"mournful numbers" (Symbol)
The word "numbers" symbolizes the rigid, authoritarian, and bleak outlook that the books of the Old Testament espouse. The young man refuses to accept this worldview, preferring to be hopeful and optimistic. Even beyond the biblical associations numbers themselves are often viewed as cool, (literally) calculating, and utilitarian –all things the young man does not want to be.
Action (motif)
Many of the words and phrases used suggest action, which is the prominent theme of the poem. These include comparing life to battle, the exhortation "Act,— act in the living Present!," the image of man walking along the sand and leaving footprints and the man sailing across the sea of life, and the concluding verbs "achieving and pursuing."
Footprints (Symbol)
Footprints symbolize what we leave behind; they are a mark, an indentation. They indicate that someone has been here before, traversing the path that one is currently traversing. There is also somewhat of a melancholy aspect to footprints, as they reference the past, absence, and spirit rather than corporeal presence. The young man sees them mostly as guides, though; he thinks men can take heart from observing the paths of those gone before them.
