alt Hacker NewsTo be clear, this "disagreement" is about arbitrary naming conventions which can be chosen as needed for the problem at hand. It doesn't make any difference to results.
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I'm not a professional, but to me it's clear that whether i and -i are "the same" or "different" is actually quite important.
In the article he says there is a model of ZFC in which the complex numbers have indistinguishable square roots of -1. Thus that model presumably does not allow for a rigid coordinate view of complex numbers.
Agreed. To me it looks like the entire discussion is just bike-shedding.
Names, language, and concepts are essential to and have powerful effects on our understanding of anything, and knowledge of mathematics is much more than the results. Arguably, the results are only tests of what's really important, our understanding.
No the entire point is that it makes difference in the results. He even gave an example in which AI(and most humans imo) picked different interpretation of complex numbers giving different result.
The author is definitely claiming that it's not just about naming conventions: "These different perspectives ultimately amount, I argue, to mathematically inequivalent structural conceptions of the complex numbers". So you would need to argue against the substance of the article to have a basis for asserting that it is just about naming conventions.