The ABC Conjecture differed from other mathematical conjectures. Its greatest difficulty lay neither in computation nor in the abstraction of the proposition itself, but in the fact that its very existence was completely "counterintuitive."
Simply put, given three numbers a, b, and c, where c = a + b, if the three numbers were coprime, then multiplying their distinct prime factors together to obtain d would seem to obviously yield a number greater than c.
For example, take a = 2, b = 7, and c = a + b = 9. Then d = 2 × 7 × 3 = 42, and d was clearly much greater than c.
Yet while this statement seemed flawless, the truth was completely contrary to human intuition.
Not only did counterexamples exist, there were quite a few of them.
For instance, for the triple (5, 27, 32), d = 30, which was clearly smaller than c, which equaled 32.
Later, mathematicians settled for a compromise and modified Joseph Oesterlé's original formulation. They enlarged rad(abc), replacing it with an r-th power greater than 1: the so-called rad(abc)^(1 + ε).
That was to say, when ε was any positive real number, counterexamples to d = rad(abc)^(1 + ε) > c existed!
However, the number of those counterexamples was finite!
Ever since it had been proposed, this problem had remained one of the foremost challenges plaguing the mathematical world because of its "counterintuitive" nature.
In algebraic terms, there were infinitely many possible interactions between addition and multiplication. Therefore, the prime factors of two natural numbers and the prime factors of their sum should theoretically have no relationship whatsoever.
Yet that was precisely what made the ABC Conjecture so remarkable.
It linked two rules of operation that appeared entirely unrelated to mathematicians in a miraculous way, and