# Number Theory

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Category: Mathematics
Slides: 31
Updated: 2026-05-15T22:18:40.732Z
Tags: mathematics, number, theory

## Summary

"Mathematics is the queen of the sciences," Gauss wrote, "and number theory is the queen of mathematics." The compliment was not idle. Gauss devoted his greatest energies to it. Key sections include: Number theory.; Opening The queen of mathematics.; Chapter I Euclid on primes.; Chapter II Diophantine equations.; Chapter III Fermat's little theorem.; Chapter IV 1637 conjecture, 1995 proof.; Chapter V Andrew Wiles.; Chapter VI Goldbach's conjecture.; Chapter VII The twin prime conjecture.; Chapter VIII Mersenne primes..

## Slide Outline

1. Number theory.
2. Opening The queen of mathematics.
3. Chapter I Euclid on primes.
4. Chapter II Diophantine equations.
5. Chapter III Fermat's little theorem.
6. Chapter IV 1637 conjecture, 1995 proof.
7. Chapter V Andrew Wiles.
8. Chapter VI Goldbach's conjecture.
9. Chapter VII The twin prime conjecture.
10. Chapter VIII Mersenne primes.
11. Chapter IX Perfect numbers.
12. Chapter X The Riemann hypothesis.
13. Chapter XI The zeta function.
14. Chapter XII The prime number theorem.
15. Chapter XIII Hardy and Ramanujan.
16. Chapter XIV Ramanujan's notebooks.
17. Chapter XV Modular forms.
18. Chapter XVI Elliptic curves.
19. Chapter XVII The modularity theorem.
20. Chapter XVIII Birch and Swinnerton-Dyer.
21. Chapter XIX Algebraic number theory.
22. Chapter XX Class field theory.
23. Chapter XXI L-functions.
24. Chapter XXII Cryptography.
25. Chapter XXIII The quantum threat.
26. Chapter XXIV The Langlands program.
27. Chapter XXV Viazovska, 2016.
28. Chapter XXVI Twenty essentials.
29. Chapter XXVII Watch & read.
30. Chapter XXVIII Where to begin.
31. The end of the deck.

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