Exercise 2: Why the Thales Caveat Matters — Possible Solution ================================================================== If Thales's traditionally-credited proofs really were his own genuine achievement, that would mean deductive, logically-justified geometric reasoning existed a full generation or more earlier than commonly assumed, and that the "Greek turn" toward proof was a real, sudden, identifiable invention by one specific named individual working around 600 BCE - a clean, satisfying origin story for the entire deductive tradition this course is about. But if Proclus's account (written roughly a thousand years after Thales lived) is instead a later retrospective systematization - Greek mathematicians of Proclus's own era reading formal proof structure back onto an earlier figure's genuine but less rigorously justified geometric discoveries - then the real emergence of deductive proof was likely a more gradual, collective development across many mathematicians over a longer period, rather than one dramatic starting point. This matters for how honestly this course itself can tell the story: treating Thales as the confirmed single inventor of proof would misstate the real state of historical evidence, and would also make it seem like deductive rigor arrived as one sudden event rather than the real, gradual process it more likely was. The honest caveat keeps the course's own account accurate to what's actually known, rather than accurate to a tidier but unverified legend. ANSWER: If Thales's proofs were genuinely his own, deductive reasoning would have a clean, dateable single origin point; if they're a later retrospective attribution (the more likely case per current scholarship), the real emergence of proof was probably more gradual and collective - and telling the story honestly, rather than repeating the tidier legend, matters because it keeps the account accurate to the real historical evidence rather than to an appealing but unverified narrative. WHY THIS WORKS AS AN ANSWER ------------------------------ This weighs both real possibilities (genuine originator vs. later retrospective attribution) and explains why the distinction has a real consequence for how the history itself should honestly be told, rather than treating the caveat as a minor footnote.