Australian Wild Gum Blossom. “Gum Tree” is the most common name for the 500 kinds of Australian Eucalyptus. They vary from forest giants to low straggling shrubs. First mentioned by Sir Joseph Banks in 1770, when he wrote of a tree having gum exudations, similar to an exotic plant he knew. The term “Gum Tree” is now usually reserved to those eucalyptus with smooth bark.