N eanderthals stone tools were unique to them, their Mousterian technology was their hallmark. Find one and it is proof that Neanderthals were there.
A recent paper  strongly suggests that Neanderthals mastered the art of crossing the sea in boats because their tools have been found on islands located between 5 and 12 km (3.1 – 7.5 mi.) from the mainland, in Greece.
This paper summarises the current development in the southern Ionian Islands (Kefallinia and Zakynthos) prehistory and places it within the context of seafaring. Archaeological data from the southern Ionian Islands show human habitation since Middle Palaeolithic going back to 110 ka BP yet bathymetry, sea-level changes and the Late Quaternary geology, show that Kefallinia and Zakynthos were insular at that time. Hence, human presence in these islands indicates inter island-mainland seafaring. Seafaring most likely started some time between 110 and 35 ka BP and the seafarers were the Neanderthals. Seafaring was encouraged by the coastal configuration, which offered the right conditions for developing seafaring skills according to the “voyaging nurseries” and “autocatalysis” concepts. 
Ok, maybe they were long distance swimmers, but some similar stones have been found in Crete, more than 40 km from any other piece of land.
The oldest evidence of Modern Human “sailing” dates back to only 50.000 years ago, when they entered Australia. So these Neanderthals and their boats dating back to 100.000 years ago are proof that humans had clearly learned how to move about in boats long ago.
Perhaps they used this ability to cross the sea and reach America.
 George Ferentinos, Maria Gkioni , Maria Geraga , George Papatheodorou (2012). Early seafaring activity in the southern Ionian Islands, Mediterranean Sea. Available online 10 February 2012. Journal of Archaeological Science.
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