alt Hacker NewsThe original article explicitly acknowledged this limitation, that while in "the classical differential-algebraic setting, one often works with a broader notion of elementary function, defined relative to a chosen field of constants and allowing algebraic adjunctions, i.e., adjoining roots of polynomial equations," the author works with the less general definition.
Neither the present article, nor the original one has much mathematical originality, though: Odrzywolek's result is immediately obvious, while this blog post is a rehash of Arnold's proof of the unsolvability of the quintic.
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> Neither the present article, nor the original one has much mathematical originality, though: Odrzywolek's result is immediately obvious, [...]
Maybe. But I found it a nice piece of recreational mathematics nevertheless.
Arnold (as reported by Goldmakher [1]) does prove the unsolvability of the quintic in finite terms of arithmetic and single-valued continuous functions (which does not include the complex logarithm). TFA's result is stronger, which is something about the solvability of the monodromy groups of all EML-derived functions. So it doesn't seem to be a "rehash", even if their specific counterexample could have been achieved either in fewer steps or with less machinery.
[1] https://web.williams.edu/Mathematics/lg5/394/ArnoldQuintic.p...
> Odrzywolek's result is immediately obvious
Many things that in retrospect seem immediately obvious weren't obvious before, let alone immediately obvious.
> Odrzywolek's result is immediately obvious
This may or may not be true; but the burden of proof should not lay with the reader.
Please provide (in absence of which every reader can draw their own conclusions) a reference which simultaneously:
1) predates Odrzywolek's result
2) and demonstrates the other unary and binary operations typically tacitly assumed can be expressed in terms of a single binary operation and a constant.
(in other news: I can spontaneously levitate, I just don't feel like demonstrating it to you right now...)
Yes, this article is kicking in open doors, the original article was quite clear about the scope.
The present article could rather have spent time arguing why this isn't like NAND gate functional completeness.
I would have thought the differences lie in the other direction: not that trees of EML and 1 can describe too little, but that they can describe too much already. It's decidable whether two NAND circuits implement the same function, I'm pretty sure it's not decidable if two EML trees describe the same function.