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Category:Journey to the Center of the Earth (2007 film)Cambridge Mathematics, but most of what we do I'd wager has been forgotten
I think it is an interesting exercise to write down the history of maths, or at least the history of the major contributions.
The following list is probably incomplete, and the poster will need to make some choices about what books are considered important.
Euclid (and his students) showed us the fundamental structures of maths. It was not without error, but it was the first time that someone had explained them clearly, and you cannot do better than to start with Euclid, no matter how many incorrect versions are available.
Hilbert was the first to introduce the idea of a proof as a finite sequence of steps leading to a conclusion. A good proof means that the conclusion must be true, and if that is the case then we must have made only a finite number of steps. This is the only way to know whether the conclusion is true or not, but this is still a much more flexible idea than a proof by contradiction. It is also the idea that we still use to prove any statement, even statements that you can make by intuition.
Brouwer showed us that real analysis can be considered as an infinitary limit, that is, if you keep adding more and more points at a series of limit points, then you will come to a result that was correct, or almost correct, at each of the intermediate stages, but which is not correct at the limit. There is an advantage in doing this, because for example we may find that the intermediate stages are usually easier to handle.
Erdős and Hunt proved the Kepler conjecture. It was proven by Andrew Wiles in 1995, but the process by which it was done was still very interesting, in particular it showed that you cannot assume that you can reduce the proof to one given by another mathematician.
Riemann's hypothesis is the idea that the zeros of the Riemann zeta function
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