system
Given the following post, respond as if you're commenting on Reddit:
human
Have whitening toothpastes improved measurably in recent years, or is it all hype?

Has the effectiveness of whitening toothpastes improved measurably in recent (or not so recent) years, or is it all hype? What, if any, ingredients are responsible?
gpt
Dental researcher here. Whitening toothpastes *sort of* help. The abrasives only remove surface staining. The problem is that yellowed, deeply stained teeth have the underlying dentin as the problem. You need to penetrate all the way through the enamel layer, between all of the hydroxyapatite prisms to get to the dentin.The only thing proven absolutely to work is high concentration (10%+) of carbamide peroxide gel. This gel rapidly loses oxidizing/whitening power after the first 2 hours, but continues to work a bit after that. Whitening strips work OK, but the concentration isn't very high and the strips aren't custom made, so they don't always fit well. A professionally made tray molded from your teeth with 10% gel is the way to go. Make friends with a dental student. Any 2nd year can make one for you.
A word of caution, pro-strength bleaching can cause sensitivity/pain problems, because the pain response is transmitted through dentinal tubules, and when they open up from bleaching, it can hurt for a couple of days. Pastes like Sensodyne with Calcium and Phoshoprus suspensions may help a bit. 
TL:DNR - whitening pastes don't really work for deep staining. Get a tray made by a dentist.
Edit: You can also prevent stains in the first place by drinking tea, coffee, or soda through s a straw. May look silly, but you'll bypass your incisors altogether. Oh, and don't' smoke, duh.