Faith
Mathematically speaking, it's impossible to disprove the existence of the afterlife. It is even harder to prove it.
Still, Charlie has difficulties with the concept.
How can someone be gone forever? How can nothing but their earthly remains and their memories stay, when their soul goes to a better place? Yet, how can something so impossible and illogical exist?
Charlie is a scientist, there is no doubt about that. His thirst to explain everything in logic overrides his ability to believe such an abstract concept as faith.
He can't search for solace in the scriptures like his brother or keep religion and science in perfect harmony like Larry when he struggles to believe that his mother isn't gone forever.
This is why he buried himself in math when his mother was sick. To Charlie, his math was an elegant and logical sanctuary. In his bubble as Don called it, Charlie was safe from the horror and pain of the world. In his math, nothing could go wrong. He could get the wrong answer, rub it out and just start over. The numbers were familiar, elegant, logical. They were safe.
They were the only way he knew to cope with what was happening around him, the confusion and pain.
But Charlie has grown so much since then.
Still, is it too much to ask when your loved one dies, a part of them stays with you. Even if it is as simple as a small smile of remembrance on her beloved husband's face, the sparkle in her oldest son's eyes or the wild curls her youngest inherited from her, a part of Margaret stays with the ones she loved.
Sometimes he thinks he hears her whispering words of encouragement or feels her gently stroke his curls and tell him he is doing the right thing. Sometimes he thinks he sees her, standing in the mirror, smiling at him, until he wakes up, realizing it is only a dream. A dream, and yet, so real.
He cannot prove it, even if he tried. He cannot explain it, even if he tries.
But she is there, always. He knows, she is.