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33 sats \ 8 replies \ @gmd OP 7h \ parent \ on: Mathematics AI Aristotle proves 30 year old Erdos Problem #124 AI
I love how one guy (tsaf) in the thread says "Aristotle's solution is as follows. It is surprisingly easy." then proceeds to spit out what to most people is incomprehensible gibberish :P These guys are truly a completely different species of chimp from me.
These guys are truly a completely different species of chimp from me.
you might find this video about one specific AI proof easier for building your intuition, because it focuses on a geometrical problem rather than number theory.
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there's a common joke among mathematicians, that as your mathematical mind develops, so does your arithmetic computer atrophy.
I think it's quite understandable; as a mind becomes aware of more useful kinds of numbers1, and more kinds of patterns2 that enable computational tricks, there is a temptation to explore new possibilities rather than charge forth along whichever computational path was learned at a younger age.
I honestly don't think that the capability of reckoning accurately and rapidly in decimal base is worth retaining at grade-school levels. Even if you're e.g. checking over a bill at a restaurant, the important tasks are probably remembering who ordered what and comparing the billed prices to the listed ones, rather than verifying that their point-of-sale performed arithmetic correctly.
Footnotes
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most useful kinds are ideals or fields; the most familiar ideals are multiples of any prime, while e.g. "all ratios with a power of two in the denominator" is a field ↩
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consider the trick of doubling and shifting the decimal point left, as a shortcut for
multiplyingdividing by five; it's only the first in an infinite series of similar tricks, formultiplyingdividing by powers of five ↩
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well some people specifically practice lightning calculation; similarly to how some kid who grew up playing catch might keep on practicing with friends or the next generation, despite not needing the affordance.
I think lightning calculation has always had a bit of an "autistic savant" reputation, because it is so sterile when compared to even things like playing chess or solving a Rubik's Cube.
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The industry of medicine, or taking medicine? Either way, a cautionary tale.
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