I have never memorized times tables. I am a successful professional mathematician and human. So I argue that rote was not critical to me, and I'm sure it's not just me.https://twitter.com/davidmanheim/status/1029088301448347648 …
The best mental calculators -- people who can compute the decimal expansion of 1/97 as quickly as they can intelligibly speak its digits -- reason in exactly this way, fluently exploiting diverse numerical relations of exactly this kind. That's what arithmetic mastery looks like.