"Counter-intuitive" Conjecture
Editor: Henyee Translations
The ABC conjecture was not the same as other mathematical conjectures. Its biggest difficulty was not in calculations, nor in the abstraction of the proposition itself, but the fact that its existence was completely counter-intuitive.
Simply put, let three numbers be a, b, and c, where c=a+b. If these three numbers were relatively prime, then to multiply the prime factors of these three numbers to get d. It seemed like d would obviously be larger than c.
For example, let a=2, b=7, c=a+b=9, d=2×7×3=42, d was obviously much larger than c.
However, this was completely contrary to people's intuition.
There were many counterexamples.
For example, let the triplet be (5, 27, 32), d=30, which was obviously smaller than 32.
Mathematicians went to the next level and modified Joseph Oesterlé's original expression, magnifying rad(abc) and replacing it with a power of r greater than 1. Which became rad(abc)^(1+ε).