In 2012, Shinichi Mochizuki published a paper claiming to provide a proof for the ABC conjecture in number theory Newscom/Alamy One of the most bitterly contested proofs in modern mathematics may be on the verge of being untangled. Two projects, both aiming to use a computer program to cast new light on the controversy, are now up and running – with one having operated in secret for more than two years already. The developments are a positive sign that the row might find a solution, say mathematicians. The saga began in 2012 when Shinichi Mochizuki at Kyoto University, Japan, claimed to have proved a famous idea called the ABC conjecture, posting a 500-page proof online. The conjecture is simple to state, concerning prime numbers involved in solutions to the equation a + b = c and how these numbers relate to each other. But solving it requires deep insights into the nature of how addition and multiplication interact. The answer also has far-reaching implications for other mathematical disciplines.…