A Dutch artist left Cape Cod alone in a boat twelve and a half feet long, bound for England, as the middle chapter of a work titled In Search of the Miraculous. Radio contact stopped after three weeks. Nine months later a Spanish trawler found his empty boat drifting off Ireland, and then even the boat vanished.

Enrico Fermi placed him in the category of Galileo and Newton. In March 1938 Ettore Majorana withdrew his money, took his passport, wrote two farewell letters, cancelled them by telegram the next day, boarded the night ferry from Palermo to Naples and was never seen again. Italian prosecutors did not close the file until 2015.

He was the son of a governor, twenty-three years old, and ten miles from a mangrove coast with two empty cans strapped to his body. His father chartered a jet and sent ships, aircraft and thousands of searchers after him. They found nothing at all, and sixty years later the argument over what happened has still not ended.

On a summer evening in 1983 a fifteen-year-old flute student walked out of a music school near Piazza Navona and was never seen again. She was a citizen of Vatican City. Four decades later, after anonymous callers, two empty princely tombs and three separate investigations, her family is still asking the same question.

On Australia Day 1966 three children caught a bus to the beach and were never seen again. A stranger played with them in the sand for hours. A shopkeeper watched the eldest pay for lunch with a banknote her mother had never given her. Six decades and three excavations later, Australia still has no answer.

For years it burned across northern skies in plain sight, a slender river of mauve no textbook could explain. Then a handful of aurora chasers gave it a name, and professional science was forced to admit it had overlooked something enormous overhead.

For four centuries sailors have described whole oceans turning to cold white fire, glowing to the horizon under a dark sky. Satellites have finally caught the phenomenon in the act, yet what tips a patch of ordinary sea into a hundred thousand square kilometers of silent light remains one of the last mysteries hiding in plain sight.

On a December evening in 1997, four million Japanese children sat down to watch Pokemon. Four seconds of flashing red and blue light later, hundreds were convulsing on living-room floors. It became the most infamous television broadcast in history, and the strangest thing about it is how many of the victims had never had a seizure before, or since.

In a quiet farm town, teenage girls began to jerk, stutter and convulse one after another, with no fever, no lesion, no poison anyone could find. Doctors called it mass hysteria. The families called it something in the ground. Fifteen years later, the honest answer is still uncomfortable.

Again and again, hundreds of healthy whales swim as one onto the same fatal beaches and refuse to leave, even after rescuers drag them back to sea. Decades of science have offered sonar, solar storms, sick leaders and treacherous sand. Not one of them fully explains why the pods keep dying together.

For a few nights in April 2005, more than a thousand toads in a quiet Hamburg pond swelled to bursting and detonated, flinging their entrails a full metre across the water. A Berlin vet named a culprit nobody had imagined. The official file still reads: no satisfactory explanation.

At daybreak on 14 April 1561, the citizens of a great German city looked up and saw spheres, crosses and blood-red globes wheeling in combat above their rooftops. A single printed sheet preserved the account. Nearly five centuries later, we still argue about what they saw.