I don't think it matters? It's completely standard for "galactic" algorithms and not relevant to big-O runtime.

The complaint that these algorithms aren't "realistic" is ostensibly valid, but you could just as well aim that cannon at 95%+ of math research too. Complexity theory is interesting and fun. Isn't that enough?

> It's completely standard for "galactic" algorithms and not relevant to big-O runtime.

This is true, but if doing brute-force search for all instances below some super-astronomic threshold is part of the algorithm, you typically want to understand

- where this constant comes from,

- how much this constant can be decreased (or why it can't)

- etc.

So, proving the correctness of an algorithm which is doing brute-force search for all instances below some super-astronomic threshold is typically just the first step towards getting an understanding of the complexity-theoretic phenomenon.

So: There is indeed nothing wrong with such aspects of galactic algorithms, but exactly understanding and improving the super-astronomic thresholds involved is the next step.

I hate to use absolutely but it absolutely does matter from an education perspective. To put things in perspective to a layperson explain to them this particular galactic theorem requires full search below some titanic |x|. That should prompt some excellent lay questions that a serious computer scientist ought to reckon with.

It is not to say the approach has been wrong (as the author strongly believes in his reframing) but that this clarity does matter for purposes of, ahem, mathematical understanding.