https://github.com/vaibhavkarve/leanteach2020

Formalizing geometry in Lean : IGL/UniHigh Summer 2020 research project
https://github.com/vaibhavkarve/leanteach2020

axioms geometry lean math mathematics

Last synced: about 2 months ago
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Formalizing geometry in Lean : IGL/UniHigh Summer 2020 research project

• Host: GitHub
• URL: https://github.com/vaibhavkarve/leanteach2020
• Owner: vaibhavkarve
• Created: 2020-06-12T15:09:33.000Z (over 4 years ago)
• Default Branch: master
• Last Pushed: 2022-01-17T19:35:57.000Z (about 3 years ago)
• Last Synced: 2024-08-09T14:10:06.359Z (6 months ago)
• Topics: axioms, geometry, lean, math, mathematics
• Language: Lean
• Homepage: https://wiki.illinois.edu/wiki/display/LT2020
• Size: 63.3 MB
• Stars: 23
• Watchers: 1
• Forks: 5
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# LeanTeach2020 #

*Summer 2020 Illinois Geometry Lab (University of Illinois at Urbana-Champaign) + Uni-High research project*

Interactive theorem proving in Lean : teaching mathematics to a computer

## Formalizing Euclid's and Hilbert's axioms in Lean ##

- `euclid.lean` : Euclid's axioms

- `euclid_props.lean` : Euclid's propositions using Euclid's axioms

- `hilbert.lean` : Hilbert's axioms

- `hilbert_props.lean` : Euclid's propositions using Hilbert's axioms

- `tarski.lean` : Tarski's axioms

More mathematical details available at the wiki:

[IllioisWiki for LeanTeach](https://wiki.illinois.edu/wiki/display/LT2020) 

## Project Goals: ##

### Goal 0 : Teach Lean to Humans. ###

Humans involved : **Alex Dolcos, Edward Kong, Lawrence Zhao, Nicholas

Phillips, Vaibhav Karve**.

We meet 9 hours per week to discuss math, philosophy and programming

as it relates to formalizing mathematics in a theorem prover. We will

be using Microsoft Research's Lean Theorem Prover and its Mathematical

Library (mathlib) as our proof assistant for this. Each of us has

experience programming in Python before this. We will explore how

things work differently in a purely functional language. We will also

learn about tactics in Lean. We will use Slack for text-based

communication, Zoom for video meetings and CoCalc for sharing and

collaboratively editing code.

### Goal 1 : Teach Math to a Computer. ###

The idea is that we can take a piece of familiar mathematics and

translate it into code that is acceptable to Lean. Lean already

understands basic logic and does not accept incorrect mathematics as

input.

We wanted to choose a topic in mathematics that,

- is known to us with a high degree of familiarity – because intuition

  comes in handy when we are stuck in a Math → Lean translation,

- is preferably already in an axiomatized form – we wanted to follow

  the workflow of Definitions → Axioms/Postulates →

  Propositions/Theorems,

- is not already in mathlib – this ruled out group theory, number

  theory, category theory ...

We settled on formalizing Axiomatic Geometry of three types:

- Euclid's axioms

- Hilbert's axioms

- Tarski's axioms (partial progress)