{"id":13993145,"url":"https://github.com/vaibhavkarve/leanteach2020","last_synced_at":"2026-01-16T12:01:01.351Z","repository":{"id":77455061,"uuid":"271827027","full_name":"vaibhavkarve/leanteach2020","owner":"vaibhavkarve","description":"Formalizing geometry in Lean : IGL/UniHigh Summer 2020 research project","archived":false,"fork":false,"pushed_at":"2022-01-17T19:35:57.000Z","size":66425,"stargazers_count":29,"open_issues_count":0,"forks_count":5,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-07-22T17:46:35.268Z","etag":null,"topics":["axioms","geometry","lean","math","mathematics"],"latest_commit_sha":null,"homepage":"https://wiki.illinois.edu/wiki/display/LT2020","language":"Lean","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/vaibhavkarve.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null}},"created_at":"2020-06-12T15:09:33.000Z","updated_at":"2025-06-14T06:09:46.000Z","dependencies_parsed_at":"2023-04-14T11:44:19.225Z","dependency_job_id":null,"html_url":"https://github.com/vaibhavkarve/leanteach2020","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/vaibhavkarve/leanteach2020","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/vaibhavkarve%2Fleanteach2020","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/vaibhavkarve%2Fleanteach2020/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/vaibhavkarve%2Fleanteach2020/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/vaibhavkarve%2Fleanteach2020/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/vaibhavkarve","download_url":"https://codeload.github.com/vaibhavkarve/leanteach2020/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/vaibhavkarve%2Fleanteach2020/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":28478399,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-01-16T11:59:17.896Z","status":"ssl_error","status_checked_at":"2026-01-16T11:55:55.838Z","response_time":107,"last_error":"SSL_read: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["axioms","geometry","lean","math","mathematics"],"created_at":"2024-08-09T14:02:14.937Z","updated_at":"2026-01-16T12:01:01.325Z","avatar_url":"https://github.com/vaibhavkarve.png","language":"Lean","funding_links":[],"categories":["Lean"],"sub_categories":[],"readme":"# LeanTeach2020 #\n*Summer 2020 Illinois Geometry Lab (University of Illinois at Urbana-Champaign) + Uni-High research project*\n\nInteractive theorem proving in Lean : teaching mathematics to a computer\n\n## Formalizing Euclid's and Hilbert's axioms in Lean ##\n- `euclid.lean` : Euclid's axioms\n- `euclid_props.lean` : Euclid's propositions using Euclid's axioms\n- `hilbert.lean` : Hilbert's axioms\n- `hilbert_props.lean` : Euclid's propositions using Hilbert's axioms\n- `tarski.lean` : Tarski's axioms\n\nMore mathematical details available at the wiki:\n[IllioisWiki for LeanTeach](https://wiki.illinois.edu/wiki/display/LT2020) \n\n\n## Project Goals: ##\n\n### Goal 0 : Teach Lean to Humans. ###\nHumans involved : **Alex Dolcos, Edward Kong, Lawrence Zhao, Nicholas\nPhillips, Vaibhav Karve**.\n\nWe meet 9 hours per week to discuss math, philosophy and programming\nas it relates to formalizing mathematics in a theorem prover. We will\nbe using Microsoft Research's Lean Theorem Prover and its Mathematical\nLibrary (mathlib) as our proof assistant for this. Each of us has\nexperience programming in Python before this. We will explore how\nthings work differently in a purely functional language. We will also\nlearn about tactics in Lean. We will use Slack for text-based\ncommunication, Zoom for video meetings and CoCalc for sharing and\ncollaboratively editing code.\n\n\n### Goal 1 : Teach Math to a Computer. ###\n\nThe idea is that we can take a piece of familiar mathematics and\ntranslate it into code that is acceptable to Lean. Lean already\nunderstands basic logic and does not accept incorrect mathematics as\ninput.\n\nWe wanted to choose a topic in mathematics that,\n\n- is known to us with a high degree of familiarity – because intuition\n  comes in handy when we are stuck in a Math → Lean translation,\n- is preferably already in an axiomatized form – we wanted to follow\n  the workflow of Definitions → Axioms/Postulates →\n  Propositions/Theorems,\n- is not already in mathlib – this ruled out group theory, number\n  theory, category theory ...\n\nWe settled on formalizing Axiomatic Geometry of three types:\n\n- Euclid's axioms\n- Hilbert's axioms\n- Tarski's axioms (partial progress)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fvaibhavkarve%2Fleanteach2020","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fvaibhavkarve%2Fleanteach2020","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fvaibhavkarve%2Fleanteach2020/lists"}