At 1,141.1 metres the Brocken is the highest summit in the Harz and in the whole of northern Germany. Prussian military surveyors fixed that figure in 1850 and it still stands. The name means roughly a lump or a boulder, and from a distance the mountain earns it — something set down on the landscape rather than pushed up.

Witches gathered here on Walpurgisnacht, the eve of 30 April, long before anyone wrote it down. Goethe made it permanent in Faust, published in 1808, and the summit rocks — the Teufelskanzel, or Devil's Pulpit, and the Hexenaltar, the Witches' Altar — read as stage directions once you know the play. Heinrich Heine climbed in 1824 and wrote that on the upper half one cannot help thinking of the German national tragedy of Dr Faust: even Mephisto, he suspected, must struggle for breath getting up his own favourite peak. The devil still pays rent up here. The hotel café is the Hexenklause, the souvenir shop is the Urian, and a Faust rock opera ran in the hotel's Goethehall 387 times between 2006 and 2019.

Goethe himself came up on 10 December 1777, from Torfhaus, with a forester named Degen. His notes are almost telegraphic. They set off at a quarter past ten through snow an ell deep that held their weight, stood on top at a quarter past one, and were back down by four. In between: "the whole world in clouds and fog and above it everything clear."

He returned twice, on 21 September 1783 and 3 September 1784. The route he took is now the Goetheweg, walked by around 250,000 people a year and rebuilt in 2008 and 2009 with a three-metre gravel surface so it can be ploughed through winter. He was not the first on record: the physician Johannes Thal of Nordhausen climbed in 1572, and his Sylva Hercynia of 1577 described the whole Harz flora rather than only the useful plants.

Roughly 1.4 million people come each year, and the summit is in cloud on something like 300 days of it — 330 in the record year 1958. It has a subalpine climate with the tree line at 1,110 metres, and because a steam train runs to the top it gets badly underestimated. Weather here turns Alpine fast. Summer thunderstorms build in minutes, winter storms bury the roads, and ice sheds off the masts and buildings without warning. On 24 November 1984 the anemometer recorded 263 km/h.

The cloud does give something back. On the right foggy day you can see a Brocken spectre: your own shadow thrown enormous onto the mist below, often ringed with coloured halos. The effect carries this mountain's name because this is the place where people kept encountering it.

The summit's twentieth century was industrial before it was military. A mobile 10 kW transmitter sent the first television broadcasts from the Brocken in 1935; the present weather station dates from 1939; American bombing destroyed the Brocken Hotel on 17 April 1945.

Then the border hardened. In 1961, with the Berlin Wall going up and the inner-German frontier reinforced, the Brocken — sitting almost on the line — was closed to the public and sealed behind a wall of concrete slabs. Two signals-intelligence stations moved in: Jenissej for Soviet military intelligence and Urian for the Stasi, which ran three shifts with a couple of dozen staff and vacuumed up West German military, police and radio-relay traffic. Locals called the domes the Stasi mosque.

The demonstration walk of 3 December 1989 ended it. The Hochharz National Park was founded on 1 October 1990, the steam railway reopened on 15 September 1991 after considerable argument about running trains through protected land, and the last Russian troops left on 30 March 1994. The wall came down and its footprint became the Gipfelrundweg, a 1.6 km path circling the plateau. The Brockenhaus museum now occupies the old Stasi installation, antenna gear still sitting in the dome.

Since the last ice age the Brocken has functioned as an alpine island, holding species that otherwise belong in far higher mountains. The alpine pasqueflower grows here as the Brockenanemone and crowberry is known locally as Brockenmyrte. Among the animals are ice-age relics — the alpine shrew, the northern bat, the ring ouzel — plus a distinctly dark local form of the viviparous lizard and a cabbage white butterfly that manages only one generation a year where lowland populations manage two.

That fragility was learned the hard way. In the nineteenth century innkeepers sent departing hikers off with bouquets of Brocken flowers, and the hillsides were stripped bare year after year until species were lost outright. Picking is now prohibited, and the alpine flora is shown instead in the Brockengarten, opened in 1890 by Professor Albert Peter of Göttingen. The mountain that was sealed off for twenty-eight years came back to the public as a national park.