Rational or Not? This Basic Math Question Took Decades to Answer.
An editorially independent publication supported by the Simons Foundation.
I n June 1978, the organizers of a large mathematics conference in Marseille, France, announced a last-minute addition to the program. During the lunch hour, the mathematician Roger Apéry would present a proof that one of the most famous numbers in mathematics — “zeta of 3,” or ζ(3), as mathematicians write it — could not be expressed as a fraction of two whole numbers. It was what mathematicians call “irrational.”
Conference attendees were skeptical. The Riemann zeta function is one of the most central functions in number theory, and mathematicians had been trying for centuries to prove the irrationality of ζ(3) — the number that the zeta function outputs when its input is 3. Apéry, who was 61, was not widely viewed as a top mathematician. He had the French equivalent of a hillbilly accent and a reputation as a provocateur. Many attendees, assuming Apéry was pulling an elaborate hoax, arrived ready to pay the prankster back in his own coin. As one mathematician later recounted, they “came to cause a ruckus.”
The lecture quickly descended into pandemonium. With little explanation, Apéry presented equation after equation, some involving impossible operations like dividing by zero. When asked where his formulas came from, he claimed, “They grow in my garden.” Mathematicians greeted his assertions with hoots of laughter, called out to friends across the room, and threw paper airplanes.
