Photography is a mechanical art. The photographer points a lens at an object, records the image on a plate or film or, today, in digital memory. Therefore all photographs should be similar, the hands of individual photographers unrecognisable. Yet the new Photographs Gallery at the V&A, which opened on Monday to showcase the world's oldest museum collection of photographs, reveals the apparently limitless variety of the art and the utterly personal genius of great photographers.

A photograph of a steam train taken by Alfred Stieglitz in 1902 hangs near Henri Cartier-Bresson's 1932 picture Behind Gare St Lazare, Paris, on the blue-painted wall of the long, elegantly restored, Victorian gallery.

Both black and white prints portray a ragged industrial landscape of rail tracks in brooding weather. But they are so profoundly different that you almost feel you are looking at two different art forms, two technologies. Cartier-Bresson's image is so light and mobile, an impression of a passing moment, whose meaning is as enigmatic as it is poignant. Stieglitz gives his print a monumental power, a weight, that is the very opposite: a column of black smoke assumes iron authority.

Lightness and weight, the momentary and the enduring: right from its invention at the close of the Romantic age, photography displayed these extreme possibilities in its nature. The oldest photograph in the V&A collection is an ethereal silvery phantom of a London street in 1839, taken using Louis Daguerre's pioneering method in the year he made it public. By the 1850s photographers were shooting such diverse masterpieces as Robert Howlett's 1857 portrait of the engineer Isambard Kingdom Brunel, cigar at the corner of his mouth, tall hat on his head, the chains of the Great Eastern falling into Miltonic darkness behind him, and John Murray's icily majestic panorama of the Taj Mahal, taken in about 1855. The camera could capture the craggily real – Brunel lives for ever in his portrait – or the stupendously beautiful.