Many projects jump directly into the UI design and make the most expensive mistake over and over again just to make 'quick progress'. Wireframe and prototype stages are the way to catch the wrong decisions while they are still cheap.
Wireframe offers a skeleton free of visual details. At this stage, the color or font is not discussed; only the flow and hierarchy are verified. If the structure of a screen is wrong, even the most beautiful UI can't save it.
The prototype makes the design clickable. Without a single line of code written yet, you see where users are hanging out in the actual stream. Even a small five-user test is enough to reveal most of the problems.
Mathematics is simple: correcting a problem in the design phase means minutes, hours in the development phase, and days after publishing it, and loss of reputation. Early testing teams eliminate the risk of developing the wrong thing from scratch. The test is not an expense; it is the cheapest insurance.