Michael, a retired high-rise window washer, wrote in: "When acid rain gets baked onto your windows from the sun without regular cleaning, it can be impossible to get off with regular window cleaner. So I suggest using oven cleaner on your grimy old windows and they'll come out looking sparkling clean."
I have always used oven cleaner to get that grime off the window that was covered by an aluminum window screen. It does work. But watch out for the paint below, and protect your hands with gloves as well!
Perhaps less corrosive is to use speciality cleaners for glass stove tops.