Twenty generations passed between Adam and Abraham without old age being mentioned once. Not because people didn't age — but because no one had earned the particular beauty of visible, dignified aging. Then Abraham appeared, and the verse says he was "old, coming with days" (Genesis 24:1). The phrase "coming with days" means something more than just "getting on in years" — each day had been lived fully enough to accumulate into something visible on his face.
Isaac after him, then Jacob — each received the same gift. The rabbis said that Isaac, at a certain age, asked God to make the distinction between youth and old age visible, so that a father could be honored as a father. God agreed, and the lines appeared on Isaac's face first. Before that, father and son looked indistinguishable. After it, you could see the generations in the room.
Psalm 102 adds the spiritual dimension: "He will regard the prayer of the destitute, and not despise their prayer" (Psalm 102:17). The only path to this level of prayer, the midrash says, runs through old age — through the accumulation of loss and survival, through the decades in which a person learns what they cannot control and what they can ask for. Old age in the Torah is not a decline. It is an achievement. The "coming with days" is the sign that someone has been paying attention.