Rational or Not? This Basic Math Question Took Decades To Answer.

Three mathematicians have developed a breakthrough method for proving whether numbers can be written as fractions, solving a problem that has puzzled researchers for decades. Frank Calegari, Vesselin Dimitrov and Yunqing Tang proved the irrationality of an infinite collection of numbers related to the Riemann zeta function, building on Roger Apery's landmark 1978 proof about a single such number.

The new approach, which relies on 19th-century mathematical techniques, has already helped settle a 50-year-old conjecture about modular forms and could lead to more advances in number theory.

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