"study of extinct or fossil plants," 1872, from paleo- + botany.
Entries linking to paleobotany
paleo-
before vowels pale- word-forming element used in scientific combinations (mostly since c. 1870) meaning "ancient, early, prehistoric, primitive, fossil," from Latinized form of Greek palaios "old, ancient," from palai "long ago, far back" (from PIE root *kwel- (2) "far" in space or time).
botany n.
"the science of plants," 1690s, from botanic. The -y is from astronomy, etc. Botany Bay in Australia was named by Captain Cook (1770) on account of the great variety of plants found there; later it was a convict settlement (1778).