The first European explorer widely credited with sighting the islands is Sebald de Weert, a Dutch sailor, in 1600. Although several English and Spanish historians maintain their own explorers discovered the islands earlier, some older maps, particularly Dutch ones, used the name "Sebald Islands", after de Weert. However, the islands appear on numerous Spanish and other maps beginning in the 1520s.
This paragraph is a grand example an unsupported claim in Wikipedia, one which has quite literally caused wars and deaths. There is no evidence to support the final sentence. What is even more interesting is the history article, which has more extensive discussion regarding Ferdinand Magellan and others including an archipelago at the location of the Falklands in their charts.
The reason I mention this is I happen to have read rather a lot regarding Mr Magellan and his passage through the region, which he made along shore, within sight of land. I've also examined several copies of charts from the 1500s of this region, and none show the islands. It's not until Shouten's 1619 that I can first find the islands in their position.