No sooner had the Metropolitan Transportation Authority introduced a new map of the New York subway system on Aug. 7, 1972, than complaints flooded in. Many stations seemed to be in the wrong places. The water surrounding the city was colored beige, not blue. As for Central Park, it appeared to be almost square, rather than an elongated rectangle, three times bigger than the map suggested, and was depicted in a dreary shade of gray.

The map was, indeed, riddled with anomalies, but that was the point. Its designer, Massimo Vignelli, had sacrificed geographical accuracy for clarity by reinterpreting New York’s tangled labyrinth of subway lines as a neat diagram. Each station was shown as a dot and linked to its neighbors by color-coded routes running at 45- or 90-degree angles. Mr. Vignelli had used his design skills to tidy up reality.

Design buffs have always loved his map for its rigor and ingenuity. When the future graphic designer Michael Bierut made his first trip to New York in 1976, he took one home to Ohio as a souvenir. But many New Yorkers were outraged by what they saw as the misrepresentation of their city, while tourists struggled to relate Mr. Vignelli’s design to what they found above ground. In 1979, the M.T.A. bowed to public pressure by replacing his diagrammatic map with a geographical one.

On the eve of its 40th anniversary, the story of the Vignelli map reads like a cautionary tale of a gifted designer expecting too much of the public or, as my grandmother used to say, being “too clever by half.” But its fate may have been different had the M.T.A. implemented Mr. Vignelli’s original scheme correctly.