alt Hacker NewsHis claim is that we exp-minus-log cannot compute the root of an arbitrary quintic. If you consider the root of an arbitrary quintic "elementary" the exp-minus-log can't represent all elementary functions.
I think it really comes down to what set of functions you are calling "elementary".
The author discusses this in his third paragraph, and states explicitly in his fourth that he considers the result faulty for its unrealistically narrow definition of elementarity.
(I'm not a mathematician, so don't expect me to have an opinion as far as that goes. But the author also writes well in English, and that language we do share.)