museum, which long waited for its wake-up call, seems to have received it and is positively buzzing. This led me to think about the importance of personal style of leadership of such institutions and activities. In some curious way leadership affects atmosphere. Ideally it shouldn’t matter, but it does. Another case in point may be this year’s Sydney Festival, which seems to be barely creeping into town.

The festival has lost its flashy free opening night, which may be part of the problem, but that has to be overcome. Another difficulty arises from the decision to present about half the festival in Parramatta, which is an important cultural and population centre and therefore should have its own separate festival and not be sold as part of Sydney.

Meanwhile, over at the Belvoir, director Ralph Myers has just opened a new adaptation of J.M. Barrie’s 113-year-old classic Peter Pan, which should appeal to the theatre’s ageing middle-class audience. That audience will almost certainly see a fresh re-examination of the story that will be anything but twee featuring charismatic newcomer Meyne Wyatt as the wild boy.

Donald McDonald was chairman of the Australian Broadcasting Corporation from 1996 to 2006.