{"type":"rich","version":"1.0","title":"Motivating The Math wrote","author_name":"Motivating The Math (npub1hp…6tzy4)","author_url":"https://yabu.me/npub1hpzy3w20jkwh7a7z45ev58vkc3370xva0q78rs0c0npww5smeltsc6tzy4","provider_name":"njump","provider_url":"https://yabu.me","html":"Did you know that the points on an elliptic curve form an Abelian group?\n\nNow I’m glad we suffered through 2 podcasts to explain what groups are and how we don’t know why but it’s important to know something is a group!\n\nWe (on this podcast) still don’t know why this fact matters for elliptic curves yet - but it seems plausible in the context of what we discussed that we like:\n\n1) closure under point addition (adding any two points gives us a point that is definitely on the curve)\n\n2) infinity point is the identity (always wondered what that point meant in the coding books like nostr:npub10vlhsqm4qar0g42p8g3plqyktmktd8hnprew45w638xzezgja95qapsp42 Programming Bitcoin)\n\n3) order of addition doesn’t matter (P1+P2) = (P2+P1)\n\nSo the points being an abelian group makes all of the arithmetic around adding points nice.   VERY NICE!"}