According to Catholic teaching and theology, can man ever see God as he really is?

According to Catholic teaching and theology, can man ever see God as he really is?

Not in this present life, when the soul is united to body.

St. Thomas, in addressing the question "Whether in the present state of life the contemplative life can reach to the vision of the Divine essence?," quotes St. Augustine, who says in his Literal Interpretation of Genesis xii, 27:

no one seeing God lives this mortal life wherein the bodily senses have their play: and unless in some way he depart this life, whether by going altogether out of his body, or by withdrawing from his carnal senses, he is not caught up into that vision.

cf. 1 Cor. 13:12:

We see now by a glass in the dark sort: but then face to face. Now I know in part: but then I shall know as also I am known.

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Has anyone man ever seen God in the past? Who was it?

You may think Jacob saw the essence of God when he said in Gn. 32:30: "I have seen God face to face, and my soul has been saved." In reply to the first objection of the question "Whether anyone in this life can see the essence of God?," St. Thomas writes:

when Jacob says, "I have seen God face to face," this does not mean the Divine essence, but some figure representing God.

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Will man be able to see God as he really is in the future?

Yes, but not of his own powers.

Answering the question "Whether any created intellect by its natural powers can see the Divine essence?," St. Thomas Aquinas explains why:

It is impossible for any created intellect to see the essence of God by its own natural power. For knowledge is regulated according as the thing known is in the knower. But the thing known is in the knower according to the mode of the knower. Hence the knowledge of every knower is ruled according to its own nature. If therefore the mode of anything's being exceeds the mode of the knower, it must result that the knowledge of the object is above the nature of the knower. Now the mode of being of things is manifold. For some things have being only in this one individual matter; as all bodies. But others are subsisting natures, not residing in matter at all, which, however, are not their own existence, but receive it; and these are the incorporeal beings, called angels. But to God alone does it belong to be His own subsistent being. Therefore what exists only in individual matter we know naturally, forasmuch as our soul, whereby we know, is the form of certain matter. Now our soul possesses two cognitive powers; one is the act of a corporeal organ, which naturally knows things existing in individual matter; hence sense knows only the singular. But there is another kind of cognitive power in the soul, called the intellect; and this is not the act of any corporeal organ. Wherefore the intellect naturally knows natures which exist only in individual matter; not as they are in such individual matter, but according as they are abstracted therefrom by the considering act of the intellect; hence it follows that through the intellect we can understand these objects as universal; and this is beyond the power of the sense. Now the angelic intellect naturally knows natures that are not in matter; but this is beyond the power of the intellect of our soul in the state of its present life, united as it is to the body. It follows therefore that to know self-subsistent being is natural to the divine intellect alone; and this is beyond the natural power of any created intellect; for no creature is its own existence, forasmuch as its existence is participated [in God's]. …

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What will enable man to do that?

God's grace.

Concluding from above, St. Thomas writes:

… Therefore the created intellect cannot see the essence of God, unless God by His grace unites Himself to the created intellect, as an object made intelligible to it.

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Also, it must be kept in mind that "seeing God's essence" ≠ "comprehending Him" (i.e., 'completely knowing' or 'infinitely knowing' Him).

St. Thomas writes in the question "Whether those who see the essence of God comprehend Him?:"

God, whose being is infinite, as was shown above (Question [7]) is infinitely knowable. Now no created intellect can know God infinitely. For the created intellect knows the Divine essence more or less perfectly in proportion as it receives a greater or lesser light of glory. Since therefore the created light of glory received into any created intellect cannot be infinite, it is clearly impossible for any created intellect to know God in an infinite degree. Hence it is impossible that it should comprehend God.

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Also, Pope Benedict XII (1335-1342) in Benedictus Deus of January 29th 1336 defined it a dogma:

We, with apostolic authority, define the following: According to the general disposition of God, the souls of all the saints […] already before they take up their bodies again and before the general judgment, have been, are and will be with Christ in heaven […] and these souls have seen and see the divine essence with an intuitive vision and even face to face, without the mediation of any creature

(See this for background.)

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^{As an aside, the schismatic Eastern 'Orthodox' disagree sharply with the above Thomist understanding of light of glory and seeing God's essence. For an excellent comparison of the two views, which really helps clarify the Thomistic view, see James Larson's article "A Study of The Radical Divide Between Catholicism and Eastern Orthodox Theology." Cf. also this video from an 'Orthodox''s perspective.}