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   Paul Cantrell (inthehands@hachyderm.io)'s status on Friday, 06-Sep-2024 23:54:18 JST Paul Cantrell

   • Steve Wart

   Ha, this from @swart is lovely.

   1/ https://mastodon.cloud/@swart/113086043018659766

   • Embed this notice
     Paul Cantrell (inthehands@hachyderm.io)'s status on Friday, 06-Sep-2024 23:56:08 JST Paul Cantrell

     in reply to

     • Steve Wart

     @swart It reminds me of the classic:

     THEOREM: Horses have an infinite number of legs.

     PROOF: All horses have the two hind legs in the back, and the fore legs in the front. 2 + 4 = 6. Now 6 is an even number, but 6 is certainly an odd number of legs for a horse. The only number that is both even and odd is infinity. QED

     2/

   • Embed this notice
     Paul Cantrell (inthehands@hachyderm.io)'s status on Friday, 06-Sep-2024 23:59:54 JST Paul Cantrell

     in reply to

     Behind this ridiculous silliness is a serious point: proof is a rhetorical device, not a mechanical process; the purpose of proof is to •convince•. Language is slippery. Thought is slippery. There is always a gap between (language + assumptions + human thought) and Platonic mathematical abstraction. Attempts to mechanize proof do not actually close this gap; they just move some things to the other side of it. You can’t escape that gap — and that gap is the •heart• of mathematics.

     3/

   • Embed this notice
     Paul Cantrell (inthehands@hachyderm.io)'s status on Saturday, 07-Sep-2024 00:02:33 JST Paul Cantrell

     in reply to

     The way mathematics actually develops, the whole history of it, is a process of exploring that gap between human thought and abstract ideas: letting imaginary things surprise us, uncovering hidden assumptions, reworking proofs, sharpening definitions, finding new imaginary things to surprise us more.

     And this is the point where I, like a broken record, tell you to read _Proofs and Refutations_, because it is profound and also delightful.

     /end

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     Paul Cantrell (inthehands@hachyderm.io)'s status on Saturday, 07-Sep-2024 00:20:47 JST Paul Cantrell

     in reply to

     • Michael Busch
     • Steve Wart

     @michael_w_busch @swart
     Yes, it is a very Minnesotan theorem!

     In Colorado, where I grew up, the theorem would be that all ducks are geese.

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     Michael Busch (michael_w_busch@mastodon.online)'s status on Saturday, 07-Sep-2024 00:20:48 JST Michael Busch

     in reply to

     • Steve Wart

     @inthehands @swart "Duck, Duck, Grey Duck" ?