Shelley's concept of "beauty" is a vigorously debated one with some scholars connecting it with metaphysical or mystical meaning and others connecting it with a rejection of knowing beauty through either metaphysical of mystical pathways. Shelley had rejected Christianity by 1816 when he and Byron went together to Geneva, Switzerland. While sailing on Lake Geneva, Shelley was overwhelmed by the majesty, power and beauty of of the Swiss Alps that towered overhead. He had a memory of an event in his childhood during which he was overcome by a sense of transcendent power which--now floating on lake Geneva under the mighty influence of the Alps--he connected to the awe inspiring transcendence of what he was experiencing in the presence of the Alps. It was after this life altering experience that Shelley penned "Hymn to Intellectual Beauty."

The expression "intellectualize beauty" is taken from the title and can be misleading for many readers. To "intellectualize beauty" would mean to take what is an emotional and aesthetic experience, stirring feeling of joy or awe, and rationally conceptualize the meaning and mechanism behind it. But is this what Shelley actually intends by "Intellectual Beauty"? Most scholars readily agree that this is not what he means, although some criticize Shelley by saying that he fails to achieve the universality of poetic expression by making an intellectual conceptualization of beauty his actual objective (the positions varying schools of scholarship express may be seen as contradicting each other).

The most solid analysis of "intellectualization of beauty" holds that Shelley had equated transcendent spiritual power--the power of God, if you will--with beauty as expressed by the Alps and by the overpowering experience of revelation in his childhood. This means that "intellectual" refers to non-corporeal, non-physical beauty and to the spiritual perception of it through the Romantic concept of "imagination": that which transcends thought and is the inspiration, usually from "Nature," that moves the poet to intuitive understanding and expression of universal truth and universally recognizable visions of beauty. Thus to intellectualize beauty means to define it, perceive it and express it as the power that is in all and over all; that cannot be equated with physical substance (though physical substance  may emanate it like the Alps do); and that is not constant in its revelation but that reveals itself in sudden flashes of epiphany. Some scholars say that Shelley made this Beauty, with a capital [b], his religious inspiration, his connection to the supernatural and omnipotent.

This explanation of intellectualization of beauty is expressed in the first three lines of "Hymn":

The awful shadow of some unseen Power
         Floats though unseen among us; visiting
         This various world with as inconstant wing

Here we see the awe creating "Power" such as Shelley felt in childhood and under the shadow of the Alps; the transcendent, supernatural nature of the Power; and the suddenness of visitations of the Power. At the end of the first stanza, we see the godlike quality ascribed to Beauty by Shelley, confirming the analysis that Shelley felt he had found the spiritually inspiring religious source he had searched for:

Like hues and harmonies of evening,
                [...]
                [...]
                Like aught that for its grace may be
Dear, and yet dearer for its mystery.