How long can the Americas remain undiscovered?

Well, you'd have to prevent the migration of Native Americans from Asia to the Americas across the Ice Bridge somehow...
 
Defining "discovery" as the initiation of sustained contact between Eurasia and the Americas, I doubt you could delay it more than a decade or two without a very early POD. The Earth is already known to be spherical (this was known to the ancient Greeks, and is well known among both sailors and anyone with a decent education in Europe in the late 1400s), so a western route to Asia is a widespread idea, the only debate being whether it's short enough to be more practical than the Cape of Good Hope route (Columbus was wrong about this, badly underestimating the Earth's circumference and badly overestimating the size of Eurasia, but he's not the only one). Beyond that, shipbuilding and navigation technology are good enough that ships are already traveling deep into the Atlantic for other reasons: Portuguese ships bound for the Cape of Good Hope often detour deep into the South Atlantic to take advantage of wind and current patterns (Brazil was discovered in 1500 by a Portuguese fleet taking this route that got blown off course and sighted signs of nearby land), and English cod fishers had been fishing in the Northwestern Atlantic since the 1480s (and indeed probably had been making landfall in New England or Nova Scotia to process their catch).
 
What he said.

Defining "discovery" as the initiation of sustained contact between Eurasia and the Americas, I doubt you could delay it more than a decade or two without a very early POD. The Earth is already known to be spherical (this was known to the ancient Greeks, and is well known among both sailors and anyone with a decent education in Europe in the late 1400s), so a western route to Asia is a widespread idea, the only debate being whether it's short enough to be more practical than the Cape of Good Hope route (Columbus was wrong about this, badly underestimating the Earth's circumference and badly overestimating the size of Eurasia, but he's not the only one). Beyond that, shipbuilding and navigation technology are good enough that ships are already traveling deep into the Atlantic for other reasons: Portuguese ships bound for the Cape of Good Hope often detour deep into the South Atlantic to take advantage of wind and current patterns (Brazil was discovered in 1500 by a Portuguese fleet taking this route that got blown off course and sighted signs of nearby land), and English cod fishers had been fishing in the Northwestern Atlantic since the 1480s (and indeed probably had been making landfall in New England or Nova Scotia to process their catch).
 
Not more than decades, and centuries more independent development probably wouldn't be long enough to significantly change the outcome of European Imperialism.
 
And how far could technology advance before their discovery?
The answer is "Given what range of PoDs?".
:rolleyes:

Of cause, if you go far enough back you could come up with an excuse to prevent any form of civilisation developing in Eurasia or the like... But I presume we're talking something more along the lines of "If no Columbus, how long...".

As others have said, probably only a matter of decades until discovery with enither fishermen establishing themselves in OTL Canada or the Portugese blundering into Brazil... perhaps another 20-30 years beyond that before Europeans find the "juicy bits" (Aztecs et al.) and we hit the drivers for invasion and ocupation of the mainland rather than establishment of small trading posts and colonisation of off-shore islands for plantations.

So, best case for the natives is maybe 50-70 years before the Europeans come after the Aztecs or Incas. This really is not much time for any serious technological advancement by the natives.
 
If the east-west extent of the eurasian continent and the circumference of the earth had been calculated correctly, it is very well possible that no one would have sailed directly west to reach Asia for as long as 200 more years, for this would - without the knowledge of the existence of the Americas - have meant to cross an ocean covering more than 200° of longitude to get there, nothing any ship could have done earlier than the late 16th / early 17th century. The only way to sail west deemed possible prior to that would have been the northern route following the danish sponsored expedition by João Vaz Corte-Real and Didrik Pining of 1473. The question is how long it would have taken to realise that Labrador is not Manchuria, Newfoundland not Hokkaido and Nova Scotia not Honshu.
 
If the east-west extent of the eurasian continent and the circumference of the earth had been calculated correctly, it is very well possible that no one would have sailed directly west to reach Asia for as long as 200 more years, for this would - without the knowledge of the existence of the Americas - have meant to cross an ocean covering more than 200° of longitude to get there, nothing any ship could have done earlier than the late 16th / early 17th century. The only way to sail west deemed possible prior to that would have been the northern route following the danish sponsored expedition by João Vaz Corte-Real and Didrik Pining of 1473. The question is how long it would have taken to realise that Labrador is not Manchuria, Newfoundland not Hokkaido and Nova Scotia not Honshu.

Is that a matter of ships themselves, or just how much they can carry in supplies?
 
The Corte-Real Expedition was not to discover a western sea route to India but to reestablish contact with Greenland.
If Columbus had not "discovered" America becaus he believed that it was not possible to reach India that way, Pedro Álvares Cabral would be the one because his expedition discovered Brazil by pure chance during his Expedition to India planning to follow Vasco da Dama's rout around the Cape of Good Hope.
 
If the east-west extent of the eurasian continent and the circumference of the earth had been calculated correctly, it is very well possible that no one would have sailed directly west to reach Asia for as long as 200 more years.

But as said previously, they already sailed along the African coast to Asia and by chance discovered Brasil. With everybody going around the Cape of good Hope, such a lucky discovery could only be delayed by some years. Once Brasil is discovered, the Europeans will sail along its shores and all of America is open to them.
 
the existence of the americas was known quite early, of course we know about Leif Ericson but also the Irish Saint Brendan is said to have sailed to the americas as early as around 520AD.

As the others said, the longest you can get is decades, unless the pod involves something dramatic (like a worse plague etc). In fact i think the americas were discovered/colonized late considering the knowledge that was already around.

just look at thishttp://en.wikipedia.org/wiki/Piri_Reis_map
 
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Defining discovery as the arrival of Amerindians presumably the Last Glacial Maximum could be extended by a few thousand years but that butterflies away civilization as we know it and thus all of history. Defining discovery as accidental byproduct of quests for cheaper spice/northwest passage anywhere from a few decades to at most a century.
 
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