Learn Russian: Вверху страницы мы видим число.

You are right that число means "number" in a mathematical sense, but it is also the most common word used for the day of the month. For instance, the standard way to ask "What is the date today?" is Какое сегодня число?

Why is страницы in the genitive case?

The word вверху (at the top) is functioning as a spatial preposition here. In Russian, compound prepositions that specify a precise relative location (like "at the top of", "at the bottom of", or "in the middle of") require the noun that follows to be in the genitive case.

Could I use сверху instead of вверху here?

Not usually. Вверху answers the question "where?" (где?) and describes a stationary location ("at the top"). Сверху generally answers the question "from where?" (откуда?) and implies a direction ("from the top" or "from above"). Since the date is simply resting stationary on the page, вверху is the correct choice.

Why isn't the preposition на used here, since the date is "on" the page?