I think that it's him coming to the realization that his dream doesn't die. He's just not understanding his dream properly. That is, he will never achieve his dream of accumulating all knowledge by learning on how to be immortal. Remember the famous Thomas Edison quote. When asked why he made 99 attempts to make a lightbulb before getting it right, Edison retorted "I didn't do that. I learned 99 ways to not make a lightbulb." Your character could realize that there is no possible immortality. It's not the answer most people want to hear, but he's not motivated by helpful knowlege. Just knowledge. He has learned many attempted ways to achieve immortality do not work and that is knowledge that has led him to conclude it not only is impossible but is counter to his dream.
To someone motivated by knowledge for knowledge's sake, he must come to realize that there exists a phenomena called qualia: a characteristic of a thing that cannot be described in words. Color is an excellent example of this: Color can only be described in it's relationship to things that have color as a characteristic. If I ask "What is Red?" You would describe it as the color of an apple, or its computer RGB values (255, 0, 0) or it's wave length on the light spectum... but you cannot describe the color we see that we call red, without pointing to something outside of the question. If I cannot see red, then your answer is Red is whatever color I do see when I look at an apple.
One other fun bit about the nature of colors. The human eye can see in a wider range of colors than can be digitally duplicated. There are shades of colors you cannot google and see completely on your screen... Nor read in a book that has been printed in a modern printing process, nor can words describe it in a way you can see. You must go to the things of these colors and see with your own eyes, if you want to truly know what it looks like.
That is qualia. Knowledge that can only be aquired through personal experiance and defies any ability to communicate to anyone. To be an immortal, is to shut yourself off from one of the most famous questions ever asked: "What is it like to experience death?" No one can describe it from the point of view of the dead. It must be experienced. To the person who dreams of knowledge of all things, Immortality, if possible, is denial of a piece of knowledge. The dream of knowledge cannot be achieved if he does not know what it is like to experience death.
If nothing we do matters, than all that matters is everything we do. We can relate to a character who finds meaning in the importance of death because everyone tries to make sense of it. In the parable of the Starfish, from the point of view of the man, the boy's actions are meaningless as the boy cannot possibly save all the beached starfish and shouldn't matter to the boy as so many will die and his actions won't change the world. The boy responds that from the point of the Starfish, what he does next will change the world.