The poem falls into two sections, even though they are not indicated on the page. In the first, the narrator is inside the lecture room, listening to a well educated astronomer, a "learned" man, explain the universe in terms of mathematics, with his charts and diagrams to be added, divided, and measured. In the second part of the poem, the narrator goes outside alone. The poem is developed in the contrast between these two settings.

Inside the lecture room, there is "much applause" by the audience, but the narrator begins to feel "tired and sick." When he removes himself from the room and from the astronomer's lecture, however, the change of setting suggests a change in his feelings:

. . . I wandered off by myself,

In the mystical moist night air, and from time to time,

Looked up in perfect silence at the stars.

The narrator has placed himself in a romantic natural setting that is beautiful and appealing with the reference to the "mystical moist night air." In this setting, he does not see the stars as objects on charts and diagrams. He views them "in perfect silence" in the heavens, their natural setting. The silence itself is an natural element of beauty that contrasts the noisy lecture room.

The poem can be interpreted as expressing a romantic view. The beauty, mystery, and grandeur of the universe cannot be grasped intellectually, only spiritually.

Whitman's tendency to assign primacy to the subjective experience is something that emerges from the poem.  Whitman's meaning is to explore how personalised, the idea of the individual experience being vital to consciousness, is something that permeates all study and all aspects of being.  Even when one is confronted by the supposed strict domain of science, Whitman argues that there is an intellectual process that is personalized, an approach that argues individuals do not need to be tethered to how things should be.  When the speaker of the poem "wanders" or explores the world of space and astrological dimension on their own, away from the "learn'd astronomer," there is real meaning present.  It is through this personalized and individualized exploration where meaning is derived.  In this light, Whitman is calling on individuals to explore their passions and field of study with a sense of personalized voice to what they do.  In Whitman's world, it is not nearly enough to be successful or demonstrate competency in what one does.  Rather, one has to find and harness their personalized voice in this process.

What is Walt Whitman saying in his poem, When I Heard the Learn'd Astronomer? Is the learn'd astronomer supposed to be intelligent and brilliant?

Whitman seeks to expand the appreciation of both scientific phenomena and the natural world in this particular poem.  Representing a sense of American Romanticism, Whitman appreciates to a certain extent the astronomer's explanations (The title does not seem to be a sardonic reference of the astronomer's knowledge.)  Whitman does possess an appreciation for "the proofs" and "the figures," and does hold a certain respect for "the diagrams" and "the charts" along with the processes that account for them.  Where Whitman holds some level of divergence with this rationalist approach to the scientific phenomena is that Whitman feels there is a sense of wonderment and amazement that is not fully recognizable through the scientific method.  When Whitman describes his leaving the lecture hall as "riding" and "gliding off," it marks an active break with the established normative process of science and begins an embracing of the imaginative aspects of astronomy, and science in general. This is heightened with the use of the verb "wandering," indicating a certain heavenly and unexplained quality to the phenomena of stars and their alignment in the sky.  The "perfect silence" and image of the night sky lends an air of reverence which is not necessarily evident in the objective approach of the "learn'd astronomer"  and his applauding audience.  It seems that Whitman is embracing a form of negative capability in the picture he sees in the last line.  This idea of being comfortable with the unknown is something which is not amplified through the scientific approach, in its very nature seeking to quantify and explain.  Whitman is pointed in suggesting that while Science and rational thought does have a place in re-describing the natural world, there is a level of individual amazement and wonderment which will and should never be supplanted with rational thought.  This level or sphere which signifies the expansion of moral and individual imagination is intrinsic to the individual, the reason why he leaves the lecture hall when the group applauds the astronomer.