Concerning the famous map of Ottoman Admiral Piri Reis, the veteran Turkish scientific historian Fuat Sezgin writes in 'The Pre-Columbian Discovery of the American Continent By Muslim Seafarers':
"First, I would like to put two maps under closer examination: “the lost Columbus-map of America dated 1498” in a version of the Ottoman Admiral Pīrī Reīs and the Portuguese copy of a Javanese map showing the east coast of South America. The Pīrī Reīs-map was discovered in the library of the Topkapı Sarayı in 1929 and published by Paul Kahle in 1931. It was examined some years later by Kahle and by several other historians of cartography who followed him. Interest in this map has once more increased during the past two decades and even expanded beyond circles of experts.
I had previously studied this map but my focus then was confined to aspects that had been dealt with by Kahle, whose treatise I believe is still the most thorough one dedicated to the subject. Hence I assumed that this map, drawn by Pīrī Re¸īs at Gallipoli and presented in 923/1517 to Sultan Selīm the Grim, consisted of two parts: one part comprising the eastern regions of Middle America and the Caribbean, the second part with the eastern shores of South America. The northern part would supposedly correspond to the lost Columbus-map. Kahle suggested that Pīrī Reīs had obtained this source from a Spanish mariner whom (his uncle) Kemāl Reīs had captured on a seized Spanish vessel in 1501. According to his own account this captive had accompanied Columbus on his first three journeys across the Atlantic. The importance of this map—which mainly shows several archipelagos in the Caribbean mistaken as part of the coastline of East Asia—would then primarily be imputed to it being a copy of the Columbus-map that had long been considered lost. As far as the southern part was concerned one had to presume it was based on a Portuguese map.
In the course of preparations for a lecture on the topic of pre-Columbian discovery of America I dealt with the Pīrī Reīs map once more at some length whereupon I came to revise my opinion. When I first read the detailed and excellent description of the South American part of the Pīrī Reīs map in Paul Kahle’s commendable article, I received the impression that Pīrī Reīs was the first cartographer who undertook to compile a map of the new continent using all the results from encounters of Portuguese navigators with the shores of South America (between the southern part of the Caribbean to about 50° south of the equator) that we know today and even some that have meanwhile fallen into oblivion, with astounding exactitude—actually quite incredible by the standards of European navigators and cartographers of that time. This however would lead to new questions: would these mariners who reached South America mostly by coincidence and stayed only briefly, be at all in the position to determine longitudes?
Did Pīrī Reīs use a graduated map of South America from which he extracted his data? According to Kahle,
Pīrī Reīs supposedly based his map on a model of Portuguese provenance. Let us therefore
compare the Pīrī Reīs map with the earliest surviving Portuguese maps up to 1502. Although the representation of a part of South America found there betrays a certain affinity with Pīrī Re¸īs’,
it is still substantially less developed both in terms of content and the area covered. An example that Kahle had already noticed is the estuary of the river La Plata in the vicinity of modern Buenos Aires which is clearly delineated by Pīrī Reīs even though it was supposedly not discovered until 1515. Particularly perplexing too is the result of superimposing the Pīrī Reīs-map on the modern atlas with a computer. The coordinates of the La Plata estuary (Parana, ca. Long. 58°; Lat. 35° south) for example turn out almost congruent. As seen on a map, the match is very close in the northern part of the coastline between about Long. 75° in the north-west to about Long. 45°. In other words, the coastline of the Pīrī Reīs map deviates in longitudes and latitudes in some points hardly at all, in some points only 0.5° to 2° from the modern atlas.
This is a degree of exactitude which was unknown in the history of European cartography prior to the 18th century ..."
http://www.laits.utexas.edu/gma/mappamundi/docs/precolumbamerica.pdf-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
For the record, compare the high degree of exactitude in the Piri Reis map with the lack of detail in extant maps of Columbus upon whom many claim Piri Reis's map is allegedly founded bearing in mind the ominous factor of the contribution of Arab Islamic science. Ignorance of Arab science has been an essential characteristic of the education systems of western colonialism and post-medieval western civilization generally:
Columbus's Map of the West Indies (1492-1493)
http://www.henry-davis.com/MAPS/Ren/Ren1/302.htmlMap of the Discoveries of Columbus (1493)
By Christopher Columbus & Carolus Verardus
http://www.henry-davis.com/MAPS/Ren/Ren1/303.html