Who cares about Euclidean geometry? Miroslav Olk Euclidean - PowerPoint PPT Presentation

Apr 07, 2024 •145 likes •342 views

Who cares about Euclidean geometry? Miroslav Olk Euclidean geometry Points, lines and circles in the plane Nice but Without applications Algorithmically decidable AITP Automated theorem proving Machine learning Me

Who cares about Euclidean geometry? Miroslav Olšák
Euclidean geometry ● Points, lines and circles in the plane ● Nice but… – Without applications – Algorithmically decidable
AITP ● Automated theorem proving ● Machine learning
Me
! s w e n g n k i a e r B A computer program exceeded world best mathematicians
Mathematics ● Abstraction ● Reasoning ● Problem solving
Abstraction A conceptual process where general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods. (Wikipedia)
Abstraction – Logician’s approach ● Replacing constants with variables ● Construction of lambda function (HOL) ● ...
Machine learning approach These are dogs c g i a m L M Now I have an idea what a "dog" means
Elementary school ● Arithmetic ● Word problems ● Euclidean geometry – One abstraction level – Teaches reasoning
Problem solving – benchmark
International Mathematical Olympiad (IMO) ● Prestigious competition for high school students ● 4 “domains” – Algebra – Number theory – Combinatorics – Euclidean geometry ● National rounds – Plenty of problems of various difficulty ● Thousands for geometry
One more point ● People at IMO are really clever
One more point ● People at IMO are really clever ● The plan 1) Solve geometry 2) Get AI generated problems to competitions 3) Get attention of talented people 4) Invite them into a project of solving entire IMO Let's solve the problem solving
Euclidean geometry ● Problems from elementary school to IMO ● Relatively simple → suitable for experiments ● Concrete → suitable for image processing ● We can attract IMO people ● Without applications? – Not the ultimate goal ● Algorithmically decidable? – Ignorable
Suggestions ● Data collection – Prasolov, Chan, 106, 107, AOPS, … – ... ● Reinforcement learning – Guide by image / structure – Problems to prove – Constructional problems – ... ● ...
What do you think?

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