William Henry Fox Talbot had many accomplishments. He was Liberal MP for Chippenham; at Cambridge he won a prize for translating a passage from Macbeth into Greek verse. Over the years he published numerous articles in scholarly journals on subjects ranging from astronomy to botany. One thing he could not do, however, was draw well — and it was this inadequacy that changed the world.

While on holiday in Italy in 1832, he became so frustrated by his failure to draw Lake Como satisfactorily using a pencil and a drawing aid known as the camera lucida — his efforts were well below GCSE art standard — that he resolved to find another way to preserve such views. The results are on show in an exhibition at the Science Museum, Fox Talbot: Dawn of the Photograph.

Talbot (1800–77) was not the sole inventor of photography, an honour that belongs to several individuals, independently and collectively, both French and British. In other words, it was a technique whose time had come. But was it a scientific discovery or an artistic one? A case can be made for each.

The Science Museum’s acquisition in 1934 of some 6,500 photographs from Talbot’s collection — the basis of the current exhibition — suggests that his achievement was scientific. Its essence — reproducing images by using negative to make positive prints, and fixing them using chemicals — was indeed technological (his French rival Louis Daguerre came up with a quite different process that created a unique, one-off image on metal). But Talbot — the man who could not draw, even with a camera lucida — became an artist by using a different sort of camera, one with a piece of light-sensitive paper in it.

There is a delicately romantic quality to many of his photographs — especially those taken in and around his house, Lacock Abbey in Wiltshire, and featuring his family, servants and farm-workers. These are rustic vignettes from an early Victorian idyll. To the eyes of contemporaries they seemed so marvellous as to be almost supernatural — Talbot was jokingly accused of necromancy and having made a pact with the devil.

Nearly two centuries later, however, in a world crammed with the successors of Talbot’s works, cascading by the billion on Instagram, these first photographs seem tiny, brown, faded — which many are — and sometimes hard to see at all. At first glance, they seem more like evidence than art and — like so many photographic works — look much better in the catalogue than on the wall.

The same question — is it art or science? — is raised by a nice little seasonal display in Room 1 of the National Gallery: Dutch Flowers. This array of painted bouquets, more than 20 of them crammed into the small gallery and giving it the feeling of a florist’s shop or a tent at Chelsea, is both seductive and repetitive.

The earlier ones are the best; the most beautiful of all were by the first Dutch master of this genre, Ambrosius Bosschaert the Elder (1573–1621). His works are delightful botanical group portraits, in which roses and tulips, fritillaries and irises are arrayed side by side in implausibly lofty arrangements, each petal given meticulous attention.

They are evidence of globalisation — both the plants themselves and the Chinese porcelain vases in which they are often arranged were imports — and also of developing middle-class tastes. Many 17th-century Dutch — not only the wealthy and aristocratic — liked to collect pictures and cultivate their gardens.

As is often pointed out, Bosschaert cannot have worked — as Monet or Van Gogh did — with a bunch of blooms in front of him: the flowers he depicted often come out at quite different times of year. He must, however, have made careful studies of every specimen, then fitted them together into a composition. The effect is close to botanical illustration — to science, in fact. But during Bosschaert’s lifetime, both scientists and artists were engaged in looking more closely, through telescopes, microscopes or just by precise examination of the world around them.

One Bosschaert is delightful, half a dozen — as in this micro-exhibition — are quite enough. The later exhibits are less engaging. As time went on, the pictures, and the blooms in them, became bigger and blowsier. So the National Gallery was wise to leave it at one room. A Dutch flower blockbuster would be fun only for horticulturalists.

At the British Museum, Sicily: Culture and Conquest is a fine, medium-sized affair that could potentially have been much larger. The subject is a huge one, spanning thousands of years and taking in multiple civilisations — since the distinctive feature of Sicilian history has been the way in which this island has seen the fusion of styles and peoples from east and west, north and south.

The lion’s share of the space goes to the ancient Greek city states, perhaps rightly, but personally I find the era of Norman Sicily, with its fusion of Islamic, Byzantine and Western European cultures, even more fascinating. Neither Greek nor Norman Sicily is easy to exhibit, because their greatest achievements were mosaics and buildings, but the BM curators have assembled plenty of sculptures, manuscripts, cameos and other transportable items.

The most impressive of all, though, is a huge photograph showing part of the ceiling of the chapel of the Royal Palace in Palermo. This gives a better and closer view of the paintings, of figurative subjects by Muslim artists in an Egyptian manner, than you get when you’re below the original. If he could see it, Talbot would be proud — and amazed.