"The quintic has no closed form solution" is a theorem that is more precisely stated (in the usual capstone Galois proof) as follows: The quintic has no closed form solution in terms of arbitrary compositions of rational numbers, arithmetic, and Nth roots. We can absolutely express closed form solutions to the quintic if we broaden our repertoire of functions, such as with the Bring radical.

The post's argument is different than the usual Galois theory result about the unsolvability of the quintic, in that it shows a property that must be true about all EML(x,y)-derived functions, and a hypothetical quintic-solver-function does not have that property, so no function we add to our repertoire via EML will solve it (or any other function, elementary or not, that lacks this property).

Can anyone provide a link that "Some are going as far as to suggest that the entire foundations of computer engineering and machine learning should be re-built as a result of this", or anything similarly grandiose?

I am a professional mathematician, though nowhere near this kind of thing. The result seems amusing enough, but it doesn't really strike me as something that would be surprising. I confess that this thread is the first I've heard of it...

The argument is that a universal basis would be capable of solving arbitrary polynomial roots. The rest is an argument that the group constructed by eml is solveable, and hence not all the standard elementary functions.

It wouldn't be a math discussion without people using at least two wildly different definitions.

His 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".

Yes, that blog post could have been much shorter….