How this alarm works
This page is the alarm from the online alarm clock with the time already filled in: 9:08 AM. Press Set alarm and it counts down to the next time the clock shows 9:08 AM, tonight or tomorrow, whichever comes first. When it rings, the sound starts quiet and gets louder over a minute, a notification goes up if you let the browser send one, and if you tick the math box it will not stop until you type the right answer to something like 23 + 41. Snooze does not need the answer.
If 9:08 AM is when you have to be up, the harder question is when to turn the light off. I count back in sleep cycles, and the sleep calculator does that arithmetic for you: enter 9:08 AM as the wake time and it gives you four bedtimes that end a cycle right at the alarm. I wrote up the research behind the numbers in what time should I go to bed.
What it cannot do
It rings while this page is open, in a tab or as the installed app; a locked phone is not guaranteed, because there is no server that can wake it from outside. That gap is one reason I am building a real alarm app for heavy sleepers, and until it is ready I set the phone's own alarm as well and use this one at a desk.