The Polynesians used stick maps to identify currents and land masses relative positions.

With no evidence I believe navigation cues were built into the vessel. By keeping celestial bodies aligned with marks on the vessel one can achieve a seasonal calendar as well as documentation on how to modify the configuration for the next leg of the journey.

IIRC the 'maps' made of organic materials were very much a rarity slash teaching aid for the later incarnations of traditional navigation cultures of the Pacific which we have surviving material on. Mostly they used mental maps, and of course the most sensitive instruments available at the time ... at least one example of which was hanging their balls off the edge of the canoe to see if they could detect a temperature shift. A good book on the subject is We: The Navigators though it draws only from one area.

Source: Have a Pacific art collection, have been to most of the major museums on the subject, interested in sailing, authored some of the Wikipedia (featured) articles on related watercraft.

Yes, I would believe that some as fragile as the stick maps was no way to cross an ocean.

What I think is interesting is the physical representation of an oral tradition. This is different than writing as employed today.

Yep. All art is interesting for its relative flattening of multi-dimensional realities in to lesser-dimensional representations. Key concerns for the navigators were signals such as migration patterns, seaweed and other flotsam drift currents, temperatures of said currents, star positions, wave qualities, dominant wind directions, conditions and precipitation and cloud over seasons. These dynamic realities cannot be flattened in to any standard two dimensional representations even today, yet often emanate from or are disturbed by the often-tiny landmasses they would specify as origin, destination or reference points within the navigation problem. In the same way modern navigation uses multi-layered systems like bathymetric maps, local depth sensors, RADAR, GPS and navigation lights to provide orientation and safe passage amongst static and dynamic obstacles, so too the traditional navigators combined layers of sensory input considered too subtle for modern systems yet potentially equally effective in their place and season.

Probably the migratory patterns were as import at as any other reason to travel.

What I seem to be noticing is that the ancients used calculus all the time but it was the geometric tools that they used.

This gave technology a form.

Arabic numerals made tabular data more useful leading to the more number based tools.

This seems to have removed the form from technology.

Even without an ice sheet, would antarctica be hospitable? It'd still be cold and a desert I imagine, in darkness through the winter, etc.