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On the one hand, Europeans knew about the roundness and size of our planet since Eratosthenes (third century BCE). The measurement was extraordinarily precise (~1% error).

On the other hand, the eastbound ground distance to India was known at least since the Romans.

Taking these two pieces of information together, Christopher Columbus could have estimated the distance going westbound. However, he underestimated it dramatically.

Why was it so?

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    Short answer was that he was a believer in what I call The Unscientific Method: Think up a fact you want to be true, then cast about for evidence that supports it, discarding any that doesn't.
    – T.E.D. ♦
    May 29 at 18:14
  • Columbus problem was that he used an Italian/Roman Mile (1,479 meters) instead of the Arabic mile (1,973 meters) for the 56⅔ miles miles per degree calculation. Had this been known by the Spanish court's mathematicians at the time, they would have used that as the reason why they thought that Columbus calculation was wrong. But they didn't, so I assume that this knowlage had simply been 'forgotten'.
    – Mark Johnson
    May 29 at 20:18
  • See: What did Native Americans know, or speculate, about the Old world?
    – Mark Johnson
    May 29 at 20:18
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    @MarkJohnson - Well, my point was sort of that his problem was that he wanted it to be a small distance so his idea would be feasible. Which miscalculation he found or came up with to get that small number he wanted was really beside the point for him.
    – T.E.D. ♦
    May 30 at 1:32
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    @MarkJohnson - The Spanish Monarchs referred Columbus' claims to a committee of experts. Whatever exact argument they used, they did in fact confidently report back to the monarchs that he'd grossly underestimated the size of the earth. That didn't end up mattering for political reasons (the Portugese had just rounded the Cape) that had nothing to do with the quality of anyone's math.
    – T.E.D. ♦
    May 30 at 15:23

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