{"slug":"thinker-leonhard-euler","verification":{"valid":true,"entries":3,"head":"e7285b5861dd35d1c80410fabd5f13ceba7d577852020cc326c16a36bbcae702"},"count":3,"sources":[{"id":"s1","type":"other","url":"https://archive.org/details/methodusinvenie00eule","title":"Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes","quote":"Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive, Solutio problematis isoperimetrici latissimo sensu accepti","summary":"1744 publication by Euler that introduces the systematic calculus of variations.","claim_ids":["c1","c4"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-07T07:08:57.887Z","link_status":"ok","quote_status":"verified","prev":"genesis","hash":"ea56064f6b8af86f51281f48af04d4411ea918438ff062b58ad568f3975bd3e0"},{"id":"s2","type":"other","url":"https://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation","title":"Euler–Lagrange equation","quote":"The Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional.","summary":"Standard definition tying the equation to extremal paths.","claim_ids":["c2"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-07T07:08:57.887Z","link_status":"ok","quote_status":"unverified","prev":"ea56064f6b8af86f51281f48af04d4411ea918438ff062b58ad568f3975bd3e0","hash":"0517441d31d8d739c936a4efea6024c532fed30743a2b1a2855008d44e84c936"},{"id":"s3","type":"other","url":"https://www.eftaylor.com/pub/HancEulerEJP.pdf","title":"The original Euler's calculus-of-variations method","quote":"Leonhard Euler's original version of the calculus of variations (1744) used elementary mathematics and was intuitive, geometric, and easily visualized.","summary":"Confirms Euler's foundational role in variational methods used in mechanics.","claim_ids":["c3"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-07T07:08:57.887Z","link_status":"ok","quote_status":"unverified","prev":"0517441d31d8d739c936a4efea6024c532fed30743a2b1a2855008d44e84c936","hash":"e7285b5861dd35d1c80410fabd5f13ceba7d577852020cc326c16a36bbcae702"}]}