Why do we still teach people to calculate?

Because being able to do basic order-of-magnitude arithmetic in one's head is a critical thinking tool essential to detecting nonsense claims in real time.

> Dude was a math grad student. I narrowly restrained myself from saying ...

Do not show restraint, and neither will I. For I am a mathematician, not a fucking calculator.

But once, early in undergrad, I was capable of multiplying 4-digit numbers rather quickly. But tallying never seemed useful except while grading exams -- during which my brain populates a lookup table over the course of an hour, and then I can tally small sums without hesitation. But after that day of grading, the lookup table is flushed for more important uses of short term memory.

He is making a really long winded point I'm not sure I completely understand, so feel free to correct me if I am off here, but I could not really disagree more.

While there is value in emphasizing things like defining/abstracting a problem rather than calculating the result of it, things like the "algorithm" typically taught to elementary schoolers to do long division is pretty much how you would naively/algorithmically program a division operator that can give a remainder. The multiplication "algorithm" given to me at a young age was what first gave me the insight into the connection between addition and multiplication. Abstracting this away in education could not possibly be doing society, math, or computation any service whatsoever, at least not in the way (I think?) he is imagining.

I do think there is value to asking whether a problem needs to be solved or redefined or abstracted in a different manner. I had a calculus teacher in college a long time ago that had a really hilarious way of emphasizing this - he'd often bury "trap" questions into his tests that looked really simple but would test your knowledge of a simple algebraic or trigonometric trick he'd only covered during lecture, and lack of knowledge of this trick would lead one down a hopeless 20+ page response to the problem, to the point where if you found yourself going off the rails with a complex solution, you knew you messed up somewhere. This forced me to look at the problem from a variety angles to see if I could solve it in a more clever, general, or simpler way, or if it could be rewritten (this was usually the correct way to solve it). I really valued that, even years and years later, but maybe that's not the kind of thing Wolfram is getting after in this interview.

Customary units are given in fractions of an inch. Eg half, quarter, eighth, sixteenth etc. So you’re dealing with simple fractions. That is why I buy tape measures that also have metric scale - to sidestep all that bullshit entirely when adding, multiplying, dividing or subtracting, yet be able to measure distances in inches too

If you run every basic calculation through a calculator, you'll make every task take 3x time it requires today, in best case.

I have seen people eyeball measurements and taking notes, and bringing in perfectly manufactured goods (blinds, cupboards, etc.) in return. Esp, in construction, nothing is precise, so being able to eyeball correctly after a quick measurement with a tape and doing some basic math on the numbers, not only accelerates tasks, but is a crucial pillar of being able to work on construction sites, and be productive.