Big Advance on Simple-Sounding Math Problem Was a Century in the Making | Quanta Magazine

Chilean mathematician Hector Pasten solves math's thorny relationship between addition and multiplication.

The n2 + 1 sequence offers a good starting point for investigating the relationship between multiplication and addition.

Pasten's technique also enabled him to make progress on certain cases of the abc conjecture, yet another question.

The largest prime factor of n2 + 1 must always be at least as large as log(log n) for any value of n 2 + 1 .

The problem has been at an impasse for mathematicians since the 1930s .

A new theory involving modular forms and related entities called Shimura curves allowed him to tackle many of the questions.

Pasten’s new growth rate is much higher than the previous record, though mathematicians suspect it is higher still.

Pasten was able to use his techniques to improve estimates for certain cases of the abc conjecture.

The conjecture, one of the most important in number theory, has been at the center of a decade -long controversy.