The way I see it Mochizuki's work could turn out to be like Maxwell's theory of electromagnetism. It could give us a definitive theory on the nature of prime numbers, but first someone needs to come and understand and solve it. A 'solution' of a differential equation system would be a formula, a 'solution' of Mochizuki's system would be an algorithm. Many new algorithms could come out of this, and one of them could be an algorithm for prime factorization.
But: I'm not a mathematician, so maybe I'm just fantasizing right now.
Comments
Any implications for RSA and other algorithms? [RSA relies on factoring the product of primes being a hard problem]
The claimed proof doesnt directly help us in factoring primes. At least not now. It has more to do with "structure" of primes.
The way I see it Mochizuki's work could turn out to be like Maxwell's theory of electromagnetism. It could give us a definitive theory on the nature of prime numbers, but first someone needs to come and understand and solve it. A 'solution' of a differential equation system would be a formula, a 'solution' of Mochizuki's system would be an algorithm. Many new algorithms could come out of this, and one of them could be an algorithm for prime factorization.
But: I'm not a mathematician, so maybe I'm just fantasizing right now.