You can't choose your disciples. Andrea Palladio, the most influential individual architect of all time, has had more problems in this area than most. He was lucky, early on, to have followers who took his classical models and made them their own (in the case of Christopher Wren and Inigo Jones) or invested them with character and idealism (in the case of Thomas Jefferson, who built the monuments of the American republic on Palladian principles). His off-the-peg harmonies, however, set out in I Quattro Libri dell'Architettura, four books that represent the Matthew, Mark, Luke and John for neoclassical architects, have also been licence for every pretentious portico and pediment since. They have been the style magazine of choice for snobby Grand Tourists such as Lord Burlington, and for empire builders and dictators the world over in need of a quick fix of grandeur.
Palladio's current followers include many Premiership footballers and - worse - Prince Charles's posse of "New Palladians", led by Robert Adam and Quinlan Terry, who insist that nothing much else has happened in architecture in the 500 years since Palladio was born.
Just up the road from the Royal Academy on Piccadilly, adjacent to Wren's quiet masterpiece St James's, is Adam's pristine office building at 198-202 Piccadilly, completed in 2007, a cut and paste of Palladian stonework - abjectly faithful slabs of façade hung on a steel-and-concrete frame. At a recent Palladian revivalist celebration, Adam bizarrely took Barack Obama's "time for change" message and made it into a rallying cry for country-house pastiche. Modernism was dead; neo-neoclassicism was the new new thing. Would Palladio himself have approved of the New Palladians? Would he have wanted his classical toolbox to be exploited so slavishly? Or would he have looked on them with a wince of embarrassment, like Christ might view a televangelist, and thought it demeaning, kitsch, that his followers brought only puffed-up imitation to the table?
If you would like to find the answers to any of these questions this Royal Academy exhibition will not, unfortunately, leave you any the wiser. What manner of man was Palladio? I'm no surer now than I was before I walked through the four painstakingly collected rooms of his exquisitely detailed plans, drawings and wooden scale models of his buildings. It is never easy to contain an architect inside a gallery - even a gallery whose design that architect inspired - but what is presented here is really only a preliminary sketch of what Palladio meant and believed; the context in which he emerged, 16th-century Venice, is documented without ever coming to life. That Palladio was a lover of abstraction, of Pythagorean principle, is abundantly clear, but the show never examines what forces made him so.
Rule-makers are always divisive figures. A brilliant polemicist - with an eye to the new media created by the printing press - as well as a brilliant draughtsman, Palladio sought, literally, to set architecture in stone. His first patron, Count Gian Giorgio Trissino, who rechristened him after Pallas Athene, goddess of wisdom, sent him away to Rome from his adoptive town of Vicenza and encouraged him to re-create the classicism of the Republic in his redesign of their provincial capital. Wealthy Venetians, particularly the Barbaro family, were quick to see the prestige in Palladio's contemporary take on the Pantheon and the Colosseum, and had him build their country villas in the Veneto. His masterpieces Villa Foscari and Villa la Rotonda were both idealised and genteel; Palladio never put a footing wrong. The algebra of his elevations is preserved in his drawings and plans here, each fifth and quarter and eighth lovingly noted.
Romantic figures have always loathed him for that fastidiousness, or at least they have always loathed Palladians brandishing their rule books as if they were tablets from the mountain. At last year's 500th anniversary celebrations of his birth in Vicenza, local architects organised an anti-Palladio demonstration, a protest against the choke-hold his influence continues to put on the city's imagination. John Ruskin said of Palladio's church San Giorgio Maggiore in Venice that it was "impossible to conceive a design more gross, more barbarous, more childish in conception, more servile in plagiarism, more insipid in result, more contemptible under every point of rational regard". What Ruskin objected to was Palladio's reduction of architecture to a set of logarithms, his imposition of stately order on the rollicking, free-spirited medievalism of Venice. This is Ruskin at his most aesthetically dogmatic - you cannot look at the Canalettos in the London exhibition and agree with his vehemence, but you can still take his point.
One of the more revealing features of the Royal Academy show is that it includes not only templates for the buildings that Palladio made, but also plans for competitions he lost. Among these are his drawings for the reconstruction of the Doge's Palace in Venice, which had been partly destroyed by fire in 1574. He proposed a dignified colonnaded edifice to replace the original Gothic; in the event, happily, his plans were rejected and the vivid original was restored.
It is at moments like this, moments of defeat, that Palladio the working architect begins to come alive. Even his contemporaries could see his rigour as a constraint. Like all great buildings, his were always arguments - for order over chaos, for system over instinct - but there was more to him than cool grandeur. He was also a democratiser in principle: his designs for simple, low-cost housing in Venice, and for barns, cowsheds and dovecotes out in the country demonstrate his faith that his principles could have universal application. His patrons admired him, not only as a purist, but because he always had an eye on cost.
Recently, it has been claimed that an El Greco portrait included in the show is of the architect. This is disputable, but the face is certainly as you might imagine it: stolid, determined, as much an artisan as a visionary, and apparently swearing an oath on the leatherbound book in his hand, careful what he wishes for.
"Andrea Palladio: His Life and Legacy" is at the Royal Academy of Arts, London W1, until 13 April. www.royalacademy.org.uk