Within a shiur entitled "The Infinite Value of Human Life" by Rav Yitzchak Blau in the course on Understanding Aggada from Yeshivat Har Etzion, I found these words that I think express this point beautifully.
[Within the Halakhic Man] Rav Soloveitchik argues that the man of science shows interest only in this world of physics and biology, while the standard man of religion would like to escape this limited world and move on to a transcendent plane. Unlike the above two figures, Halakhic Man attempts to realize transcendence in this world, employing Halakha as a means for such realization.
According to Rav Soloveitchik, this explains why tumat meit , impurity caused by a human corpse, is the most severe form of ritual defilement. This halakha conveys the strongly negative attitude of halakha towards death. Unlike Socrates, we do not look forward to death as a golden chance to be released from the limiting shackles of the body. Instead, we treasure every day of life as a precious chance to engage in Torah and mitzvot. The world to come may be the place to receive our final reward, but "the receiving of a reward is not a religious act" (Halakhic Man, p. 32). It is only this flesh-and-blood world that is the world of spiritual toil and accomplishment.
Here are couple more quotes from Halakhic Man on this point:
It is here, in this world, that halakhic man acquires eternal life! “Better is one hour of Torah and mitzvoth in this world than the whole life of the world to come,” stated the tanna in Avot [4:17], and this declaration is the watchword of the halakhist. 30
However, receiving of a reward is not a religious act; therefore, halakhic man prefers the real world to a transcendent existence because here, in this world, man is given the opportunity to create, act, accomplish, while there, in the world to come, he is powerless to change anything at all. 32
Halakhic man, on the contrary, longs to bring transcendence down into this valley of the shadow of death—i.e., into our world—and transform it into a land of the living. 40
Every day, at every moment, with every person we meet this is the challenge -- how can I hallow this moment, this person?