Trying to understand the philosophical aspect of Advaita stimulates your intellect. But true understanding has to come from your Inner Self which is subtler than your intellect.
Before any idea can be truly understood, it has to pass the various aspects of your being. Your senses have to be able to first perceive and identify the idea. Then your mind has to have enough focus to start developing an interest in that idea. The idea then has to go past the gates of your rational intellect. Only once it is accepted by your intellect can you truly surrender to it and only this pure surrender can bring the idea into your inner self.
The concept of Advaita - idea that the Atman is the same as the Brahman and the implications of this idea - must first be contemplated and accepted by your intellect. Then you have to surrender to it in its entirety.
True understanding of this has to and will end in Silence.