After 30 months of fast-paced innovation in quantum algorithms, six research groups are hoping to hit paydirt. But there can be only one big winner—if there is a winner at all.

Gerd Faltings proved a conjecture that had been unsolved for six decades, using connections between numbers and geometry.

Gerd Faltings shocked mathematicians around the world for his 1983 proof of the Mordell conjecture, which brought together ...