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Birkhoff proved Poincaré's Last Geometric Theorem , a special case of the 3-body problem, in 1913. He also studied the foundations of relativity and quantum mechanics. Birkhoff also did important work on the four colour theorem. He developed a mathematical theory of aesthetics which he applied to art, music and poetry. Among his works are Relativity and Modern Physics (1923), Dynamical Systems (1928), Aesthetic Measure (1933), and Basic Geometry (1941).
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Tell me about Birkhoff's work on the four colour theorem and on orbits and gravitation
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