jusuhi

Feel free to generalize my argument to i31 and i15.

Also, look around you and realize that non-64-bit microprocessors outnumber 64-bit machines by orders of magnitude. There is more to the world than your laptop and smartphone. (Just within 1m of myself at this very moment I see 4 devices with a 32 bit microprocessor in them, and I'm sitting in a coffee shop reading a book. Well, and browsing HN now and then.)

Because i63 won't help with 32 bit variables.

The keywords here are operational transform (OT) and conflict-free replicated data types (CRDT). Fun to implement, there are lots of libs.

At current rates, whatever is done on a supercomputer today is done by a cheap pocket-size device just decades later. So, I'm not too worried about this case.

One of the first famous examples of this is the four-coloring theorem. I don't know any serious mathematician who is not certain of that result.

The task proving some statement and the task of finding the shortest, or a "reasonably short" proof, are very different endeavours.

The first is about certainty that a statement is valid ("true"). The other is about simplifying the understanding of _why_ it is valid. Most of the time, you don't care much about the latter.

The "best answer" perhaps from the POV of your own intuition. But the question is about a historical fact, and those don't work that way.

If you'd actually read wherever the link is going then you could get an idea instead of just speculating wildly.

Phenomenon. That's the singular form.