Here are three things that modern physics cannot answer:

1: Why does matter exist? Why wasn't an equal amount of matter and antimatter created at the Big Bang, leading to mutual annihilation and a universe of neutral energy and no particles?

2: Why does every galaxy we can observe appear to be affected by dark matter in identical ways regardless of how old the galaxy is or how big the galaxy is or any other attributes of the galaxy? The rotation curve of almost every galaxy shows that stars at the edges are moving at the same speed as stars in the core.

3: How is it possible for neutrinos to change type? Neutrinos should be a massless particle and thus they should not experience time; however they do change type which means that they are time-bound which implies they must have mass.