Part I of The Stranger presents the first of three deaths: Meurault's mother's. Meursault has no connection or role in her death, unlike the death of the Arab in Part II and his own execution in Part III. Therefore, death is seen by Meursault in an external, detached, and absurd way. As critic Alan Gullette says:
Death marks all things equal, and equally absurd. And death itself is absurd in the sense that reason or the rational mind cannot deal with it: it is a foregone conclusion, yet it remains an unrealized possibility until some indeterminate future time. The "meaning" of death is not rational but, again, is existential – its implications are to be found not in abstraction but in the actuality of one's life, the finality of each moment.
Remember, Meursault is an anti-hero in his society: few people like him, even in Part I. The old people and the caretaker judge him for falling asleep during the vigil and for not viewing his mother's body. They believe that every son should mourn, cry, stay awake, not smoke, and generally go out of one's way to show respect for death, even to the point of nearly dying in the process (as Perez does). This is not Merusault, who sees death as absurd.
Also remember, Meursault is Camus' absurd hero. An absurd hero hates death, loves life, and scorns the gods (those who judge). As such, Meursault hates the culture of death. He does not mourn because death means nothing to him: he cannot conceive it. And he will certainly not honor it by going out of his way to stay awake or nearly kill himself in the heat, as Perez does. Why should one
For Meursault, an atheist we will find out later, does not conceive of God or an afterlife. He refuses to see some supernatural connection; instead, he chooses to remember his mother alive and happy, and he wishes the same for himself. He wants to return home to Algiers to spend the weekend with Marie, swimming. For Meursault, life is a celebration of the moment, not a ritual of self-loathing. As an absurd hero, he will not cry over his mother because, quite simply, she lived a good life. Meursault scorns the gods (those who say a son must cry) because he lives in denial of death, the mark of an absurd hero.