Mathematics and logic

1. Infinity of primes 2. Arbitrarily long sequences of successive integers, all not primes 3. Number of primes between 1 and n 4. Euler’s formula yields primes for x=0,1,2,3,…39 5. Irrational numbers: Algebraic, Transcendental (transcends operations of ordinary arithmetic) 6. Irrationality of square root of 2 7. Covering intervals 8. Euler’s constant C: 9. Approximating irrationals by rational numbers 10. Cantor’s existence proof of transcendental numbers 11. Non-constructibility of cube root of 2 12. Impossibility of finding center of circle with straightedge alone 13. Impossibility of covering modified chessboard with dominoes 14. Impossibility of decomposing cube into smaller cubes all of different size 15. Sperner’s Lemma: enumeration of patterns, fixed-point theorem follows 16. 292 ways of changing a dollar 17. The number system 18. The number of ways of partitioning a number into sums 19. The number of ways of partitioning a number into squares 20. Coin tossing: probability of m heads in n tosses 21. DeMoivre - Laplace Theorem 22. Axioms of probability theory equivalent to axioms of measure theory 23. Independent events implies normal distribution 24. Permutation group and so