[diebeforei485]

You can set an app to only notify you silently. This means it won't buzz or beep, but when you pick up your phone it will be on the lock screen. Android has similar (and more) customizability options.

[whalesalad]

Notifications are still cognitive asteroids. I use my phone predominantly as a clock so a clean lock screen means nothing to worry about.

[diebeforei485]

There is also the option to bypass the lock screen and only go to the Notification Center. On iOS this is called "deliver quietly".