Objection 1. It would seem that the damned are unable to make use of the knowledge they had in this world. For there is very great pleasure in the consideration of knowledge. But we must not admit that they have any pleasure. Therefore they cannot make use of the knowledge they had heretofore, by applying their consideration thereto.
Objection 2. Further, the damned suffer greater pains than any pains of this world. Now in this world, when one is in very great pain, it is impossible to consider any intelligible conclusions, through being distracted by the pains that one suffers. Much less therefore can one do so in hell.
Objection 3. Further, the damned are subject to time. But "length of time is the cause of forgetfulness" (Phys. lib. iv, 13). Therefore the damned will forget what they knew here.
On the contrary, It is said to the rich man who was damned (Luke 16:25): "Remember that thou didst receive good things in thy lifetime," etc. Therefore they will consider about the things they knew here.
Further, the intelligible species remain in the separated soul, as stated above (70, 2, ad 3; I, 89, 5,6). Therefore, if they could not use them, these would remain in them to no purpose.
I answer that, Even as in the saints on account of the perfection of their glory, there will be nothing but what is a matter of joy so there will be nothing in the damned but what is a matter and cause of sorrow; nor will anything that can pertain to sorrow be lacking, so that their unhappiness is consummate. Now the consideration of certain things known brings us joy, in some respect, either on the part of the things known, because we love them, or on the part of the knowledge, because it is fitting and perfect. There may also be a reason for sorrow both on the part of the things known, because they are of a grievous nature, and on the part of the knowledge, if we consider its imperfection; for instance a person may consider his defective knowledge about a certain thing, which he would desire to know perfectly. Accordingly, in the damned there will be actual consideration of the things they knew heretofore as matters of sorrow, but not as a cause of pleasure. For they will consider both the evil they have done, and for which they were damned, and the delightful goods they have lost, and on both counts they will suffer torments. Likewise they will be tormented with the thought that the knowledge they had of speculative matters was imperfect, and that they missed its highest degree of perfection which they might have acquired.
Reply to Objection 1. Although the consideration of knowledge is delightful in itself, it may accidentally be the cause of sorrow, as explained above.
Reply to Objection 2. In this world the soul is united to a corruptible body, wherefore the soul's consideration is hindered by the suffering of the body. On the other hand, in the future life the soul will not be so drawn by the body, but however much the body may suffer, the soul will have a most clear view of those things that can be a cause of anguish to it.
Reply to Objection 3. Time causes forgetfulness accidentally, in so far as the movement whereof it is the measure is the cause of change. But after the judgment day there will be no movement of the heavens; wherefore neither will it be possible for forgetfulness to result from any lapse of time however long. Before the judgment day, however, the separated soul is not changed from its disposition by the heavenly movement.
Source: Summa Theologica (New Advent)