Georges Gonthier - Computer Proofs - Teaching Computers Mathematics, and Conversely

Georges Gonthier - Computer Proofs - Teaching Computers Mathematics, and Conversely

International Mathematical Union via YouTube Direct link

All finite groups of odd order are solvable. Proof: Let G be a minimal counter-example...

19 of 37

19 of 37

All finite groups of odd order are solvable. Proof: Let G be a minimal counter-example...

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Georges Gonthier - Computer Proofs - Teaching Computers Mathematics, and Conversely

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  1. 1 Intro
  2. 2 Is formalization a formality?
  3. 3 Some computer proof landmarks
  4. 4 An old puzzle's story
  5. 5 Saved by the computer?
  6. 6 The whole proof
  7. 7 Proof Algorithms
  8. 8 Reflecting reducibility
  9. 9 Building a square
  10. 10 Building configurations
  11. 11 Colouring interpretation
  12. 12 The Poincaré principle
  13. 13 Minimal logic
  14. 14 Functions in logic The Moderns
  15. 15 Crafting map descriptions
  16. 16 Proof by folklore
  17. 17 Size matters
  18. 18 The Odd Order Theorem
  19. 19 All finite groups of odd order are solvable. Proof: Let G be a minimal counter-example...
  20. 20 A mathematical library shelf
  21. 21 Textbook vs. digital formal text
  22. 22 Interactive Math
  23. 23 Algebraic Notation
  24. 24 Implementing notation
  25. 25 Algebra interfaces Equality
  26. 26 Inferring notation
  27. 27 Basic interfaces and objects bool
  28. 28 Ad hoc inference
  29. 29 Interfacing big operators
  30. 30 Coprime cycle coherence
  31. 31 A dot product matrix puzzle
  32. 32 An integer norm problem
  33. 33 Sorting a combinatorial mess
  34. 34 Homotopy type theory Type A
  35. 35 Synthetic Homotopy Type Theory
  36. 36 Cubical Type Theory
  37. 37 Conclusion

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