I find notifications of new messages (even seeing the number of unread new messages) very distracting. But I value using Gmail's interface - with labels, conversation view, keyboard shortcuts, and syncing drafts across my machines. Are there any ways in which I can do so but block notifications of new messages? The simplest way would be to make Gmail only check for new messages manually, as you can do with desktop clients like Apple Mail.
The only way I've found is to use the Gmail Offline extension in Chrome but disable my internet.