Matthew 5:8 reads, "Blessed are the pure in heart: for they shall see God."
3 Nephi 12:8 reads, "And blessed are all the pure in heart, for they shall see God."
As Mormons, we often associate the concept of "pure in heart" with the concept of Zion. We will often cite 4 Nephi 1-18 as the model for Zion and the pure in heart. As I noted yesterday, Spencer W. Kimball gave a talk about being pure in heart. His talk was essentially about how we, as a church, can bring about Zion on earth. Even the Book of Mormon version of this Beatitude adds and extra word - "all". Instead of "the pure in heart", the Book of Mormon version reads "all the pure in heart" connoting social order rather than an individual admonishment.
Today, I did a general search on this beatitude - knowing full well that most hits would not come from LDS related pages, but rather from Catholic or Protestant related pages. I like to do this with the Beatitudes to see other opinions and insights into Christ's teachings. This search revealed that the "pure in heart" Beatitude is more generally viewed at the individual level than at the congregation level. It is more equated to the concept of sanctification.
The first stop in my Internet search took me to an article by Eric Simpson entitled The Pure in Heart Shall See God. He talked about fragmented and whole hearts. Hearts can be fragmented by many things such as serving Mammon or other desires. While the pure in heart have hearts that are whole and that are committed and centered on Christ. To accomplish this one must pray and fast often. The author connected the teaching of prayer to the concept of Nepsis. I had never heard of this before, so I searched on Nepsis.
Wikipedia's entry states, "Nepsis (or nipsis; Greek: νῆψις) is an important idea in Orthodox Christian theology, considered the hallmark of sanctity. Nepsis is a state of watchfulness or sobriety acquired following a long period of catharsis." To me, this is essentially the concept of sanctification as taught in the LDS church. Later in the same wiki entry on nepsis, it talks about nepsis in Eastern Christianity. In that section it states, "As the Christian becomes purified, in time he reaches the stage of illumination. At this point, the contemplative life begins, and watchfulness takes on a whole other meaning. Ultimately, the goal of the Eastern Christian is called theosis, the "deification" of man. According to St. Athanasius and others, "God became man so man can become god.""
A search of this phrase was quite revealing. Of course, there are a number of wiki entries, but there are also other single-page essays on this topic. One article on The Catholic Exchange, entitled Is Man to Become God?, brings up the things I learned in my Humanities class at BYU - that the idea man could become like God was openly discussed a long, long time ago.
Practically speaking, what does all this mean? To me, it means I am not pure in heart as I've not seen God yet. Is it possible? I think it is not only possible, but it is our duty to become pure in heart. I've learned that to be pure in heart requires, first, a desire to have a pure heart. Second, a pure heart not only is clean, but it is single to (focused only on) Christ and the glory of God. Third, to achieve purity of heart, we must pray often, fast often, meditate, think of Christ and His teachings and strive to act in accordance with those teachings. We are to attune our desires and will to God's desires and will. Lastly, this process takes a lifetime of daily commitment.