How does Wave Structure of Matter solve problems "of all human knowledge?" The author claims this describes reality in terms of Space as a wave medium?
It would be helpful to note which author you're describing. The Wave Structure of Matter may provide a theory as to exactly what matter is and its relationship to the rest of existence, but to make the claim that it solves problems of all human knowledge seems to be a stretch.
No doubt understanding the exact nature of matter will lead to the Grand Unification of the Fundamental Forces (Strong, Weak, Electromagnetic, and Gravitational Forces) that scientists have been seeking since the early 20th century, notably to understand exactly what gravity is and how it interplays with the other 3 forces. That will give us a very complete understanding of how the Universe works.
We know that matter and energy are convertible; we understand that time and space are necessary, one for the existence of the other. The Wave Structure of Matter may show that matter, like energy, is composed of waves, and uncover the exact mechanism of gravity, and how it propagates through space.