Of course people can write and wear whatever they like. I am simply explaining why it smells like crackpottery, since it seems you thought it was only due to that one sentence.
And, for the record, anything aspiring to be a grand unified theory of mathematics has to go far beyond algebra.
That's fair. In my initial comment I was using the quote as an exemplar of an idea running throughout the article--but my reply was directed more to the three comments implying the author is a crank than to yours in particular. As for the unified theory bit, I agree (you can see this in my previous comment) that Geometric Algebra wouldn't cover all of mathematics.
And, for the record, anything aspiring to be a grand unified theory of mathematics has to go far beyond algebra.