Exercise 3: Why the Real Inconsistency Undermines the Popular Story — Possible Solution
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If the ancient sources genuinely agreed on the core facts - the same
name, the same discovery, the same fate - even a large time gap
between the events and their recording wouldn't necessarily be fatal
to the story's reliability, since consistent independent accounts can
sometimes still preserve a real oral tradition accurately.

But the real sources don't agree. Pappus, the earlier of the two real
sources (4th century CE), names no one at all - he simply says an
unnamed Pythagorean drowned for revealing irrationality. Iamblichus,
writing in the 3rd century CE, offers several genuinely different
versions: in some, the punishment is expulsion rather than drowning;
in others, the discovery being punished is a completely different
one, how to construct a dodecahedron inside a sphere, not irrationality
at all. Only some later versions bring in Hippasus's name specifically
and combine these threads together.

This pattern - vague, unnamed, and even contradictory details across
the only sources that survive - is a real, classic sign that a legend
has been constructed by later writers piecing together fragments and
filling in the gaps, rather than a real, well-preserved historical
account passed down accurately. If multiple independent, consistent
ancient sources had named Hippasus specifically and agreed on the same
discovery and punishment, that would be real evidence for the story;
instead, the specific, dramatic version told today (Hippasus, √2,
drowned by his own school) appears to be a later synthesis that
smooths over real, genuine disagreements in what actually survives from
antiquity.

ANSWER: The real sources genuinely disagree with each other - Pappus
names no one, and Iamblichus offers inconsistent versions that
sometimes involve a completely different mathematical discovery and a
different punishment - and that kind of internal inconsistency across
the only surviving accounts is itself evidence of a later-constructed
legend rather than a reliably preserved historical event, regardless of
how dramatic or memorable the popular modern version has become.

WHY THIS WORKS AS AN ANSWER
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This explains why source disagreement specifically (not just old age or
a long time gap alone) is the real evidence undermining reliability,
using the chapter's own specific inconsistencies as the supporting
detail.