Gymnasion derives from gymnazein, to exercise naked, from gymnos. Athletes trained and competed nude, coated in olive oil, scraped afterward with the strigil. Thucydides credits the Spartans with inventing public stripping; rival traditions blame a runner whose loincloth cost him a race, or Orsippos of Megara, who lost his and won in 720 BCE. The institution was more than fitness: philosophy, rhetoric, music, and civic education happened there. Plato's Academy and Aristotle's Lyceum were both gymnasia precincts.
The standard explanations: oil made clothing filthy; nudity honored the gods and the male form; and stripping erased class markers, every athlete equally equipped. Germans kept the educational sense, Gymnasium is still their academic high school, while English kept the sweat. One word, two inheritances, and the naked part quietly dropped by both.
The claim: nakedness was the point, not the byproduct, training before peers with nothing to hide behind was the moral content of the gymnasium: the body as argument, excellence that cannot be tailored. Verdict: fits the Greeks' own rhetoric about arete and the gaze of the city, and the modern gym's mirrored anxiety suggests we rebuilt the exposure without the philosophy. The word kept the nakedness; the practice kept only the watching.
What did the Greeks know about training that made clothing the obstacle?