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| 作为一门历史悠久的学问，数学有她自身的文化和美学，就像文学和艺术一样。一方面，数学家们在努力开拓新领域、解决老问题；另一方面他们也在不断地从不同的角度反复学习、理解和欣赏前辈们的工作。的确，数学中有许多不仅值得反复推敲理解，更值得细心品味和欣赏的杰作。有些定理的证明不仅想法奇特、构思精巧，作为一个整体更是天衣无缝。难怪，西方有些虔诚的数学家将这类杰作比喻为上帝的创造。 |
| Number Theory. 1. Six proofs of the infinity of primes 2. Bertrand‘s postulate 3. Binomial coefficients are (almost) never powers 4. Representing numbers as sums of two squares 5. Every finite division ring is a field 6. Some irrational numbers 7. Three times π2/6 Geometry 8. Hilbert‘s third problem: decomposing polyhedra 9. Lines in the plane and decompositions of graphs 10. The slope problem 11. Three applications of Euler‘s formula 12. Cauchy‘s rigidity theorem 13. Touching simplices 14. Every large point set has an obtuse angle 15. Borsuk‘s conjecture Analysis 16. Sets， functions， |
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