This is mainly a test post to check whether the LaTeX support works here and to discuss briefly what may in broadest terms be thought of as the philosophy of Mochizuki’s proof.
In polynomials, there is a very easy proof of the ABC conjecture (more correctly, the Mason-Stothers theorem) due to Noah Snyder. We give that proof here. If
with relatively prime polynomials over the complex numbers then we also have . From this we see that
Another way of saying that is that the wronskian of and is the same as . We let be the product of all factors which are common to either and or and or and . Then is the quotient of by the radical. If for instance has degree and has degree and has degree then the Wronskian has degree at most so the radical has degree at least . All other cases follow in the same way.
What we learn from this is that being able to take the derivative helps to prove the abc conjecture. In the integer case, we should be taking the derivative in the direction of choices of primes. It is probably for this reason that Mochizuki wants to monkey around with the definition of schemes and introduce so many objects. He hopes to find a way to make sense of this differentiation process.