There'a a story that when someone wrote up a famous mathematician's work (Euler?), he found many errors, some quite serious. But all the theorems were true anyway.
Sounds like Tao's third stage, of informed intuition.
This beats TFA. Interesting relation between cumulativeness and distribution ("Yule process"). But how does this explain variation is how quickly children pick up maths - would you argue it's due to prior exposure e.g. parental tutoring?
Being more precise: I like Spivak not defining addition, multiplication or number. I just want the other steps explicit, like equality transitivity, enough to implement it (for a computer without "mathematical maturity".)
I feel I already know what's needed - but I didn't catch the 0.a=0 omission at first, and there's surely others I'm still missing... Part of the problem is I have too much implicit knowledge.
Read of a study years ago that had postmenopausal wpmen do weight training - giving a dramatic 40% increase in bone density in 6 weeks IIRC the details.
It's not that frail people need to be inactive, but that inactivity causes frailty.
Also "working memory" is short-term storage, like registers, the details of what you're thinking about right now. Not memory of past events, like your wedding day.
"Giving the world a solution" vs. "showing the world how flawlessly smart they are" reminds me of being "visited" by a genius (muse, inspiration). You now have the gift to share, but it doesn't show you're a genius.
"There's no bragging rights to your software, because it's too simple to use", a developer criticized my product. This reduced its viral spread, though managers liked it.