The answer is that mathematics is a thing that you can actually assert that someone is doing incorrectly, but for which it will not be obvious to non-mathematicians. If a programmer writes a bad program, the user can tell. If a mathematician writes a bad proof, basically it takes a mathematician to tell. It doesn't take an incredible mathematician, but it does take one.

If you want to say that you learned mathematics, you have to do more than this student did. you may have chosen to give him the benefit of the doubt, but I did not. I checked his work, and its mostly wrong. The reason that it is mostly wrong is because the practice of mathematics requires some training to get to the point where you can be relied upon to know if you are lying, and the author of this blog did not reach that point.