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Visual and Logical Beauty in Mathematics L á szl ó Lov á sz Eötvös Loránd University, Budapest

Visual and Logical Beauty in Mathematics L á szl ó Lov á sz Eötvös Loránd University, Budapest lovasz@cs.elte.hu. Quote from a mathematician. The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words

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Visual and Logical Beauty in Mathematics L á szl ó Lov á sz Eötvös Loránd University, Budapest

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  1. Visual and Logical Beauty in Mathematics László Lovász Eötvös Loránd University, Budapest lovasz@cs.elte.hu

  2. Quote from a mathematician The mathematician's patterns, like the painter's or the poet'smust be beautiful; the ideas, like the colors or the words must fittogether in a harmonious way. Beauty is the first test: there isno permanent place in this world for ugly mathematics. G.H. Hardy

  3. Quote from a logician Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. Bertrand Russel

  4. Quotes from physicists To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... Richard Feynman Elegance should be left to shoemakers and tailors. Ludwig Boltzmann

  5. Quotes from „everyday life” Tao and co-author Allen Knutsonproduced beautiful work on a problem known as Horn's conjecture… Report on the work of Fields medalist Terence Tao Zermelo gave a beautiful proof that every set can be well ordered… Daniel Grayson lecture notes on the internet Hey guys … … Just wondering what is the most elegant proof of this? From an internet forum

  6. Beautiful formulas geometry Euler’s Formula: algebra analysis Cauchy’s Formula:

  7. The book of the most elegant proof for every theorem „This is straight from the Book.” Paul Erdős

  8. What is a beautiful proof? An elegant proof is a proof which would not normally cometo mind, like an elegant chess problem: the first move should be paradoxical . Claude Berge

  9. A beautiful proof Theorem: The side and diagonal of a square are not commensurable. A.k.a. „2 is irrational.” Hippasus

  10. Beautiful objects: fractals

  11. Beautiful objects: internet models

  12. Beautiful objects: tilings

  13. Beautiful objects: tilings/Alhambra All 17 wallpaper groups represented? Lynn Bodner: 15

  14. Beautiful objects: tilings/Escher

  15. Beautiful objects: tilings/Penrose

  16. Beautiful objects: tilings/squares Smallest number (21) of „small” squares, all different, tiling a „large” square (demo)

  17. Self-organization The Biham-Middleton-Levine traffic model (demo) 256x256 Experiments by Raissa d’Souza

  18. Self-organization Experiments by Raissa d’Souza

  19. Self-organization Experiments by Raissa d’Souza 233x377 Fibonacci numbers: 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,…

  20. Self-organization Experiments by Raissa d’Souza 233x377 3-in-one: - phase transition - self-organization - Fibonacci numbers

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