How did the Second Punic War prove, according to Polybius and Livy, to be the true test of Roman character (which accounted for Rome's future...

The
Second Punic War was a huge test for Rome because the Republic could have been obliterated if
things had gone slightly differently. Hannibal's invasion devastated Italy and threw Rome into a
panic. The entire Adriatic coast (and the region Polybius calls Magna
Graecia) fell to the Carthaginians, and the battle of Cannae was one of the most
horrifying defeats in history for any power, especially one with the pretensions to power of
Rome. Livy gives accounts of the thousands of dead heaped on the field and the wounded men
committing suicide by suffocating themselves in the earth.

The implication of
both Polybius and Livy is that ultimately, when a people are brought into the most desperate
situation, they are paradoxically strengthened. Polybius says it was the constitutional system
of the Roman Republic that enabled it to survive. The war was an immense turning point in the
centuries old conflicts between Rome and Carthage for dominance of the central
Mediterranean.

One might ask why the Hannibalic war was different from
earlier times when Rome was attacked (for instance, by the Gauls 150 years earlier), and the
answer probably lies in the fact that the enormity of Hannibal's campaign was seen as an
existential occurrence without precedent. Rome emerged from near destruction to become a world
power.

The subsequent Third Punic War set the pattern for the ruthlessness of
Roman "justice," but in this Rome was hardly different from other powers in antiquity.
And the cruelty of Rome came to be exaggerated. The urban legend (which we would call it today)
of the Romans "sowing salt" in the earth of Carthage so that nothing could grow there
again was just thatan apocryphal account repeated to the point where even legitimate historians
sometimes stated it.