Iliou Melathron was the work of Ernst Ziller, the Saxon architect who shaped so much of nineteenth-century Athens. He blended Renaissance Revival grandeur with strict Neoclassicism, then borrowed the painted interiors of Pompeii for the inside. At its completion, the three-story house on Panepistimiou Street was considered the most magnificent private residence in the city. Schliemann filled it with antiquity, the way another rich man might fill a house with portraits of himself. After his death, his widow Sophia sold the building to the Greek state in 1927. For decades it served sober legal purposes, housing the Council of State and later the Court of Cassation, before finding its present role.

The Numismatic Museum's holdings rank among the richest on Earth, spoken of in the same breath as the British Museum, the Bibliothèque Nationale in Paris, the Hermitage in St. Petersburg, the Bode Museum in Berlin, and the American Numismatic Society in New York. The collection runs to roughly 600,000 objects: coins above all, but also medals, weights, dies, gems, and seals. They span from the fourteenth century BC to modern times, an unbroken thread of currency stretching across more than three millennia of human exchange, conquest, and trade.

The galleries are arranged to follow the story of coinage itself, so that walking through the rooms is like walking forward through time. Here are the coins of the Greek city-states, the poleis whose silver owls and turtles funded democracy and war. Here are the issues of the Hellenistic kingdoms and the Roman Empire, then the gold of Byzantium, medieval Europe, the East, and the Ottoman Empire. Many pieces surfaced in hoards, buried by people who never returned to reclaim them. Others descend from the old collection on Aegina or from excavations across the Greek mainland. A specialized library of 12,000 volumes and a conservation laboratory keep the scholarship alive.

For all its imperial ambition, the museum offers something gentle. It sits at 12 Panepistimiou Street, a short walk from Syntagma Square and its busy metro station, in the heart of Athens. Behind the ornate facade waits a quiet garden where a coffeehouse lets visitors sit among the greenery, the roar of the avenue softened to a murmur. It is an odd and lovely pairing, half a million coins and a cup of coffee under the trees, inside the house a Troy-obsessed dreamer built to outlast him. In that, at least, he succeeded.