In 1968 Donald Knuth reduced it to 92 tiles. Then he reduced the number of tiles to 104. In the 1960s mathematician Hao Wang came up with a solution consisting of 20,426 different tiles. Penrose managed to create the most optimal solution for a non-periodical tiling. Escher to create artworks of other impossible shapes and structures like the Waterfall and Ascending and Descending. While still a student in the 1950s, he popularised an impossible shape known as 'Penrose triangle'. Penrose has always liked weird types of geometry, especially the conformal ones which take a huge part in his Conformal Cyclic Cosmology that he devised in 2006. Later he moved to Oxford University, where most of his scientific career has taken place. Penrose did his Master of Sciences and PhD at Cambridge University (both in mathematics). His sister is a geneticist and his wife is a mathematician. Penrose's father was a geneticist, his maternal grandfather was a biochemist, his elder brother is a theoretical physicist, his younger brother is a chess Grandmaster who's won the British Chess Championship ten years in a row. The Penrose family has been well acquainted with science. Later he moved back to England, where he attended University College London and graduated with a first class degree in mathematics. During the World War II he was in Canada. Penrose was born in Colchester, England in 1931. 2.2.1 Penrose-Hawking singularity theorems.
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