If everything is mathematically calculated, what part of the deep learning network is actually a blackbox?

In a simple neural network, weights are randomly assigned, loss, gardient is calculated mathematically and weights are then readjusted. Isn't this all maths? Consider even a CNN, Image is converted to lets say 224\*224 pixel values and then convolution, maxpooling etc is performed..again mathematically...given a person has eternity, can he perform the same functions and mathematically train a model manually?

blackbox cnn convolution deep learning deeplearning etc everything image isn loss maths network neural network part pixel simple values