Why did he write it up so badly? He could make his arguments so much clearer if he just stated them fully. Maybe this piece was meant for math PhDs, not a general audience. To me, it comes across as an attempt to impress the reader with the semblance of authority and knowledge, not to guide the reader through the reasoning. This style of writing is often used to hide bad reasoning, to gloss over weak arguments or deliberately deceive. He could have done a better job.