https://mathworld.wolfram.com/RootedTree.html: “A rooted tree is a tree in which a special ("labeled") node is singled out. This node is called the "root" or (less commonly) "eve" of the tree. Rooted trees are equivalent to oriented trees (Knuth 1997, pp. 385-399). A tree which is not rooted is sometimes called a free tree, although the unqualified term "tree" generally refers to a free tree.”
> A tree which is not rooted is sometimes called a free tree, although the unqualified term "tree" generally refers to a free tree.
I wonder if that was once the case but no longer is. I'm learning I think of trees mostly through the lens of data structures and not graph theory and I imagine more people do than not.
Slight nitpick: in mathematics, a tree need not have a root.
https://mathworld.wolfram.com/FreeTree.html: “a normal tree with no node singled out for special treatment”
https://mathworld.wolfram.com/RootedTree.html: “A rooted tree is a tree in which a special ("labeled") node is singled out. This node is called the "root" or (less commonly) "eve" of the tree. Rooted trees are equivalent to oriented trees (Knuth 1997, pp. 385-399). A tree which is not rooted is sometimes called a free tree, although the unqualified term "tree" generally refers to a free tree.”