[3][4] By 1789 Haenke was a prominent young scholar whose name was put forward by Jacquin and Ignaz von Born when Spain was recruiting a scientific corps for the Malaspina expedition.
A long, roundabout journey from Vienna brought Haenke to Cadiz on 30 July 1789, just hours after the two ships of the expedition, the Descubierta and Atrevida, had set sail.
This vessel was shipwrecked near his destination and Haenke was forced to swim for the shore, salvaging only his collecting equipment and his copy of Genera Plantarum.
They initially traveled up the west coast of the Americas as far as Alaska, then returned south to Acapulco and crossed the Pacific to explore the Philippines, Australia, and New Zealand.
Haenke was permitted to leave the ship with an assistant and cross overland to Buenos Aires with the intention of undertaking botanical and other scientific work along the way.
Instead of rejoining the fleet again in the fall of 1794 as planned, Haenke became engrossed with the local botany and settled in Cochabamba, Bolivia to continue his scientific studies.
[4] When Malaspina returned from his voyage he became embroiled in a dispute with Spain's minister, Manuel de Godoy, and was subsequently imprisoned for seven years.
The Czech botanist Carl Bořivoj Presl spent nearly 15 years producing the "Reliquiae Haenkeanae" (published from 1825 to 1835), a work based on Haenke's botanical specimens collected in the Americas and the Philippines and purchased in Cadiz.
A small private museum, "Muzeum Tadeáše Haenkeho", was established at Haenke's birth home in Chřibská, Czech Republic.