Barry Mazur is Gerhard Gade University Professor of Mathematics at Harvard University, Massachusetts. He is the author of Imagining Numbers: (Particularly the Square Root of Minus Fifteen) and co-editor, with Apostolos Doxiadis, of Circles Disturbed: The Interplay of Mathematics and Narrative.
1. Thoughts about numbers; 2. What are prime numbers?; 3. 'Named' prime numbers; 4. Sieves; 5. Questions about primes; 6. Further questions about primes; 7. How many primes are there?; 8. Prime numbers viewed from a distance; 9. Pure and applied mathematics; 10. A probabilistic 'first' guess; 11. What is a 'good approximation'?; 12. Square root error and random walks; 13. What is Riemann's hypothesis?; 14. The mystery moves to the error term; 15. Césaro smoothing; 16. A view of Li(X) -
(X); 17. The prime number theorem; 18. The staircase of primes; 19. Tinkering with the staircase of primes; 20. Computer music files and prime numbers; 21. The word 'spectrum'; 22. Spectra and trigonometric sums; 23. The spectrum and the staircase of primes; 24. To our readers of part I; 25. Slopes and graphs that have no slopes; 26. Distributions; 27. Fourier transforms: second visit; 28. Fourier transform of delta; 29. Trigonometric series; 30. A sneak preview; 31. On losing no information; 32. Going from the primes to the Riemann spectrum; 33. How many
i's are there?; 34. Further questions about the Riemann spectrum; 35. Going from the Riemann spectrum to the primes; 36. Building
(X) knowing the spectrum; 37. As Riemann envisioned it; 38. Companions to the zeta function.
1. Thoughts about numbers; 2. What are prime numbers?; 3. 'Named' prime numbers; 4. Sieves; 5. Questions about primes; 6. Further questions about primes; 7. How many primes are there?; 8. Prime numbers viewed from a distance; 9. Pure and applied mathematics; 10. A probabilistic 'first' guess; 11. What is a 'good approximation'?; 12. Square root error and random walks; 13. What is Riemann's hypothesis?; 14. The mystery moves to the error term; 15. Césaro smoothing; 16. A view of Li(X) - pi(X); 17. The prime number theorem; 18. The staircase of primes; 19. Tinkering with the staircase of primes; 20. Computer music files and prime numbers; 21. The word 'spectrum'; 22. Spectra and trigonometric sums; 23. The spectrum and the staircase of primes; 24. To our readers of part I; 25. Slopes and graphs that have no slopes; 26. Distributions; 27. Fourier transforms: second visit; 28. Fourier transform of delta; 29. Trigonometric series; 30. A sneak preview; 31. On losing no information; 32. Going from the primes to the Riemann spectrum; 33. How many thi's are there?; 34. Further questions about the Riemann spectrum; 35. Going from the Riemann spectrum to the primes; 36. Building pi(X) knowing the spectrum; 37. As Riemann envisioned it; 38. Companions to the zeta function.
